ITP001 Axioms: ITP061^7.ax


%------------------------------------------------------------------------------
% File     : ITP061^7 : 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    : Past_Temporal_Logic.ax [Gau19]
%          : HL4061^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   88 (   6 unt;  37 typ;   0 def)
%            Number of atoms       : 2441 ( 404 equ;  36 cnn)
%            Maximal formula atoms :   76 (  27 avg)
%            Number of connectives : 4644 (  36   ~;  13   |; 409   &;4107   @)
%                                         (  64 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   76 (  13 avg;4107 nst)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  207 ( 207   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   37 (  35 usr;   4 con; 0-4 aty)
%            Number of variables   :  803 ( 649   ^ 142   !;   8   ?; 803   :)
%                                         (   4  !>;   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(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

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_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_2EPast__Temporal__Logic_2EInitPoint,type,
    c_2EPast__Temporal__Logic_2EInitPoint: tyop_2Enum_2Enum > $o ).

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

thf(c_2EPast__Temporal__Logic_2EPALWAYS,type,
    c_2EPast__Temporal__Logic_2EPALWAYS: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPBEFORE,type,
    c_2EPast__Temporal__Logic_2EPBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPEVENTUAL,type,
    c_2EPast__Temporal__Logic_2EPEVENTUAL: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPNEXT,type,
    c_2EPast__Temporal__Logic_2EPNEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Eprim__rec_2EPRE,type,
    c_2Eprim__rec_2EPRE: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2EPast__Temporal__Logic_2EPSBEFORE,type,
    c_2EPast__Temporal__Logic_2EPSBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPSNEXT,type,
    c_2EPast__Temporal__Logic_2EPSNEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPSUNTIL,type,
    c_2EPast__Temporal__Logic_2EPSUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPSWHEN,type,
    c_2EPast__Temporal__Logic_2EPSWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPUNTIL,type,
    c_2EPast__Temporal__Logic_2EPUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2EPast__Temporal__Logic_2EPWHEN,type,
    c_2EPast__Temporal__Logic_2EPWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

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

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_2EWHEN,type,
    c_2ETemporal__Logic_2EWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

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_2EPast__Temporal__Logic_2EInitPoint,axiom,
    ( c_2EPast__Temporal__Logic_2EInitPoint
    = ( ^ [V0t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V0t @ c_2Enum_2E0 ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSNEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0a @ V1t0 )
    <=> ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1t0 )
        & ( V0a @ ( c_2Eprim__rec_2EPRE @ V1t0 ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPNEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPNEXT @ V0a @ V1t0 )
    <=> ( ( V1t0 = c_2Enum_2E0 )
        | ( V0a @ ( c_2Eprim__rec_2EPRE @ V1t0 ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPALWAYS,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V0a @ V1t0 )
    <=> ! [V2t: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V2t @ V1t0 )
         => ( V0a @ V2t ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPEVENTUAL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a @ V1t0 )
    <=> ? [V2t: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V2t @ V1t0 )
          & ( V0a @ V2t ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSWHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V0a @ V1b @ V2t0 )
    <=> ? [V3delta: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V2t0 )
          & ( V0a @ V3delta )
          & ( V1b @ V3delta )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( c_2Eprim__rec_2E_3C @ V3delta @ V4t )
                & ( c_2Earithmetic_2E_3C_3D @ V4t @ V2t0 ) )
             => ( (~) @ ( V1b @ V4t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSUNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a @ V1b @ V2t0 )
    <=> ? [V3delta: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V2t0 )
          & ( V1b @ V3delta )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( c_2Eprim__rec_2E_3C @ V3delta @ V4t )
                & ( c_2Earithmetic_2E_3C_3D @ V4t @ V2t0 ) )
             => ( ( V0a @ V4t )
                & ( (~) @ ( V1b @ V4t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSBEFORE,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a @ V1b @ V2t0 )
    <=> ? [V3delta: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V2t0 )
          & ( V0a @ V3delta )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V4t )
                & ( c_2Earithmetic_2E_3C_3D @ V4t @ V2t0 ) )
             => ( (~) @ ( V1b @ V4t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPWHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V0a @ V1b @ V2t0 )
    <=> ( ! [V3t: tyop_2Enum_2Enum] :
            ( ( c_2Earithmetic_2E_3C_3D @ V3t @ V2t0 )
           => ( (~) @ ( V1b @ V3t ) ) )
        | ? [V4delta: tyop_2Enum_2Enum] :
            ( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V2t0 )
            & ( V0a @ V4delta )
            & ( V1b @ V4delta )
            & ! [V5t: tyop_2Enum_2Enum] :
                ( ( ( c_2Eprim__rec_2E_3C @ V4delta @ V5t )
                  & ( c_2Earithmetic_2E_3C_3D @ V5t @ V2t0 ) )
               => ( (~) @ ( V1b @ V5t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPUNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V0a @ V1b @ V2t0 )
    <=> ( ! [V3t: tyop_2Enum_2Enum] :
            ( ( c_2Earithmetic_2E_3C_3D @ V3t @ V2t0 )
           => ( V0a @ V3t ) )
        | ? [V4delta: tyop_2Enum_2Enum] :
            ( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V2t0 )
            & ( V1b @ V4delta )
            & ! [V5t: tyop_2Enum_2Enum] :
                ( ( ( c_2Eprim__rec_2E_3C @ V4delta @ V5t )
                  & ( c_2Earithmetic_2E_3C_3D @ V5t @ V2t0 ) )
               => ( ( V0a @ V5t )
                  & ( (~) @ ( V1b @ V5t ) ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPBEFORE,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0a @ V1b @ V2t0 )
    <=> ( ! [V3t: tyop_2Enum_2Enum] :
            ( ( c_2Earithmetic_2E_3C_3D @ V3t @ V2t0 )
           => ( (~) @ ( V1b @ V3t ) ) )
        | ? [V4delta: tyop_2Enum_2Enum] :
            ( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V2t0 )
            & ( V0a @ V4delta )
            & ! [V5t: tyop_2Enum_2Enum] :
                ( ( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V5t )
                  & ( c_2Earithmetic_2E_3C_3D @ V5t @ V2t0 ) )
               => ( (~) @ ( V1b @ V5t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EINITIALISATION,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a @ c_2Enum_2E0 )
        = c_2Ebool_2ET )
      & ( ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a @ c_2Enum_2E0 )
        = c_2Ebool_2EF )
      & ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a @ c_2Enum_2E0 )
        = ( V1a @ c_2Enum_2E0 ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a @ c_2Enum_2E0 )
        = ( V1a @ c_2Enum_2E0 ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b @ c_2Enum_2E0 )
        = ( V0b @ c_2Enum_2E0 ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b @ c_2Enum_2E0 )
      <=> ( ( V1a @ c_2Enum_2E0 )
          & ( V0b @ c_2Enum_2E0 ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b @ c_2Enum_2E0 )
      <=> ( ( V1a @ c_2Enum_2E0 )
          & ( (~) @ ( V0b @ c_2Enum_2E0 ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b @ c_2Enum_2E0 )
      <=> ( ( V1a @ c_2Enum_2E0 )
          | ( V0b @ c_2Enum_2E0 ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b @ c_2Enum_2E0 )
      <=> ( ( V1a @ c_2Enum_2E0 )
          | ( (~) @ ( V0b @ c_2Enum_2E0 ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b @ c_2Enum_2E0 )
      <=> ( (~) @ ( V0b @ c_2Enum_2E0 ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ERECURSION,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1a ) @ V2t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) @ V3t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V0b @ V4t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) @ V4t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V0b @ V5t ) @ ( V1a @ V5t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V6t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V6t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) @ V6t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V0b @ V7t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) @ V7t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V0b @ V8t ) @ ( V1a @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) @ V8t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V9t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) @ V9t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) @ V10t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) @ V11t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0b @ V12t ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b ) @ V12t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V13t ) @ ( V0b @ V13t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V13t ) ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b ) @ V13t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V14t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b ) @ V14t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0b @ V15t ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b ) @ V15t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V16t ) @ ( V0b @ V16t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V16t ) ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b ) @ V16t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V17t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b ) @ V17t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EFIXPOINTS,axiom,
    ! [V0y: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( V0y
          = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V3t ) ) ) )
      <=> ( ( V0y
            = ( c_2ETemporal__Logic_2EALWAYS @ V2a ) )
          | ( V0y
            = ( ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ) )
      & ( ( V0y
          = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V5t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V5t ) ) ) )
      <=> ( ( V0y
            = ( c_2ETemporal__Logic_2EEVENTUAL @ V2a ) )
          | ( V0y
            = ( ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) ) ) )
      & ( ( V0y
          = ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V1b @ V7t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V7t ) ) ) ) )
      <=> ( ( V0y
            = ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
          | ( V0y
            = ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) ) ) )
      & ( ( V0y
          = ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V1b @ V8t ) @ ( V2a @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V8t ) ) ) )
      <=> ( ( V0y
            = ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
          | ( V0y
            = ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) ) ) )
      & ( ( V0y
          = ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V9t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V2a @ V9t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V9t ) ) ) ) )
      <=> ( ( V0y
            = ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) )
          | ( V0y
            = ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) ) ) )
      & ( ( V0y
          = ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V10t ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) ) )
      & ( ( V0y
          = ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V11t ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) ) )
      & ( ( V0y
          = ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V12t ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V12t ) ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b ) ) )
      & ( ( V0y
          = ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V13t ) @ ( V1b @ V13t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V13t ) ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V13t ) ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b ) ) )
      & ( ( V0y
          = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V14t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V2a @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V14t ) ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b ) ) )
      & ( ( V0y
          = ( ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V15t ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V15t ) ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b ) ) )
      & ( ( V0y
          = ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V16t ) @ ( V1b @ V16t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V16t ) ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V16t ) ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b ) ) )
      & ( ( V0y
          = ( ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V17t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V17t ) ) ) ) )
      <=> ( V0y
          = ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESUNTIL__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
                @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
                @ V2t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESUNTIL
              @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
              @ V1a
              @ V5t ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
                @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V11t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V11t ) ) )
                @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
                @ V10t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V14t ) )
                @ V0b
                @ V13t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( ^ [V15t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESUNTIL
              @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V16t ) )
              @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( V0b @ V17t ) )
              @ V15t ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( ^ [V18t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESUNTIL
              @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V19t ) )
              @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V20t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V20t ) ) )
              @ V18t ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EUNTIL__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EUNTIL @ V1a
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V2t ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V4t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EUNTIL
                @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V5t ) )
                @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V4t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EUNTIL
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
                @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EUNTIL
              @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V11t ) )
              @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
              @ V10t ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EUNTIL
                @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V14t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V14t ) ) )
                @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
                @ V13t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EUNTIL
              @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
              @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V18t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V18t ) ) )
              @ V16t ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( ^ [V19t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EUNTIL
                @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V20t ) )
                @ V0b
                @ V19t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EWHEN__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EWHEN
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
              @ V2t ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EWHEN
                @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V1a
                @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EWHEN
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V9t ) @ ( V0b @ V9t ) )
                @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EWHEN @ V0b
              @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
              @ V10t ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( ^ [V12t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EWHEN
                @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
                @ V0b
                @ V12t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( ^ [V14t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EWHEN
              @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V15t ) )
              @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V16t ) @ ( V0b @ V16t ) )
              @ V14t ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( ^ [V17t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EWHEN @ V0b
                @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
                @ V17t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESWHEN__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESWHEN
                @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
                @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
                @ V2t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESWHEN
              @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
              @ V1a
              @ V5t ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESWHEN @ V0b
              @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V8t ) @ ( V0b @ V8t ) )
              @ V7t ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESWHEN
                @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V10t ) )
                @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
                @ V9t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( ^ [V12t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESWHEN
                @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
                @ V0b
                @ V12t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( ^ [V14t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESWHEN @ V0b
                @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V15t ) @ ( V0b @ V15t ) )
                @ V14t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESWHEN
              @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
              @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
              @ V16t ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EBEFORE__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EBEFORE
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
              @ V2t ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EBEFORE
                @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V1a
                @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EBEFORE
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V8t ) )
                @ V0b
                @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EBEFORE @ V0b
              @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V10t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V10t ) ) )
              @ V9t ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( ^ [V11t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EBEFORE @ V0b
                @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
                @ V11t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2EBEFORE
              @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
              @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
              @ V13t ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EBEFORE @ V0b
                @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V17t ) ) )
                @ V16t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESBEFORE__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESBEFORE
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
                @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V2t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESBEFORE @ V1a
              @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V5t ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESBEFORE @ V0b
              @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V8t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V8t ) ) )
              @ V7t ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESBEFORE
                @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V10t ) )
                @ V0b
                @ V9t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( ^ [V11t: tyop_2Enum_2Enum] :
              ( c_2ETemporal__Logic_2ESBEFORE @ V0b
              @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
              @ V11t ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESBEFORE @ V0b
                @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
                @ V13t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( ^ [V15t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESBEFORE @ V0b
                @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V16t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V16t ) ) )
                @ V15t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSUNTIL__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
                @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
                @ V2t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSUNTIL
              @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
              @ V1a
              @ V5t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
                @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V11t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V11t ) ) )
                @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
                @ V10t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V14t ) )
                @ V0b
                @ V13t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( ^ [V15t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSUNTIL
              @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V16t ) )
              @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( V0b @ V17t ) )
              @ V15t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( ^ [V18t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSUNTIL
              @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V19t ) )
              @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V20t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V20t ) ) )
              @ V18t ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPUNTIL__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V2t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V4t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPUNTIL
                @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V5t ) )
                @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V4t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPUNTIL
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
                @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPUNTIL
              @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V11t ) )
              @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
              @ V10t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPUNTIL
                @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V14t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V14t ) ) )
                @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
                @ V13t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPUNTIL
              @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
              @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V18t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V18t ) ) )
              @ V16t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( ^ [V19t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPUNTIL
                @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V20t ) )
                @ V0b
                @ V19t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPWHEN__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPWHEN
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
              @ V2t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPWHEN
                @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V1a
                @ V5t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPWHEN
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V9t ) @ ( V0b @ V9t ) )
                @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPWHEN @ V0b
              @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
              @ V10t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( ^ [V12t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPWHEN
                @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
                @ V0b
                @ V12t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( ^ [V14t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPWHEN
              @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V15t ) )
              @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V16t ) @ ( V0b @ V16t ) )
              @ V14t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( ^ [V17t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V0b
                @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
                @ V17t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSWHEN__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSWHEN
                @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
                @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
                @ V2t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSWHEN
              @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
              @ V1a
              @ V5t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSWHEN @ V0b
              @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V8t ) @ ( V0b @ V8t ) )
              @ V7t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSWHEN
                @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V10t ) )
                @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
                @ V9t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( ^ [V12t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSWHEN
                @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
                @ V0b
                @ V12t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( ^ [V14t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V0b
                @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V15t ) @ ( V0b @ V15t ) )
                @ V14t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSWHEN
              @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
              @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
              @ V16t ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPBEFORE__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPBEFORE
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
              @ V2t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V1a
                @ V5t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V8t ) )
                @ V0b
                @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0b
              @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V10t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V10t ) ) )
              @ V9t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( ^ [V11t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0b
                @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
                @ V11t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPBEFORE
              @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
              @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
              @ V13t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0b
                @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V17t ) ) )
                @ V16t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPSBEFORE__EXPRESSIVE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
        = ( ^ [V2t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSBEFORE
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
                @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2EF
                @ V2t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
        = ( ^ [V5t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a
              @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V5t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
              @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V8t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V8t ) ) )
              @ V7t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSBEFORE
                @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V10t ) )
                @ V0b
                @ V9t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( ^ [V11t: tyop_2Enum_2Enum] :
              ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
              @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
              @ V11t ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
                @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
                @ V13t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( ^ [V15t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_7E
              @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
                @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V16t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V16t ) ) )
                @ V15t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ENEGATION__NORMAL__FORM,axiom,
    ! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( (~) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2EALWAYS @ V2a @ V0t ) )
      <=> ( c_2ETemporal__Logic_2EEVENTUAL
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V4t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a @ V0t ) )
      <=> ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V5t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V6t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V7t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V8t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V9t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V10t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V11t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPSNEXT
          @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V12t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V13t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPEVENTUAL
          @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V14t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V15t ) )
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPSWHEN
          @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V16t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPSBEFORE
          @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V17t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V18t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPWHEN
          @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V19t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPBEFORE
          @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V20t ) )
          @ V1b
          @ V0t ) )
      & ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t ) )
      <=> ( c_2EPast__Temporal__Logic_2EPUNTIL
          @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V21t ) )
          @ V1b
          @ V0t ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ECONJUNCTIVE__NORMAL__FORM,axiom,
    ! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( V1b @ V3t ) ) )
        = ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V4t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V5t ) @ ( V1b @ V5t ) ) )
        = ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EALWAYS @ V2a @ V6t ) @ ( c_2ETemporal__Logic_2EALWAYS @ V1b @ V6t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( V1b @ V7t ) )
          @ V0c )
        = ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V0c @ V8t ) @ ( c_2ETemporal__Logic_2EWHEN @ V1b @ V0c @ V8t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V9t ) @ ( V1b @ V9t ) )
          @ V0c )
        = ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V0c @ V10t ) @ ( c_2ETemporal__Logic_2ESWHEN @ V1b @ V0c @ V10t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V11t ) @ ( V1b @ V11t ) )
          @ V0c )
        = ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V0c @ V12t ) @ ( c_2ETemporal__Logic_2EUNTIL @ V1b @ V0c @ V12t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V13t ) @ ( V1b @ V13t ) )
          @ V0c )
        = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V0c @ V14t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V14t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V0c
          @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( V1b @ V15t ) ) )
        = ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V0c @ V2a @ V16t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V0c @ V1b @ V16t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V0c
          @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( V1b @ V17t ) ) )
        = ( ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESBEFORE @ V0c @ V2a @ V18t ) @ ( c_2ETemporal__Logic_2ESBEFORE @ V0c @ V1b @ V18t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V19t ) @ ( V1b @ V19t ) ) )
        = ( ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V20t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSNEXT
          @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V21t ) @ ( V1b @ V21t ) ) )
        = ( ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a @ V22t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b @ V22t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V23t ) @ ( V1b @ V23t ) ) )
        = ( ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a @ V24t ) @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1b @ V24t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN
          @ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V25t ) @ ( V1b @ V25t ) )
          @ V0c )
        = ( ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V0c @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1b @ V0c @ V26t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN
          @ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V27t ) @ ( V1b @ V27t ) )
          @ V0c )
        = ( ^ [V28t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V0c @ V28t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1b @ V0c @ V28t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL
          @ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V29t ) @ ( V1b @ V29t ) )
          @ V0c )
        = ( ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V0c @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1b @ V0c @ V30t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V31t ) @ ( V1b @ V31t ) )
          @ V0c )
        = ( ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V0c @ V32t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V32t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0c
          @ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V33t ) @ ( V1b @ V33t ) ) )
        = ( ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0c @ V2a @ V34t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0c @ V1b @ V34t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0c
          @ ^ [V35t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V35t ) @ ( V1b @ V35t ) ) )
        = ( ^ [V36t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0c @ V2a @ V36t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0c @ V1b @ V36t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EDISJUNCTIVE__NORMAL__FORM,axiom,
    ! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V3t ) @ ( V1b @ V3t ) ) )
        = ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V4t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V5t ) @ ( V1b @ V5t ) ) )
        = ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a @ V6t ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V6t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V7t ) @ ( V1b @ V7t ) )
          @ V0c )
        = ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V0c @ V8t ) @ ( c_2ETemporal__Logic_2EWHEN @ V1b @ V0c @ V8t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V9t ) @ ( V1b @ V9t ) )
          @ V0c )
        = ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V0c @ V10t ) @ ( c_2ETemporal__Logic_2ESWHEN @ V1b @ V0c @ V10t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V2a
          @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V11t ) @ ( V0c @ V11t ) ) )
        = ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V12t ) @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V0c @ V12t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a
          @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V13t ) @ ( V0c @ V13t ) ) )
        = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V14t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V0c @ V14t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( V1b @ V15t ) )
          @ V0c )
        = ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V0c @ V16t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V16t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( V1b @ V17t ) )
          @ V0c )
        = ( ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V0c @ V18t ) @ ( c_2ETemporal__Logic_2ESBEFORE @ V1b @ V0c @ V18t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V19t ) @ ( V1b @ V19t ) ) )
        = ( ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V20t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL
          @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V21t ) @ ( V1b @ V21t ) ) )
        = ( ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a @ V22t ) @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1b @ V22t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN
          @ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V23t ) @ ( V1b @ V23t ) )
          @ V0c )
        = ( ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V0c @ V24t ) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1b @ V0c @ V24t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN
          @ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V25t ) @ ( V1b @ V25t ) )
          @ V0c )
        = ( ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V0c @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1b @ V0c @ V26t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a
          @ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V27t ) @ ( V0c @ V27t ) ) )
        = ( ^ [V28t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V28t ) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V0c @ V28t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a
          @ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V29t ) @ ( V0c @ V29t ) ) )
        = ( ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V0c @ V30t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE
          @ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V31t ) @ ( V1b @ V31t ) )
          @ V0c )
        = ( ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V0c @ V32t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V32t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE
          @ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V33t ) @ ( V1b @ V33t ) )
          @ V0c )
        = ( ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V0c @ V34t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V0c @ V34t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPRENEX__NEXT__NORMAL__FORM,axiom,
    ! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( (~) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
          @ V0t ) )
      & ( ( ( V2a @ V0t )
          & ( c_2ETemporal__Logic_2ENEXT @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V4t ) @ ( V1b @ V4t ) )
          @ V0t ) )
      & ( ( ( V2a @ V0t )
          | ( c_2ETemporal__Logic_2ENEXT @ V1b @ V0t ) )
      <=> ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V5t ) @ ( V1b @ V5t ) )
          @ V0t ) )
      & ( ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V2a ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
        = ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V6t ) @ ( V2a @ V6t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
        = ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V7t ) ) @ ( V2a @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPALWAYS
            @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V8t ) @ ( V2a @ V8t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL
            @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V9t ) ) @ ( V2a @ V9t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
            @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V10t ) ) @ ( V1b @ V10t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
            @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V11t ) ) @ ( V1b @ V11t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
            @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V12t ) ) @ ( V1b @ V12t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
            @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V13t ) ) @ ( V1b @ V13t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPSBEFORE
            @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V14t ) ) @ ( V2a @ V14t ) )
            @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT
          @ ( c_2EPast__Temporal__Logic_2EPUNTIL
            @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V15t ) @ ( V2a @ V15t ) )
            @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
        = ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ENEXT__INWARDS__NORMAL__FORM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) ) )
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V3t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) ) )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V5t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V6t ) @ ( V0b @ V6t ) ) )
        = ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
        = ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) )
        = V1a )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) )
        = V1a )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
        = ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V8t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
        = ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a @ V9t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V9t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b ) )
        = ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V10t ) @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b @ V10t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b ) )
        = ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V11t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b @ V11t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b ) )
        = ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V12t ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b @ V12t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b ) )
        = ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V13t ) @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V13t ) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b @ V13t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b ) )
        = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V14t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b @ V14t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b ) )
        = ( ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V15t ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b @ V15t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EPNEXT__INWARDS__NORMAL__FORM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) ) )
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a @ V3t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) ) )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a @ V5t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b @ V5t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V6t ) @ ( V0b @ V6t ) ) )
        = ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a @ V7t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) )
        = ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V8t ) @ ( V1a @ V8t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
        = ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V9t ) @ ( c_2ETemporal__Logic_2EALWAYS @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ V9t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
        = ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V10t ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ V10t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2ESWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2EUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2EWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) )
        = ( c_2ETemporal__Logic_2EBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
        = ( c_2EPast__Temporal__Logic_2EPALWAYS @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
        = ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) @ V11t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b ) )
        = ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) @ V12t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b ) )
        = ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V13t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) @ V13t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b ) )
        = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) @ V14t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b ) )
        = ( c_2EPast__Temporal__Logic_2EPUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b ) )
        = ( c_2EPast__Temporal__Logic_2EPWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b ) )
        = ( c_2EPast__Temporal__Logic_2EPBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESIMPLIFY,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V9t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL
          @ ^ [V10t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V11t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL
          @ ^ [V12t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V13t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V14t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = V0b )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V15t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
          @ ^ [V16t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V17t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
          @ ^ [V18t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V19t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V1a )
        = V1a )
      & ( ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V20t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = V0b )
      & ( ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V21t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V22t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
          @ ^ [V23t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
          @ ^ [V24t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V25t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V1a )
        = V1a )
      & ( ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V26t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V27t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V28t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
          @ ^ [V29t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V30t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
          @ ^ [V31t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = V1a )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V1a )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
      & ( ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V32t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V33t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V34t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V35t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a
          @ ^ [V36t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V37t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a
          @ ^ [V38t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = V1a )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V1a )
        = ( ^ [V39t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V40t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V41t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V42t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V43t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V43t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
          @ ^ [V44t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
          @ ^ [V45t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V46t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V1a )
        = ( ^ [V47t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V48t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V49t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V49t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V50t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V51t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V51t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
          @ ^ [V52t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V53t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
          @ ^ [V54t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V55t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V1a )
        = ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V56t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V56t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V57t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = c_2EPast__Temporal__Logic_2EInitPoint )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V58t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V59t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSNEXT
          @ ^ [V60t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V61t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSNEXT
          @ ^ [V62t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V63t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V63t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V64t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V65t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V66t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V67t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL
          @ ^ [V68t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V69t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL
          @ ^ [V70t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V71t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V72t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = V0b )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V73t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a
          @ ^ [V74t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V75t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a
          @ ^ [V76t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V77t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V1a )
        = V1a )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL
          @ ^ [V78t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = V0b )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL
          @ ^ [V79t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V80t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a
          @ ^ [V81t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a
          @ ^ [V82t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V83t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V1a )
        = V1a )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN
          @ ^ [V84t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V85t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN
          @ ^ [V86t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a
          @ ^ [V87t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V88t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a
          @ ^ [V89t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = V1a )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V1a )
        = ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN
          @ ^ [V90t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V91t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V91t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN
          @ ^ [V92t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V93t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a
          @ ^ [V94t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V95t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a
          @ ^ [V96t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = V1a )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V1a )
        = ( ^ [V97t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE
          @ ^ [V98t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V99t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE
          @ ^ [V100t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V101t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V101t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a
          @ ^ [V102t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a
          @ ^ [V103t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V104t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V1a )
        = ( ^ [V105t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE
          @ ^ [V106t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V107t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V107t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE
          @ ^ [V108t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V109t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V109t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a
          @ ^ [V110t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V111t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a
          @ ^ [V112t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V113t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V1a )
        = ( c_2EPast__Temporal__Logic_2EPALWAYS
          @ ^ [V114t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V114t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__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 ) )
      & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPWHEN
          @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V8t ) @ ( V0b @ V8t ) )
          @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPUNTIL
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V9t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
          @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPBEFORE
          @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V10t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V10t ) ) )
          @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPSWHEN
          @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
          @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V12t ) ) )
          @ V0b ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
        = ( c_2EPast__Temporal__Logic_2EPSBEFORE
          @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V13t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V13t ) ) )
          @ V0b ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2EIMMEDIATE__EVENT,axiom,
    ! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( V1b @ V0t )
     => ( ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t )
          = ( V2a @ V0t ) )
        & ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t )
          = c_2Ebool_2ET )
        & ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t )
          = c_2Ebool_2EF )
        & ( ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V2a @ V0t )
        <=> ( (~) @ ( V2a @ V0t ) ) )
        & ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t )
          = ( V2a @ V0t ) )
        & ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t )
          = c_2Ebool_2ET )
        & ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t )
          = c_2Ebool_2EF )
        & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1b @ V2a @ V0t )
        <=> ( (~) @ ( V2a @ V0t ) ) )
        & ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t )
          = ( V2a @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t )
          = c_2Ebool_2ET )
        & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t )
          = c_2Ebool_2EF )
        & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V2a @ V0t )
        <=> ( (~) @ ( V2a @ V0t ) ) )
        & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t )
          = ( V2a @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t )
          = c_2Ebool_2ET )
        & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t )
          = c_2Ebool_2EF )
        & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V2a @ V0t )
        <=> ( (~) @ ( V2a @ V0t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ENO__FUTURE__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_2EPast__Temporal__Logic_2ENO__PAST__EVENT,axiom,
    ! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2EPast__Temporal__Logic_2EPALWAYS
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V3t ) )
        @ V0t )
     => ( ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t )
          = c_2Ebool_2ET )
        & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t )
          = c_2Ebool_2ET )
        & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V2a @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPALWAYS
            @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V4t ) )
            @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t )
          = c_2Ebool_2EF )
        & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t )
          = c_2Ebool_2EF )
        & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V2a @ V0t )
          = c_2Ebool_2EF ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESOME__FUTURE__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_2EPast__Temporal__Logic_2ESOME__PAST__EVENT,axiom,
    ! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1b @ V0t )
     => ( ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t ) )
        & ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V2a @ V0t )
          = ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V2a @ V0t ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESEPARATE__NEXT__THM,axiom,
    ! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V3t ) ) )
        = ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1b @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V4t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V5t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b @ V5t ) ) )
        = ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1b @ V6t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V6t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V7t ) ) )
        = ( ^ [V8t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2ETemporal__Logic_2ENEXT
                @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V9t ) @ ( V0c @ V9t ) )
                @ V8t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V8t )
                @ ( c_2ETemporal__Logic_2ENEXT
                  @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V10t ) @ ( V1b @ V10t ) )
                  @ V8t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V11t ) ) )
        = ( ^ [V12t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2ETemporal__Logic_2ENEXT
                @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V13t ) @ ( c_2Ebool_2E_2F_5C @ ( V1b @ V13t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V13t ) ) ) )
                @ V12t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V12t )
                @ ( c_2ETemporal__Logic_2ENEXT
                  @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V14t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V14t ) ) )
                  @ V12t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V15t ) ) )
        = ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V16t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V16t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b @ V17t ) ) )
        = ( ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V18t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V18t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V19t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V19t ) ) )
        = ( ^ [V20t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2ETemporal__Logic_2ENEXT
                @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V21t ) @ ( V0c @ V21t ) )
                @ V20t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V20t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V20t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ENEXT
          @ ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V22t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V22t ) ) )
        = ( ^ [V23t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2ETemporal__Logic_2ENEXT
                @ ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V24t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V24t ) ) )
                @ V23t )
              @ ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V23t )
                @ ( c_2ETemporal__Logic_2ENEXT
                  @ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V25t ) @ ( V1b @ V25t ) )
                  @ V23t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESEPARATE__SUNTIL__THM,axiom,
    ! [V0d: tyop_2Enum_2Enum > $o,V1c: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o,V3a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V4t ) @ ( V1c @ V4t ) ) )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V2b @ V5t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1c @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V6t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V6t ) ) )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V7t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V7t ) )
              @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V8t ) @ ( c_2Ebool_2E_2F_5C @ ( V1c @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V8t ) ) )
                @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V9t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V9t ) ) )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V10t ) )
              @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
                @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V11t ) @ ( c_2Ebool_2E_2F_5C @ ( V1c @ V11t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V11t ) ) )
                @ V10t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
          @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1c @ V0d @ V12t ) ) )
        = ( ^ [V13t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1c @ V0d @ V13t )
                @ ( c_2ETemporal__Logic_2ESUNTIL
                  @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V14t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V14t ) )
                  @ V2b
                  @ V13t ) )
              @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
                @ ^ [V15t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V0d @ V15t )
                    @ ( c_2ETemporal__Logic_2ESUNTIL
                      @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V16t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V16t ) )
                      @ V2b
                      @ V15t ) )
                @ V13t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
          @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1c @ V0d @ V17t ) ) )
        = ( ^ [V18t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1c @ V0d @ V18t )
                @ ( c_2ETemporal__Logic_2ESUNTIL
                  @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V19t ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V19t ) ) )
                  @ V2b
                  @ V18t ) )
              @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
                @ ^ [V20t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V1c @ V20t )
                    @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V20t ) )
                      @ ( c_2ETemporal__Logic_2ESUNTIL
                        @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V21t ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V21t ) ) )
                        @ V2b
                        @ V20t ) ) )
                @ V18t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V22t ) @ ( V2b @ V22t ) )
          @ V1c )
        = ( ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1c @ V23t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2b @ V1c @ V23t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V24t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V24t ) )
          @ V1c )
        = ( ^ [V25t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( V1c @ V25t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V25t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V25t ) )
                @ ( c_2ETemporal__Logic_2ESUNTIL
                  @ ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V26t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V26t ) )
                  @ ( c_2ETemporal__Logic_2ENEXT @ V1c )
                  @ V25t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V27t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V27t ) )
          @ V1c )
        = ( ^ [V28t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( V1c @ V28t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V28t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V28t ) )
                @ ( c_2ETemporal__Logic_2ESUNTIL
                  @ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V29t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V29t ) )
                  @ ( c_2ETemporal__Logic_2ENEXT @ V1c )
                  @ V28t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V30t ) )
          @ V0d )
        = ( ^ [V31t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V31t )
                @ ( c_2ETemporal__Logic_2EBEFORE
                  @ ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V32t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V32t ) )
                  @ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V33t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V33t ) ) )
                  @ V31t ) )
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V34t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_5C_2F @ ( V2b @ V34t )
                    @ ( c_2Ebool_2E_5C_2F @ ( V1c @ V34t )
                      @ ( c_2ETemporal__Logic_2EBEFORE
                        @ ^ [V35t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V35t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V35t ) )
                        @ ^ [V36t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V36t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V36t ) ) )
                        @ V34t ) ) )
                @ V0d
                @ V31t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V37t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V37t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V37t ) )
          @ V0d )
        = ( ^ [V38t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V38t )
                @ ( c_2ETemporal__Logic_2EBEFORE
                  @ ^ [V39t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V39t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V39t ) )
                  @ ^ [V40t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V40t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V40t ) ) )
                  @ V38t ) )
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V41t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1c @ V41t ) )
                    @ ( c_2ETemporal__Logic_2EBEFORE
                      @ ^ [V42t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V42t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V42t ) )
                      @ ^ [V43t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V43t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V43t ) ) )
                      @ V41t ) )
                @ V0d
                @ V38t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESEPARATE__BEFORE__THM,axiom,
    ! [V0d: tyop_2Enum_2Enum > $o,V1c: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o,V3a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V4t ) @ ( V1c @ V4t ) ) )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V3a @ V2b @ V5t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V3a @ V1c @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V6t ) @ ( V2b @ V6t ) )
          @ V1c )
        = ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V3a @ V1c @ V7t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V2b @ V1c @ V7t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
          @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V8t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V8t ) ) )
        = ( ^ [V9t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V9t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V9t ) ) )
              @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V9t )
                @ ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V3a )
                  @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1c @ V10t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V10t ) )
                  @ V9t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
          @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V11t ) ) )
        = ( ^ [V12t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V12t ) ) )
              @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V12t )
                @ ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V3a )
                  @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1c @ V13t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V13t ) )
                  @ V12t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
          @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1c @ V0d @ V14t ) ) )
        = ( ^ [V15t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2Ebool_2E_5C_2F
                @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                  @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1c @ V16t ) )
                  @ V0d
                  @ V15t )
                @ ( c_2ETemporal__Logic_2EBEFORE
                  @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V17t ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V17t ) ) )
                  @ V2b
                  @ V15t ) )
              @ ( c_2ETemporal__Logic_2EBEFORE @ V3a
                @ ^ [V18t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V0d @ V18t )
                    @ ( c_2ETemporal__Logic_2ESUNTIL
                      @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V19t ) ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V19t ) )
                      @ V2b
                      @ V18t ) )
                @ V15t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
          @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1c @ V0d @ V20t ) ) )
        = ( ^ [V21t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2Ebool_2E_5C_2F
                @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                  @ ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1c @ V22t ) )
                  @ V0d
                  @ V21t )
                @ ( c_2ETemporal__Logic_2EBEFORE
                  @ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V23t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V23t ) )
                  @ V2b
                  @ V21t ) )
              @ ( c_2ETemporal__Logic_2EBEFORE @ V3a
                @ ^ [V24t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V1c @ V24t )
                    @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V24t ) )
                      @ ( c_2ETemporal__Logic_2ESUNTIL
                        @ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V25t ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V25t ) ) )
                        @ V2b
                        @ V24t ) ) )
                @ V21t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V26t ) )
          @ V1c )
        = ( ^ [V27t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V27t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V3a @ V27t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V27t ) ) )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V27t ) )
                @ ( c_2ETemporal__Logic_2EBEFORE
                  @ ^ [V28t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V28t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V28t ) )
                  @ ( c_2ETemporal__Logic_2ENEXT @ V1c )
                  @ V27t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V29t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V29t ) )
          @ V1c )
        = ( ^ [V30t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V30t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V3a @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V30t ) ) )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V30t ) )
                @ ( c_2ETemporal__Logic_2EBEFORE
                  @ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V31t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V31t ) )
                  @ ( c_2ETemporal__Logic_2ENEXT @ V1c )
                  @ V30t ) ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V32t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V32t ) )
          @ V0d )
        = ( ^ [V33t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V33t )
                @ ( c_2ETemporal__Logic_2ESUNTIL
                  @ ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V34t ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V34t ) ) )
                  @ ^ [V35t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V35t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V35t ) ) )
                  @ V33t ) )
              @ ( c_2ETemporal__Logic_2EBEFORE
                @ ^ [V36t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V2b @ V36t )
                    @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V36t ) )
                      @ ( c_2ETemporal__Logic_2ESUNTIL
                        @ ^ [V37t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V37t ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V37t ) ) )
                        @ ^ [V38t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V38t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V38t ) ) )
                        @ V36t ) ) )
                @ V0d
                @ V33t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V39t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V39t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V39t ) )
          @ V0d )
        = ( ^ [V40t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V40t )
                @ ( c_2ETemporal__Logic_2ESUNTIL
                  @ ^ [V41t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V41t ) ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V41t ) )
                  @ ^ [V42t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V42t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V42t ) ) )
                  @ V40t ) )
              @ ( c_2ETemporal__Logic_2EBEFORE
                @ ^ [V43t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V1c @ V43t )
                    @ ( c_2ETemporal__Logic_2ESUNTIL
                      @ ^ [V44t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V44t ) ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V44t ) )
                      @ ^ [V45t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V45t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V45t ) ) )
                      @ V43t ) )
                @ V0d
                @ V40t ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESEPARATE__PNEXT__THM,axiom,
    ! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V3t ) ) )
        = ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V4t ) @ ( c_2Ebool_2E_2F_5C @ ( V1b @ V4t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V4t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V5t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V5t ) ) )
        = ( ^ [V6t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2EPast__Temporal__Logic_2EPNEXT
                @ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( V0c @ V7t ) )
                @ V6t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V6t )
                @ ( c_2EPast__Temporal__Logic_2EPNEXT
                  @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V8t ) @ ( V1b @ V8t ) )
                  @ V6t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V9t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V9t ) ) )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2EPast__Temporal__Logic_2EPNEXT
                @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V11t ) @ ( c_2Ebool_2E_2F_5C @ ( V1b @ V11t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V11t ) ) ) )
                @ V10t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V10t )
                @ ( c_2EPast__Temporal__Logic_2EPNEXT
                  @ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V12t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V12t ) ) )
                  @ V10t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V13t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V13t ) ) )
        = ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V14t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V15t ) ) )
        = ( ^ [V16t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2EPast__Temporal__Logic_2EPNEXT
                @ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( V0c @ V17t ) )
                @ V16t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V16t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V16t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPNEXT
          @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V18t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V18t ) ) )
        = ( ^ [V19t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2EPast__Temporal__Logic_2EPNEXT
                @ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V20t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V20t ) ) )
                @ V19t )
              @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V19t )
                @ ( c_2EPast__Temporal__Logic_2EPNEXT
                  @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V21t ) @ ( V1b @ V21t ) )
                  @ V19t ) ) ) ) ) ) ).

thf(thm_2EPast__Temporal__Logic_2ESEPARATE__PSUNTIL__THM,axiom,
    ! [V0d: tyop_2Enum_2Enum > $o,V1c: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o,V3a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V4t ) @ ( V1c @ V4t ) ) )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a @ V2b @ V5t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a @ V1c @ V5t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V6t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V6t ) ) )
        = ( ^ [V7t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V7t ) )
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
                @ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V8t ) @ ( c_2Ebool_2E_2F_5C @ ( V1c @ V8t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V8t ) ) )
                @ V7t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
          @ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V9t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1c @ V0d @ V9t ) ) )
        = ( ^ [V10t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V1c @ V0d @ V10t )
                @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                  @ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V11t ) )
                  @ V2b
                  @ V10t ) )
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
                @ ^ [V12t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V0d @ V12t )
                    @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                      @ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V13t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V13t ) )
                      @ V2b
                      @ V12t ) )
                @ V10t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
          @ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V14t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1c @ V0d @ V14t ) ) )
        = ( ^ [V15t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F
              @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V1c @ V0d @ V15t )
                @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                  @ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V16t ) @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0d @ V16t ) ) )
                  @ V2b
                  @ V15t ) )
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
                @ ^ [V17t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_2F_5C @ ( V1c @ V17t )
                    @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V17t ) )
                      @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                        @ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V18t ) @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0d @ V18t ) ) )
                        @ V2b
                        @ V17t ) ) )
                @ V15t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V19t ) @ ( V2b @ V19t ) )
          @ V1c )
        = ( ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a @ V1c @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V20t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V21t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V21t ) )
          @ V1c )
        = ( ^ [V22t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_5C_2F @ ( V1c @ V22t )
              @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V22t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V22t ) )
                @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                  @ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V23t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V3a @ V23t ) )
                  @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c )
                  @ V22t ) ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V24t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2b @ V1c @ V24t ) )
          @ V0d )
        = ( ^ [V25t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V2b @ V1c @ V25t )
                @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                  @ ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V26t ) )
                  @ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V27t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V27t ) ) )
                  @ V25t ) )
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                @ ^ [V28t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_5C_2F @ ( V2b @ V28t )
                    @ ( c_2Ebool_2E_5C_2F @ ( V1c @ V28t )
                      @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                        @ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V29t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V29t ) )
                        @ ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V30t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V30t ) ) )
                        @ V28t ) ) )
                @ V0d
                @ V25t ) ) ) )
      & ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
          @ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V31t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V2b @ V1c @ V31t ) )
          @ V0d )
        = ( ^ [V32t: tyop_2Enum_2Enum] :
              ( c_2Ebool_2E_2F_5C
              @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V2b @ V1c @ V32t )
                @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                  @ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V33t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V33t ) )
                  @ ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V34t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V34t ) ) )
                  @ V32t ) )
              @ ( c_2EPast__Temporal__Logic_2EPSUNTIL
                @ ^ [V35t: tyop_2Enum_2Enum] :
                    ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1c @ V35t ) )
                    @ ( c_2EPast__Temporal__Logic_2EPBEFORE
                      @ ^ [V36t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V36t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V36t ) )
                      @ ^ [V37t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V37t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V37t ) ) )
                      @ V35t ) )
                @ V0d
                @ V32t ) ) ) ) ) ).

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