ITP001 Axioms: ITP044^5.ax


%------------------------------------------------------------------------------
% File     : ITP044^5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : Temporal_Logic^2.ax [Gau20]
%          : HL4044^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  176 (   0 unt;  11 typ;   0 def)
%            Number of atoms       : 5119 ( 132 equ;   0 cnn)
%            Maximal formula atoms :  115 (  29 avg)
%            Number of connectives : 7021 (  55   ~;  27   |; 160   &;6345   @)
%                                         (  88 <=>; 346  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  12 avg;6345 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  41 usr;  43 con; 0-2 aty)
%            Number of variables   :  655 ( 191   ^ 423   !;  41   ?; 655   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2ETemporal__Logic_2EALWAYS,type,
    c_2ETemporal__Logic_2EALWAYS: $i ).

thf(mem_c_2ETemporal__Logic_2EALWAYS,axiom,
    mem @ c_2ETemporal__Logic_2EALWAYS @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).

thf(tp_c_2ETemporal__Logic_2EBEFORE,type,
    c_2ETemporal__Logic_2EBEFORE: $i ).

thf(mem_c_2ETemporal__Logic_2EBEFORE,axiom,
    mem @ c_2ETemporal__Logic_2EBEFORE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2ETemporal__Logic_2EEVENTUAL,type,
    c_2ETemporal__Logic_2EEVENTUAL: $i ).

thf(mem_c_2ETemporal__Logic_2EEVENTUAL,axiom,
    mem @ c_2ETemporal__Logic_2EEVENTUAL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).

thf(tp_c_2ETemporal__Logic_2ENEXT,type,
    c_2ETemporal__Logic_2ENEXT: $i ).

thf(mem_c_2ETemporal__Logic_2ENEXT,axiom,
    mem @ c_2ETemporal__Logic_2ENEXT @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).

thf(tp_c_2ETemporal__Logic_2ESBEFORE,type,
    c_2ETemporal__Logic_2ESBEFORE: $i ).

thf(mem_c_2ETemporal__Logic_2ESBEFORE,axiom,
    mem @ c_2ETemporal__Logic_2ESBEFORE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2ETemporal__Logic_2ESUNTIL,type,
    c_2ETemporal__Logic_2ESUNTIL: $i ).

thf(mem_c_2ETemporal__Logic_2ESUNTIL,axiom,
    mem @ c_2ETemporal__Logic_2ESUNTIL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2ETemporal__Logic_2ESWHEN,type,
    c_2ETemporal__Logic_2ESWHEN: $i ).

thf(mem_c_2ETemporal__Logic_2ESWHEN,axiom,
    mem @ c_2ETemporal__Logic_2ESWHEN @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2ETemporal__Logic_2EUNTIL,type,
    c_2ETemporal__Logic_2EUNTIL: $i ).

thf(mem_c_2ETemporal__Logic_2EUNTIL,axiom,
    mem @ c_2ETemporal__Logic_2EUNTIL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2ETemporal__Logic_2EUPTO,type,
    c_2ETemporal__Logic_2EUPTO: $i ).

thf(mem_c_2ETemporal__Logic_2EUPTO,axiom,
    mem @ c_2ETemporal__Logic_2EUPTO @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ bool ) ).

thf(tp_c_2ETemporal__Logic_2EWATCH,type,
    c_2ETemporal__Logic_2EWATCH: $i ).

thf(mem_c_2ETemporal__Logic_2EWATCH,axiom,
    mem @ c_2ETemporal__Logic_2EWATCH @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(tp_c_2ETemporal__Logic_2EWHEN,type,
    c_2ETemporal__Logic_2EWHEN: $i ).

thf(mem_c_2ETemporal__Logic_2EWHEN,axiom,
    mem @ c_2ETemporal__Logic_2EWHEN @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2ENEXT,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ V0P )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t: $i] : ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ V1t ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EALWAYS,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ! [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EEVENTUAL,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ? [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EWATCH,axiom,
    ! [V0q: $i] :
      ( ( mem @ V0q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3t: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ V0q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  <=> $false )
                  & ( ( p @ ( ap @ V0q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                  <=> ( ( p @ ( ap @ V0q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EUPTO,axiom,
    ! [V0t0: tp__ty_2Enum_2Enum,V1t1: tp__ty_2Enum_2Enum,V2a: $i] :
      ( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( p @ ( ap @ c_2ETemporal__Logic_2EUPTO @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V1t1 ) ) @ V2a ) ) ) )
      <=> ! [V3t2: tp__ty_2Enum_2Enum] :
            ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) )
              & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t1 ) ) ) )
           => ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                       => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2EBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ( ? [V4t: tp__ty_2Enum_2Enum] :
                        ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                    | ! [V5t: tp__ty_2Enum_2Enum] :
                        ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2ESWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ? [V4t: tp__ty_2Enum_2Enum] :
                      ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2ESUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                  & ? [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(ax_thm_2ETemporal__Logic_2ESBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ? [V4t: tp__ty_2Enum_2Enum] :
                      ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWATCH__EXISTS,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
        ? [V2q: $i] :
          ( ( mem @ V2q @ ( arr @ ty_2Enum_2Enum @ bool ) )
          & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V2q ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWELL__ORDER,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
      <=> ? [V2m: tp__ty_2Enum_2Enum] :
            ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
            & ! [V3n: tp__ty_2Enum_2Enum] :
                ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
               => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE,axiom,
    ! [V0m2: tp__ty_2Enum_2Enum,V1m1: tp__ty_2Enum_2Enum,V2P: $i] :
      ( ( mem @ V2P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) )
          & ! [V3n: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) )
             => ~ ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
          & ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V0m2 ) ) )
          & ! [V4n: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ ( inj__ty_2Enum_2Enum @ V0m2 ) ) )
             => ~ ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) )
       => ( V1m1 = V0m2 ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EDELTA__CASES,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ? [V2d: tp__ty_2Enum_2Enum] :
              ( ! [V3t: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2d ) ) )
                 => ~ ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
              & ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2d ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
          | ! [V4d: tp__ty_2Enum_2Enum] :
              ~ ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4d ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__IMP,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                   => ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        | ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                         => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__IMP,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                   => ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        | ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        | ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__IMP,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                   => ( ? [V4t: tp__ty_2Enum_2Enum] :
                          ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                      | ! [V5t: tp__ty_2Enum_2Enum] :
                          ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__IMP,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                   => ? [V4t: tp__ty_2Enum_2Enum] :
                        ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__IMP,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                   => ( ! [V4t: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          | ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          | ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                      & ? [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__IMP,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                   => ? [V4t: tp__ty_2Enum_2Enum] :
                        ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ! [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ? [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWATCH__SIGNAL,axiom,
    ! [V0q: $i] :
      ( ( mem @ V0q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ( ! [V3t: tp__ty_2Enum_2Enum] :
                      ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                 => ! [V4t: tp__ty_2Enum_2Enum] :
                      ~ ( p @ ( ap @ V0q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                & ! [V5d: tp__ty_2Enum_2Enum] :
                    ( ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      & ! [V6t: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
                         => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                   => ( ! [V7t: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
                         => ~ ( p @ ( ap @ V0q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                      & ! [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3delta: tp__ty_2Enum_2Enum] :
                  ( ( ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
                       => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                    & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                 => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ( ! [V3t: tp__ty_2Enum_2Enum] :
                      ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                 => ! [V4t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                & ! [V5d: tp__ty_2Enum_2Enum] :
                    ( ( ! [V6t: tp__ty_2Enum_2Enum] :
                          ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
                         => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                      & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                   => ! [V7t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
                       => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3delta: tp__ty_2Enum_2Enum] :
                  ( ( ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
                       => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                    & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                 => ? [V5t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
                      & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3delta: tp__ty_2Enum_2Enum] :
                  ( ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
                     => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                  & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                  & ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3delta: tp__ty_2Enum_2Enum] :
                  ( ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
                     => ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                  & ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__SIGNAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3delta: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
                     => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENEXT__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ? [V2t1: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) )
              & ! [V3t3: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t3 ) ) )
                 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) @ ( inj__ty_2Enum_2Enum @ V3t3 ) ) ) )
              & ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ! [V2t1: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) )
             => ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ? [V2t1: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) )
              & ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3t1: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p @ ( ap @ c_2ETemporal__Logic_2EUPTO @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) @ V0a ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3t1: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                    & ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                    & ( p
                      @ ( ap @ c_2ETemporal__Logic_2EUPTO
                        @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
                          @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) )
                 => ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3t1: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p
                    @ ( ap @ c_2ETemporal__Logic_2EUPTO
                      @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
                        @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3t1: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                    & ( p
                      @ ( ap @ c_2ETemporal__Logic_2EUPTO
                        @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
                          @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) ) ) ) ) )
                 => ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3t1: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                  & ( p
                    @ ( ap @ c_2ETemporal__Logic_2EUPTO
                      @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
                        @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__LINORD,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ! [V3t1: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                    & ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
                    & ( p
                      @ ( ap @ c_2ETemporal__Logic_2EUPTO
                        @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
                          @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) )
                 => ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
        = ( ap
          @ ( ap @ c_2ETemporal__Logic_2EWHEN
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V1t: $i] : c_2Ebool_2EF ) )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t: $i] :
              ( ap @ c_2Ebool_2E_7E
              @ ( ap
                @ ( ap
                  @ ( ap @ c_2ETemporal__Logic_2EWHEN
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                  @ V0a )
                @ V1t ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2EWHEN
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ V2t0 ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__NOT__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ~ ( p
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2EWHEN
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                      @ V1b )
                    @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap
                      @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
                      @ V2t ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap
                      @ ( ap
                        @ ( ap @ c_2ETemporal__Logic_2EWHEN
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
                      @ V2t0 ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__WHEN__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap
                      @ ( ap
                        @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                        @ V0a )
                      @ V2t ) )
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2EWHEN
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
                      @ V0a )
                    @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__HW,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3q: $i] :
                  ( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V0a ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                      | ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
        = ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V1t: $i] : c_2Ebool_2EF ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t: $i] :
              ( ap @ c_2Ebool_2E_7E
              @ ( ap
                @ ( ap
                  @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : c_2Ebool_2EF ) )
                @ V1t ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap @ c_2Ebool_2E_7E
                      @ ( ap
                        @ ( ap
                          @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                          @ V1b )
                        @ V2t0 ) ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap
                      @ ( ap
                        @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
                      @ V2t ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ V2t0 ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap @ c_2Ebool_2E_7E
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                      @ V1b )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__BEFORE,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0b )
        = ( ap
          @ ( ap @ c_2ETemporal__Logic_2EBEFORE
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V1t: $i] : c_2Ebool_2EF ) )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__BEFORE,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t0: $i] :
              ( ap @ c_2Ebool_2E_7E
              @ ( ap
                @ ( ap
                  @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                  @ V0b )
                @ V1t0 ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__BEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap @ c_2Ebool_2E_7E
                      @ ( ap
                        @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
                        @ V2t0 ) ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__BEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap @ c_2Ebool_2E_7E
                      @ ( ap
                        @ ( ap
                          @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                          @ V1b )
                        @ V2t0 ) ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__BEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap @ c_2Ebool_2E_7E
                  @ ( ap
                    @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__BEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap @ c_2Ebool_2E_7E
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                      @ V1b )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__BEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ V2t0 ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__SWHEN__LEMMA,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( p
            @ ( ap
              @ ( ap
                @ ( ap @ ( c_2Ebool_2ECOND @ bool )
                  @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t1: $i] :
                          ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t2: $i] : ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t2 ) @ V2t1 ) ) ) ) ) ) )
                @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t0: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V0b ) @ V4t0 ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V0b ) @ V4t0 ) ) ) ) )
              @ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V5t1: $i] :
                      ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V6t2: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V6t2 ) @ V5t1 ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V6t2 ) @ V5t1 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t: $i] :
              ( ap @ c_2Ebool_2E_7E
              @ ( ap
                @ ( ap
                  @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t: $i] : c_2Ebool_2ET ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                @ V1t ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
        = ( ap
          @ ( ap @ c_2ETemporal__Logic_2ESWHEN
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V1t: $i] : c_2Ebool_2ET ) )
          @ V0a ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ V2t ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                    @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__NOT__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ~ ( p
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                      @ V1b )
                    @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap
                      @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
                      @ V2t ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap
                      @ ( ap
                        @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
                      @ V2t0 ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V5t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V5t ) ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__NOT__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap @ c_2Ebool_2E_7E
                  @ ( ap
                    @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t: $i] :
              ( ap @ c_2Ebool_2E_7E
              @ ( ap
                @ ( ap
                  @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t: $i] : c_2Ebool_2ET ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                @ V1t ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
        = ( ap
          @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
            @ ( lam @ ty_2Enum_2Enum
              @ ^ [V1t: $i] : c_2Ebool_2ET ) )
          @ V0a ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap
                      @ ( ap
                        @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                          @ ( lam @ ty_2Enum_2Enum
                            @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
                      @ V2t ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V5t ) ) ) )
                    @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ V2t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t: $i] :
                  ( ap @ c_2Ebool_2E_7E
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                      @ V1b )
                    @ V2t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap @ c_2Ebool_2E_7E
                      @ ( ap
                        @ ( ap
                          @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                          @ V1b )
                        @ V2t0 ) ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__SBEFORE,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0b )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V1t0: $i] :
              ( ap @ c_2Ebool_2E_7E
              @ ( ap
                @ ( ap
                  @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                    @ ( lam @ ty_2Enum_2Enum
                      @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) )
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : c_2Ebool_2EF ) )
                @ V1t0 ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__SBEFORE,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b )
        = ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0b )
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V1t: $i] : c_2Ebool_2EF ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__SBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_5C_2F
                    @ ( ap
                      @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) @ ( ap @ V1b @ V3t ) ) ) )
                      @ V2t0 ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__SBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap @ c_2Ebool_2E_7E
                  @ ( ap
                    @ ( ap
                      @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                        @ ( lam @ ty_2Enum_2Enum
                          @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                      @ V1b )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__SBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) @ ( ap @ V1b @ V2t ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__SBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap
                  @ ( ap @ c_2Ebool_2E_2F_5C
                    @ ( ap @ c_2Ebool_2E_7E
                      @ ( ap
                        @ ( ap
                          @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                            @ ( lam @ ty_2Enum_2Enum
                              @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                          @ V1b )
                        @ V2t0 ) ) )
                  @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__SBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V2t0: $i] :
                  ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ V2t0 ) )
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
                    @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__SIMP,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2EWHEN
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                @ V0b )
              = ( ap @ c_2ETemporal__Logic_2EALWAYS
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) ) )
            & ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2EWHEN
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : c_2Ebool_2ET ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V5t: $i] : c_2Ebool_2ET ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V6t: $i] : c_2Ebool_2EF ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V7t: $i] : c_2Ebool_2ET ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V8t: $i] : c_2Ebool_2ET ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V9t: $i] : ( ap @ V1a @ V9t ) ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V1a )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V10t: $i] : c_2Ebool_2ET ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__SIMP,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : ( ap @ V0b @ V3t ) ) )
            & ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : c_2Ebool_2ET ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V5t: $i] : c_2Ebool_2ET ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V6t: $i] : c_2Ebool_2EF ) )
              = ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V7t: $i] : c_2Ebool_2ET ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V8t: $i] : c_2Ebool_2ET ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a ) @ V1a )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V9t: $i] : ( ap @ V1a @ V9t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__SIMP,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                @ V0b )
              = ( ap @ c_2ETemporal__Logic_2EALWAYS
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) ) )
            & ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : c_2Ebool_2ET ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V5t ) ) ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V6t: $i] : c_2Ebool_2EF ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V7t: $i] : c_2Ebool_2ET ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V8t: $i] : c_2Ebool_2ET ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V9t: $i] : c_2Ebool_2EF ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V1a )
              = ( ap @ c_2ETemporal__Logic_2EALWAYS
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1a @ V10t ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__SIMP,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : c_2Ebool_2EF ) )
            & ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : c_2Ebool_2ET ) )
                @ V0b )
              = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V5t: $i] : c_2Ebool_2EF ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V6t: $i] : c_2Ebool_2EF ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V7t: $i] : c_2Ebool_2ET ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V8t: $i] : ( ap @ V1a @ V8t ) ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V1a )
              = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__SIMP,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : ( ap @ V0b @ V3t ) ) )
            & ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : c_2Ebool_2ET ) )
                @ V0b )
              = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V5t: $i] : c_2Ebool_2EF ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V6t: $i] : c_2Ebool_2EF ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V7t: $i] : c_2Ebool_2ET ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V8t: $i] : c_2Ebool_2ET ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a ) @ V1a )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V9t: $i] : ( ap @ V1a @ V9t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__SIMP,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : c_2Ebool_2EF ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V3t: $i] : c_2Ebool_2EF ) )
            & ( ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : c_2Ebool_2ET ) )
                @ V0b )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V5t ) ) ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V6t: $i] : c_2Ebool_2EF ) )
              = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V7t: $i] : c_2Ebool_2ET ) )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V8t: $i] : c_2Ebool_2EF ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V1a )
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V9t: $i] : c_2Ebool_2EF ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2EWHEN
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
              @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
              @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
              @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
              @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
              @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( ap
              @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
              @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EIMMEDIATE__EVENT,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ V0b @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
         => ( ! [V2a: $i] :
                ( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
            & ! [V3a: $i] :
                ( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $true ) )
            & ! [V4a: $i] :
                ( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $false ) )
            & ! [V5a: $i] :
                ( ( mem @ V5a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V5a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ V5a @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
            & ! [V6a: $i] :
                ( ( mem @ V6a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V6a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $true ) )
            & ! [V7a: $i] :
                ( ( mem @ V7a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V7a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $false ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENO__EVENT,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p
            @ ( ap
              @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) )
              @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
         => ( ! [V3a: $i] :
                ( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $true ) )
            & ! [V4a: $i] :
                ( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V4a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
            & ! [V5a: $i] :
                ( ( mem @ V5a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V5a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $true ) )
            & ! [V6a: $i] :
                ( ( mem @ V6a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V6a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $false ) )
            & ! [V7a: $i] :
                ( ( mem @ V7a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V7a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> $false ) )
            & ! [V8a: $i] :
                ( ( mem @ V8a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V8a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V8a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESOME__EVENT,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
          <=> ! [V2a: $i] :
                ( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
          & ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
          <=> ! [V3a: $i] :
                ( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
          & ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
          <=> ! [V4a: $i] :
                ( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
               => ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
                <=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EMORE__EVENT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
              = ( ap
                @ ( ap @ c_2ETemporal__Logic_2EWHEN
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
                @ V1b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
              = ( ap
                @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) ) )
                @ V1b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
              = ( ap
                @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) )
                @ V1b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
              = ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V5t ) ) @ ( ap @ V1b @ V5t ) ) ) )
                @ V1b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
              = ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V6t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V6t ) ) ) ) )
                @ V1b ) )
            & ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
              = ( ap
                @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                  @ ( lam @ ty_2Enum_2Enum
                    @ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V7t ) ) ) ) )
                @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__NEXT,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2ENEXT
          @ ( lam @ ty_2Enum_2Enum
            @ ^ [V1t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0P @ V1t ) ) ) )
        = ( lam @ ty_2Enum_2Enum
          @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0P ) @ V2t ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EAND__NEXT,axiom,
    ! [V0Q: $i] :
      ( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EOR__NEXT,axiom,
    ! [V0Q: $i] :
      ( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EIMP__NEXT,axiom,
    ! [V0Q: $i] :
      ( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEQUIV__NEXT,axiom,
    ! [V0Q: $i] :
      ( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1P: $i] :
          ( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
            = ( lam @ ty_2Enum_2Enum
              @ ^ [V3t: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) )
        = ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) )
        = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__NEXT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__REC,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
            & ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0P ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__REC,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
            | ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0P ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWATCH__REC,axiom,
    ! [V0q: $i] :
      ( ( mem @ V0q @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ~ ( p @ ( ap @ V0q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0q ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__REC,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__REC,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
               => ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__REC,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                & ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  | ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__REC,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__REC,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
               => ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__REC,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                & ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  | ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__FIX,axiom,
    ! [V0y: $i] :
      ( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( V0y
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V2t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
          <=> ( ( V0y
                = ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
              | ( V0y
                = ( lam @ ty_2Enum_2Enum
                  @ ^ [V3t: $i] : c_2Ebool_2EF ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__FIX,axiom,
    ! [V0y: $i] :
      ( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( V0y
              = ( lam @ ty_2Enum_2Enum
                @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V2t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
          <=> ( ( V0y
                = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
              | ( V0y
                = ( lam @ ty_2Enum_2Enum
                  @ ^ [V3t: $i] : c_2Ebool_2ET ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__FIX,axiom,
    ! [V0y: $i] :
      ( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
             => ( ( V0y
                  = ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ V3t ) ) @ ( ap @ V2a @ V3t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
              <=> ( ( V0y
                    = ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V1b ) )
                  | ( V0y
                    = ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V1b ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__FIX,axiom,
    ! [V0y: $i] :
      ( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2a: $i] :
              ( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
             => ( ( V0y
                  = ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2a @ V3t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
              <=> ( ( V0y
                    = ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V2a ) @ V1b ) )
                  | ( V0y
                    = ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V2a ) @ V1b ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__FIX,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1a: $i] :
          ( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2y: $i] :
              ( ( mem @ V2y @ ( arr @ ty_2Enum_2Enum @ bool ) )
             => ( ( V2y
                  = ( lam @ ty_2Enum_2Enum
                    @ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V3t ) ) @ ( ap @ V2y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
              <=> ( ( V2y
                    = ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V0b ) )
                  | ( V2y
                    = ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V0b ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3J: $i] :
                  ( ( mem @ V3J @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ V3J @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                     => ( p @ ( ap @ V3J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                  & ! [V5d: tp__ty_2Enum_2Enum] :
                      ( ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                     => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3J: $i] :
                  ( ( mem @ V3J @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ V3J @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                     => ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ( p @ ( ap @ V3J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ? [V3J: $i] :
                  ( ( mem @ V3J @ ( arr @ ty_2Enum_2Enum @ bool ) )
                  & ( p @ ( ap @ V3J @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                  & ! [V4t: tp__ty_2Enum_2Enum] :
                      ( ( ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                        & ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                     => ( p @ ( ap @ V3J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                  & ! [V5d: tp__ty_2Enum_2Enum] :
                      ( ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                     => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ? [V2J: $i] :
              ( ( mem @ V2J @ ( arr @ ty_2Enum_2Enum @ bool ) )
              & ( p @ ( ap @ V2J @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
              & ! [V3t: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
                 => ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
                    & ( p @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__INVARIANT,axiom,
    ! [V0b: $i] :
      ( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ? [V2J: $i] :
              ( ( mem @ V2J @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
              & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V2J @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
              & ! [V3t: tp__ty_2Enum_2Enum] :
                  ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V2J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
                  | ( ( surj__ty_2Enum_2Enum @ ( ap @ V2J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
                    = fo__c_2Enum_2E0 ) )
              & ! [V4t: tp__ty_2Enum_2Enum] :
                  ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
                    & ( ( surj__ty_2Enum_2Enum @ ( ap @ V2J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
                      = fo__c_2Enum_2E0 ) )
                 => ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ? [V3J1: $i] :
                    ( ( mem @ V3J1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                    & ( p @ ( ap @ V3J1 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                    & ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                       => ( p @ ( ap @ V3J1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                    & ! [V5d: tp__ty_2Enum_2Enum] :
                        ( ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                       => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                & ? [V6J2: $i] :
                    ( ( mem @ V6J2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
                    & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                    & ! [V7t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                        | ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                          = fo__c_2Enum_2E0 ) )
                    & ! [V8t: tp__ty_2Enum_2Enum] :
                        ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                          & ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                            = fo__c_2Enum_2E0 ) )
                       => ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ? [V3J1: $i] :
                    ( ( mem @ V3J1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                    & ( p @ ( ap @ V3J1 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                    & ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                       => ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ( p @ ( ap @ V3J1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) )
                & ? [V5J2: $i] :
                    ( ( mem @ V5J2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
                    & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V5J2 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                    & ! [V6t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V5J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) @ ( ap @ V5J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                        | ( ( surj__ty_2Enum_2Enum @ ( ap @ V5J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                          = fo__c_2Enum_2E0 ) )
                    & ! [V7t: tp__ty_2Enum_2Enum] :
                        ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V5J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                          & ( ( surj__ty_2Enum_2Enum @ ( ap @ V5J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                            = fo__c_2Enum_2E0 ) )
                       => ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__INVARIANT,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( ? [V3J1: $i] :
                    ( ( mem @ V3J1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
                    & ( p @ ( ap @ V3J1 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
                    & ! [V4t: tp__ty_2Enum_2Enum] :
                        ( ( ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                          & ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                       => ( p @ ( ap @ V3J1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                    & ! [V5d: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                       => ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
                & ? [V6J2: $i] :
                    ( ( mem @ V6J2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
                    & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
                    & ! [V7t: tp__ty_2Enum_2Enum] :
                        ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                        | ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                          = fo__c_2Enum_2E0 ) )
                    & ! [V8t: tp__ty_2Enum_2Enum] :
                        ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                          & ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
                            = fo__c_2Enum_2E0 ) )
                       => ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EALWAYS__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
        = ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
        = ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EWHEN__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EUNTIL__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2EBEFORE__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESWHEN__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESUNTIL__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ESBEFORE__IDEM,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
            = ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__ALWAYS,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ( p
            @ ( ap
              @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
              @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__EVENTUAL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1t0: tp__ty_2Enum_2Enum] :
          ( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
        <=> ( p
            @ ( ap
              @ ( ap @ c_2ETemporal__Logic_2EALWAYS
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
              @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__WHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p
                @ ( ap
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2ESWHEN
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                    @ V1b )
                  @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__UNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p
                @ ( ap
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2ESBEFORE
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                    @ V1b )
                  @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__BEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p
                @ ( ap
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2ESUNTIL
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                    @ V1b )
                  @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__SWHEN,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p
                @ ( ap
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EWHEN
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                    @ V1b )
                  @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__SUNTIL,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p
                @ ( ap
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EBEFORE
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                    @ V1b )
                  @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

thf(conj_thm_2ETemporal__Logic_2ENOT__SBEFORE,axiom,
    ! [V0a: $i] :
      ( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
     => ! [V1b: $i] :
          ( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
         => ! [V2t0: tp__ty_2Enum_2Enum] :
              ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
            <=> ( p
                @ ( ap
                  @ ( ap
                    @ ( ap @ c_2ETemporal__Logic_2EUNTIL
                      @ ( lam @ ty_2Enum_2Enum
                        @ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
                    @ V1b )
                  @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).

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