ITP001 Axioms: ITP061^7.ax
%------------------------------------------------------------------------------
% File : ITP061^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : Past_Temporal_Logic.ax [Gau19]
% : HL4061^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 88 ( 6 unt; 37 typ; 0 def)
% Number of atoms : 2441 ( 404 equ; 36 cnn)
% Maximal formula atoms : 76 ( 27 avg)
% Number of connectives : 4644 ( 36 ~; 13 |; 409 &;4107 @)
% ( 64 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 76 ( 13 avg;4107 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 207 ( 207 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 4 con; 0-4 aty)
% Number of variables : 803 ( 649 ^ 142 !; 8 ?; 803 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2ETemporal__Logic_2EALWAYS,type,
c_2ETemporal__Logic_2EALWAYS: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2EBEFORE,type,
c_2ETemporal__Logic_2EBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2ETemporal__Logic_2EEVENTUAL,type,
c_2ETemporal__Logic_2EEVENTUAL: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2EPast__Temporal__Logic_2EInitPoint,type,
c_2EPast__Temporal__Logic_2EInitPoint: tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2ENEXT,type,
c_2ETemporal__Logic_2ENEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPALWAYS,type,
c_2EPast__Temporal__Logic_2EPALWAYS: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPBEFORE,type,
c_2EPast__Temporal__Logic_2EPBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPEVENTUAL,type,
c_2EPast__Temporal__Logic_2EPEVENTUAL: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPNEXT,type,
c_2EPast__Temporal__Logic_2EPNEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Eprim__rec_2EPRE,type,
c_2Eprim__rec_2EPRE: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2EPast__Temporal__Logic_2EPSBEFORE,type,
c_2EPast__Temporal__Logic_2EPSBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSNEXT,type,
c_2EPast__Temporal__Logic_2EPSNEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSUNTIL,type,
c_2EPast__Temporal__Logic_2EPSUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSWHEN,type,
c_2EPast__Temporal__Logic_2EPSWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPUNTIL,type,
c_2EPast__Temporal__Logic_2EPUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPWHEN,type,
c_2EPast__Temporal__Logic_2EPWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2ESBEFORE,type,
c_2ETemporal__Logic_2ESBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2ESUNTIL,type,
c_2ETemporal__Logic_2ESUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2ESWHEN,type,
c_2ETemporal__Logic_2ESWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2ETemporal__Logic_2EUNTIL,type,
c_2ETemporal__Logic_2EUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2EWHEN,type,
c_2ETemporal__Logic_2EWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2EPast__Temporal__Logic_2EInitPoint,axiom,
( c_2EPast__Temporal__Logic_2EInitPoint
= ( ^ [V0t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ tyop_2Enum_2Enum @ V0t @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSNEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0a @ V1t0 )
<=> ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V1t0 )
& ( V0a @ ( c_2Eprim__rec_2EPRE @ V1t0 ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPNEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPNEXT @ V0a @ V1t0 )
<=> ( ( V1t0 = c_2Enum_2E0 )
| ( V0a @ ( c_2Eprim__rec_2EPRE @ V1t0 ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPALWAYS,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V0a @ V1t0 )
<=> ! [V2t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2t @ V1t0 )
=> ( V0a @ V2t ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPEVENTUAL,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a @ V1t0 )
<=> ? [V2t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2t @ V1t0 )
& ( V0a @ V2t ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSWHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V0a @ V1b @ V2t0 )
<=> ? [V3delta: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V2t0 )
& ( V0a @ V3delta )
& ( V1b @ V3delta )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ V3delta @ V4t )
& ( c_2Earithmetic_2E_3C_3D @ V4t @ V2t0 ) )
=> ( (~) @ ( V1b @ V4t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSUNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a @ V1b @ V2t0 )
<=> ? [V3delta: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V2t0 )
& ( V1b @ V3delta )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ V3delta @ V4t )
& ( c_2Earithmetic_2E_3C_3D @ V4t @ V2t0 ) )
=> ( ( V0a @ V4t )
& ( (~) @ ( V1b @ V4t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSBEFORE,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a @ V1b @ V2t0 )
<=> ? [V3delta: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V2t0 )
& ( V0a @ V3delta )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3delta @ V4t )
& ( c_2Earithmetic_2E_3C_3D @ V4t @ V2t0 ) )
=> ( (~) @ ( V1b @ V4t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPWHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPWHEN @ V0a @ V1b @ V2t0 )
<=> ( ! [V3t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V3t @ V2t0 )
=> ( (~) @ ( V1b @ V3t ) ) )
| ? [V4delta: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V2t0 )
& ( V0a @ V4delta )
& ( V1b @ V4delta )
& ! [V5t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ V4delta @ V5t )
& ( c_2Earithmetic_2E_3C_3D @ V5t @ V2t0 ) )
=> ( (~) @ ( V1b @ V5t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPUNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V0a @ V1b @ V2t0 )
<=> ( ! [V3t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V3t @ V2t0 )
=> ( V0a @ V3t ) )
| ? [V4delta: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V2t0 )
& ( V1b @ V4delta )
& ! [V5t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ V4delta @ V5t )
& ( c_2Earithmetic_2E_3C_3D @ V5t @ V2t0 ) )
=> ( ( V0a @ V5t )
& ( (~) @ ( V1b @ V5t ) ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPBEFORE,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0a @ V1b @ V2t0 )
<=> ( ! [V3t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V3t @ V2t0 )
=> ( (~) @ ( V1b @ V3t ) ) )
| ? [V4delta: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V2t0 )
& ( V0a @ V4delta )
& ! [V5t: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V4delta @ V5t )
& ( c_2Earithmetic_2E_3C_3D @ V5t @ V2t0 ) )
=> ( (~) @ ( V1b @ V5t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EINITIALISATION,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ( ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a @ c_2Enum_2E0 )
= ( V1a @ c_2Enum_2E0 ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a @ c_2Enum_2E0 )
= ( V1a @ c_2Enum_2E0 ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b @ c_2Enum_2E0 )
= ( V0b @ c_2Enum_2E0 ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b @ c_2Enum_2E0 )
<=> ( ( V1a @ c_2Enum_2E0 )
& ( V0b @ c_2Enum_2E0 ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b @ c_2Enum_2E0 )
<=> ( ( V1a @ c_2Enum_2E0 )
& ( (~) @ ( V0b @ c_2Enum_2E0 ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b @ c_2Enum_2E0 )
<=> ( ( V1a @ c_2Enum_2E0 )
| ( V0b @ c_2Enum_2E0 ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b @ c_2Enum_2E0 )
<=> ( ( V1a @ c_2Enum_2E0 )
| ( (~) @ ( V0b @ c_2Enum_2E0 ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b @ c_2Enum_2E0 )
<=> ( (~) @ ( V0b @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ERECURSION,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1a ) @ V2t ) ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) @ V3t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V0b @ V4t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) @ V4t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V0b @ V5t ) @ ( V1a @ V5t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) @ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V6t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V6t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) @ V6t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V0b @ V7t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) @ V7t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V0b @ V8t ) @ ( V1a @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) @ V8t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V9t ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) @ V9t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) @ V10t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) @ V11t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0b @ V12t ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b ) @ V12t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V13t ) @ ( V0b @ V13t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V13t ) ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b ) @ V13t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V14t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b ) @ V14t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0b @ V15t ) @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b ) @ V15t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V1a @ V16t ) @ ( V0b @ V16t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V16t ) ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b ) @ V16t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V17t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b ) @ V17t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EFIXPOINTS,axiom,
! [V0y: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( V0y
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V3t ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EALWAYS @ V2a ) )
| ( V0y
= ( ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ) )
& ( ( V0y
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V5t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V5t ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EEVENTUAL @ V2a ) )
| ( V0y
= ( ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) ) ) )
& ( ( V0y
= ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V1b @ V7t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V7t ) ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
| ( V0y
= ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) ) ) )
& ( ( V0y
= ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V1b @ V8t ) @ ( V2a @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V8t ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
| ( V0y
= ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) ) ) )
& ( ( V0y
= ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V9t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V2a @ V9t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0y @ V9t ) ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) )
| ( V0y
= ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) ) ) )
& ( ( V0y
= ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V10t ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) ) )
& ( ( V0y
= ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V11t ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) ) )
& ( ( V0y
= ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V12t ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V12t ) ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b ) ) )
& ( ( V0y
= ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V13t ) @ ( V1b @ V13t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V13t ) ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V13t ) ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b ) ) )
& ( ( V0y
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V14t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V2a @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0y @ V14t ) ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b ) ) )
& ( ( V0y
= ( ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V15t ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V15t ) ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b ) ) )
& ( ( V0y
= ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V16t ) @ ( V1b @ V16t ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V16t ) ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V16t ) ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b ) ) )
& ( ( V0y
= ( ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1b @ V17t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0y @ V17t ) ) ) ) )
<=> ( V0y
= ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESUNTIL__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V1a
@ V5t ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
@ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V11t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V11t ) ) )
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
@ V10t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V14t ) )
@ V0b
@ V13t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V15t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V16t ) )
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( V0b @ V17t ) )
@ V15t ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V18t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V19t ) )
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V20t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V20t ) ) )
@ V18t ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EUNTIL__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EUNTIL @ V1a
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V2t ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V4t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V5t ) )
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V4t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
@ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V11t ) )
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
@ V10t ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V14t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V14t ) ) )
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
@ V13t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EUNTIL
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V18t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V18t ) ) )
@ V16t ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V19t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V20t ) )
@ V0b
@ V19t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EWHEN__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V1a
@ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V9t ) @ ( V0b @ V9t ) )
@ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EWHEN @ V0b
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
@ V10t ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
@ V0b
@ V12t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V14t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EWHEN
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V15t ) )
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V16t ) @ ( V0b @ V16t ) )
@ V14t ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V17t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EWHEN @ V0b
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
@ V17t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESWHEN__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESWHEN
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V1a
@ V5t ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESWHEN @ V0b
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V8t ) @ ( V0b @ V8t ) )
@ V7t ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V10t ) )
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
@ V9t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
@ V0b
@ V12t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V14t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESWHEN @ V0b
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V15t ) @ ( V0b @ V15t ) )
@ V14t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESWHEN
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
@ V16t ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EBEFORE__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V1a
@ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V8t ) )
@ V0b
@ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EBEFORE @ V0b
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V10t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V10t ) ) )
@ V9t ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V11t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE @ V0b
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
@ V11t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2EBEFORE
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
@ V13t ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE @ V0b
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V17t ) ) )
@ V16t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESBEFORE__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V2t ) ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESBEFORE @ V1a
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V5t ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V8t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V8t ) ) )
@ V7t ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V10t ) )
@ V0b
@ V9t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V11t: tyop_2Enum_2Enum] :
( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
@ V11t ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
@ V13t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V15t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V16t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V16t ) ) )
@ V15t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSUNTIL__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V1a
@ V5t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
@ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V11t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V11t ) ) )
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
@ V10t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V14t ) )
@ V0b
@ V13t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( ^ [V15t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V16t ) )
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( V0b @ V17t ) )
@ V15t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( ^ [V18t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V19t ) )
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V20t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V20t ) ) )
@ V18t ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPUNTIL__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V2t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V4t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V5t ) )
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V4t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V9t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
@ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V11t ) )
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
@ V10t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1a @ V14t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V14t ) ) )
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
@ V13t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V18t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V18t ) ) )
@ V16t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( ^ [V19t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V20t ) )
@ V0b
@ V19t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPWHEN__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V1a
@ V5t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V8t ) )
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V9t ) @ ( V0b @ V9t ) )
@ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPWHEN @ V0b
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
@ V10t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
@ V0b
@ V12t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( ^ [V14t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V15t ) )
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V16t ) @ ( V0b @ V16t ) )
@ V14t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( ^ [V17t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPWHEN @ V0b
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
@ V17t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSWHEN__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V1a
@ V5t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSWHEN @ V0b
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V8t ) @ ( V0b @ V8t ) )
@ V7t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V10t ) )
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
@ V9t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V13t ) )
@ V0b
@ V12t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( ^ [V14t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V0b
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V15t ) @ ( V0b @ V15t ) )
@ V14t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V17t ) )
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V18t ) @ ( V0b @ V18t ) )
@ V16t ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPBEFORE__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V4t ) )
@ V2t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V1a
@ V5t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V8t ) )
@ V0b
@ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPBEFORE @ V0b
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V10t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V10t ) ) )
@ V9t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( ^ [V11t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0b
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( V0b @ V12t ) )
@ V11t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V15t ) ) @ ( V0b @ V15t ) )
@ V13t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0b
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V17t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V17t ) ) )
@ V16t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPSBEFORE__EXPRESSIVE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V2t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a )
= ( ^ [V5t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V5t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V8t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V8t ) ) )
@ V7t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V10t ) )
@ V0b
@ V9t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( ^ [V11t: tyop_2Enum_2Enum] :
( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V12t ) ) @ ( V0b @ V12t ) )
@ V11t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V14t ) @ ( V0b @ V14t ) )
@ V13t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( ^ [V15t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V16t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V16t ) ) )
@ V15t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ENEGATION__NORMAL__FORM,axiom,
! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( (~) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V0t ) )
<=> ( c_2ETemporal__Logic_2ENEXT
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2EALWAYS @ V2a @ V0t ) )
<=> ( c_2ETemporal__Logic_2EEVENTUAL
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V4t ) )
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a @ V0t ) )
<=> ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V5t ) )
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V6t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V7t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V8t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2EWHEN
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V9t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V10t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V11t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPSNEXT
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V12t ) )
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V13t ) )
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V14t ) )
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V15t ) )
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V16t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V17t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V18t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V19t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V20t ) )
@ V1b
@ V0t ) )
& ( ( (~) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t ) )
<=> ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V21t ) )
@ V1b
@ V0t ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ECONJUNCTIVE__NORMAL__FORM,axiom,
! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( V1b @ V3t ) ) )
= ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V4t ) ) ) )
& ( ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V5t ) @ ( V1b @ V5t ) ) )
= ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EALWAYS @ V2a @ V6t ) @ ( c_2ETemporal__Logic_2EALWAYS @ V1b @ V6t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( V1b @ V7t ) )
@ V0c )
= ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V0c @ V8t ) @ ( c_2ETemporal__Logic_2EWHEN @ V1b @ V0c @ V8t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V9t ) @ ( V1b @ V9t ) )
@ V0c )
= ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V0c @ V10t ) @ ( c_2ETemporal__Logic_2ESWHEN @ V1b @ V0c @ V10t ) ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V11t ) @ ( V1b @ V11t ) )
@ V0c )
= ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V0c @ V12t ) @ ( c_2ETemporal__Logic_2EUNTIL @ V1b @ V0c @ V12t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V13t ) @ ( V1b @ V13t ) )
@ V0c )
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V0c @ V14t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V14t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V0c
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( V1b @ V15t ) ) )
= ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V0c @ V2a @ V16t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V0c @ V1b @ V16t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V0c
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( V1b @ V17t ) ) )
= ( ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESBEFORE @ V0c @ V2a @ V18t ) @ ( c_2ETemporal__Logic_2ESBEFORE @ V0c @ V1b @ V18t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V19t ) @ ( V1b @ V19t ) ) )
= ( ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V20t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSNEXT
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V21t ) @ ( V1b @ V21t ) ) )
= ( ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a @ V22t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b @ V22t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V23t ) @ ( V1b @ V23t ) ) )
= ( ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a @ V24t ) @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1b @ V24t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V25t ) @ ( V1b @ V25t ) )
@ V0c )
= ( ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V0c @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1b @ V0c @ V26t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V27t ) @ ( V1b @ V27t ) )
@ V0c )
= ( ^ [V28t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V0c @ V28t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1b @ V0c @ V28t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V29t ) @ ( V1b @ V29t ) )
@ V0c )
= ( ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V0c @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1b @ V0c @ V30t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V31t ) @ ( V1b @ V31t ) )
@ V0c )
= ( ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V0c @ V32t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V32t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0c
@ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V33t ) @ ( V1b @ V33t ) ) )
= ( ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0c @ V2a @ V34t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V0c @ V1b @ V34t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0c
@ ^ [V35t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V35t ) @ ( V1b @ V35t ) ) )
= ( ^ [V36t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0c @ V2a @ V36t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V0c @ V1b @ V36t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EDISJUNCTIVE__NORMAL__FORM,axiom,
! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V3t ) @ ( V1b @ V3t ) ) )
= ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V4t ) ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V5t ) @ ( V1b @ V5t ) ) )
= ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a @ V6t ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V6t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V7t ) @ ( V1b @ V7t ) )
@ V0c )
= ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V0c @ V8t ) @ ( c_2ETemporal__Logic_2EWHEN @ V1b @ V0c @ V8t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V9t ) @ ( V1b @ V9t ) )
@ V0c )
= ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V0c @ V10t ) @ ( c_2ETemporal__Logic_2ESWHEN @ V1b @ V0c @ V10t ) ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V2a
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V11t ) @ ( V0c @ V11t ) ) )
= ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V12t ) @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V0c @ V12t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V13t ) @ ( V0c @ V13t ) ) )
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V14t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V0c @ V14t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( V1b @ V15t ) )
@ V0c )
= ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V0c @ V16t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V16t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( V1b @ V17t ) )
@ V0c )
= ( ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V0c @ V18t ) @ ( c_2ETemporal__Logic_2ESBEFORE @ V1b @ V0c @ V18t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V19t ) @ ( V1b @ V19t ) ) )
= ( ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V20t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V21t ) @ ( V1b @ V21t ) ) )
= ( ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a @ V22t ) @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1b @ V22t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V23t ) @ ( V1b @ V23t ) )
@ V0c )
= ( ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V0c @ V24t ) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1b @ V0c @ V24t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V25t ) @ ( V1b @ V25t ) )
@ V0c )
= ( ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V0c @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1b @ V0c @ V26t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a
@ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V27t ) @ ( V0c @ V27t ) ) )
= ( ^ [V28t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V28t ) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V0c @ V28t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a
@ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V29t ) @ ( V0c @ V29t ) ) )
= ( ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V0c @ V30t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V31t ) @ ( V1b @ V31t ) )
@ V0c )
= ( ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V0c @ V32t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V32t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V33t ) @ ( V1b @ V33t ) )
@ V0c )
= ( ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V0c @ V34t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V0c @ V34t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPRENEX__NEXT__NORMAL__FORM,axiom,
! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( (~) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V0t ) )
<=> ( c_2ETemporal__Logic_2ENEXT
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V0t ) )
& ( ( ( V2a @ V0t )
& ( c_2ETemporal__Logic_2ENEXT @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2ENEXT
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V4t ) @ ( V1b @ V4t ) )
@ V0t ) )
& ( ( ( V2a @ V0t )
| ( c_2ETemporal__Logic_2ENEXT @ V1b @ V0t ) )
<=> ( c_2ETemporal__Logic_2ENEXT
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V5t ) @ ( V1b @ V5t ) )
@ V0t ) )
& ( ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V2a ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
= ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V6t ) @ ( V2a @ V6t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
= ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V7t ) ) @ ( V2a @ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V8t ) @ ( V2a @ V8t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V9t ) ) @ ( V2a @ V9t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V10t ) ) @ ( V1b @ V10t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPSWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V11t ) ) @ ( V1b @ V11t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) @ V1b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V12t ) ) @ ( V1b @ V12t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a )
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V13t ) ) @ ( V1b @ V13t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V14t ) ) @ ( V2a @ V14t ) )
@ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT
@ ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V15t ) @ ( V2a @ V15t ) )
@ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V2a ) @ V1b )
= ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ENEXT__INWARDS__NORMAL__FORM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) ) )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V3t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) ) )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V5t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V6t ) @ ( V0b @ V6t ) ) )
= ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
= ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
= ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) @ ( c_2ETemporal__Logic_2ENEXT @ V0b ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) )
= V1a )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) )
= V1a )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
= ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V8t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
= ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a @ V9t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V9t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b ) )
= ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V10t ) @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b @ V10t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b ) )
= ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V11t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b @ V11t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b ) )
= ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V12t ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b @ V12t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b ) )
= ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V13t ) @ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V13t ) @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b @ V13t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b ) )
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V14t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b @ V14t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b ) )
= ( ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0b @ V15t ) ) @ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b @ V15t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EPNEXT__INWARDS__NORMAL__FORM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) ) )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a @ V3t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) ) )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a @ V5t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b @ V5t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V6t ) @ ( V0b @ V6t ) ) )
= ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a @ V7t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b @ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ENEXT @ V1a ) )
= ( ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V8t ) @ ( V1a @ V8t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
= ( ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V9t ) @ ( c_2ETemporal__Logic_2EALWAYS @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ V9t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
= ( ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V10t ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ V10t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2ESWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2EUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2EWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) )
= ( c_2ETemporal__Logic_2EBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
= ( c_2EPast__Temporal__Logic_2EPALWAYS @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
= ( ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) @ V11t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b ) )
= ( ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) @ V12t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b ) )
= ( ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V13t ) @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) @ V13t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b ) )
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) @ V14t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b ) )
= ( c_2EPast__Temporal__Logic_2EPUNTIL @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b ) )
= ( c_2EPast__Temporal__Logic_2EPWHEN @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0b ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b ) )
= ( c_2EPast__Temporal__Logic_2EPBEFORE @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0b ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESIMPLIFY,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V9t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL
@ ^ [V10t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V11t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL
@ ^ [V12t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V13t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V14t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= V0b )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V15t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
@ ^ [V16t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V17t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
@ ^ [V18t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V19t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V1a )
= V1a )
& ( ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V20t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= V0b )
& ( ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V21t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V22t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
@ ^ [V23t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
@ ^ [V24t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V25t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V1a )
= V1a )
& ( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V26t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V27t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V28t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
@ ^ [V29t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V30t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
@ ^ [V31t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= V1a )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V1a )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
& ( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V32t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V33t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V34t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V35t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a
@ ^ [V36t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V37t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a
@ ^ [V38t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= V1a )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V1a )
= ( ^ [V39t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V40t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V41t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V42t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V43t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V43t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
@ ^ [V44t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
@ ^ [V45t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V46t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V1a )
= ( ^ [V47t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V48t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V49t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V49t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V50t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V51t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V51t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
@ ^ [V52t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V53t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
@ ^ [V54t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V55t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V1a )
= ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V56t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V56t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V57t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= c_2EPast__Temporal__Logic_2EInitPoint )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V58t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V59t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPSNEXT
@ ^ [V60t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V61t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSNEXT
@ ^ [V62t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V63t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V63t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V64t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V65t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V66t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V67t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ^ [V68t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V69t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ^ [V70t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V71t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V72t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= V0b )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V73t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a
@ ^ [V74t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V75t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a
@ ^ [V76t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V77t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V1a )
= V1a )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V78t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= V0b )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V79t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V80t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a
@ ^ [V81t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a
@ ^ [V82t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V83t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V1a )
= V1a )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V84t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V85t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V86t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a
@ ^ [V87t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V88t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a
@ ^ [V89t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= V1a )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V1a )
= ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V90t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V91t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V91t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V92t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V93t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a
@ ^ [V94t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V95t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a
@ ^ [V96t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= V1a )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V1a )
= ( ^ [V97t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V98t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V99t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V100t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V101t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V101t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a
@ ^ [V102t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a
@ ^ [V103t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V104t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V1a )
= ( ^ [V105t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V106t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V107t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V107t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V108t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V109t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V109t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a
@ ^ [V110t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V111t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a
@ ^ [V112t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V113t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V1a )
= ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V114t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V114t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EMORE__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V4t ) ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V5t ) @ ( V0b @ V5t ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V6t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V6t ) ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V7t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V7t ) ) )
@ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V1a @ V0b )
= ( c_2EPast__Temporal__Logic_2EPWHEN
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V8t ) @ ( V0b @ V8t ) )
@ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V1a @ V0b )
= ( c_2EPast__Temporal__Logic_2EPUNTIL
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V9t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V9t ) ) )
@ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1a @ V0b )
= ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V10t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V10t ) ) )
@ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V1a @ V0b )
= ( c_2EPast__Temporal__Logic_2EPSWHEN
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V11t ) @ ( V0b @ V11t ) )
@ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a @ V0b )
= ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V12t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V12t ) ) )
@ V0b ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a @ V0b )
= ( c_2EPast__Temporal__Logic_2EPSBEFORE
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V13t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V13t ) ) )
@ V0b ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2EIMMEDIATE__EVENT,axiom,
! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( V1b @ V0t )
=> ( ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t )
= ( V2a @ V0t ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t )
= c_2Ebool_2ET )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t )
= c_2Ebool_2EF )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V2a @ V0t )
<=> ( (~) @ ( V2a @ V0t ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t )
= ( V2a @ V0t ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t )
= c_2Ebool_2ET )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t )
= c_2Ebool_2EF )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1b @ V2a @ V0t )
<=> ( (~) @ ( V2a @ V0t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t )
= ( V2a @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t )
= c_2Ebool_2ET )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t )
= c_2Ebool_2EF )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V2a @ V0t )
<=> ( (~) @ ( V2a @ V0t ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t )
= ( V2a @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t )
= c_2Ebool_2ET )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t )
= c_2Ebool_2EF )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V2a @ V0t )
<=> ( (~) @ ( V2a @ V0t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ENO__FUTURE__EVENT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V2t ) )
@ V0t0 )
=> ( ! [V3a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V3a @ V1b @ V0t0 )
= c_2Ebool_2ET )
& ! [V4a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V4a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2EALWAYS @ V4a @ V0t0 ) )
& ! [V5a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V5a @ V1b @ V0t0 )
= c_2Ebool_2ET )
& ! [V6a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V6a @ V1b @ V0t0 )
= c_2Ebool_2EF )
& ! [V7a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V7a @ V1b @ V0t0 )
= c_2Ebool_2EF )
& ! [V8a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V8a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V8a @ V0t0 ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ENO__PAST__EVENT,axiom,
! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V3t ) )
@ V0t )
=> ( ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t )
= c_2Ebool_2ET )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t )
= ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t )
= c_2Ebool_2ET )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V2a @ V0t )
= ( c_2EPast__Temporal__Logic_2EPALWAYS
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V4t ) )
@ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t )
= c_2Ebool_2EF )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t )
= c_2Ebool_2EF )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t )
= ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V2a @ V0t )
= c_2Ebool_2EF ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESOME__FUTURE__EVENT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ! [V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ! [V3a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V3a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1b @ V0t0 ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ! [V4a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V4a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2ESBEFORE @ V4a @ V1b @ V0t0 ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESOME__PAST__EVENT,axiom,
! [V0t: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1b @ V0t )
=> ( ( ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b @ V0t )
= ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b @ V0t )
= ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b @ V0t )
= ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b @ V0t ) )
& ( ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V2a @ V0t )
= ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b @ V2a @ V0t ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESEPARATE__NEXT__THM,axiom,
! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V3t ) ) )
= ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1b @ V4t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V4t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V5t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b @ V5t ) ) )
= ( ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1b @ V6t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V6t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V7t ) ) )
= ( ^ [V8t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V9t ) @ ( V0c @ V9t ) )
@ V8t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V8t )
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V10t ) @ ( V1b @ V10t ) )
@ V8t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V11t ) ) )
= ( ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V13t ) @ ( c_2Ebool_2E_2F_5C @ ( V1b @ V13t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V13t ) ) ) )
@ V12t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V12t )
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V14t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V14t ) ) )
@ V12t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V15t ) ) )
= ( ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V16t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V16t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1b @ V17t ) ) )
= ( ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V18t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2a @ V18t ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V19t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V19t ) ) )
= ( ^ [V20t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V21t ) @ ( V0c @ V21t ) )
@ V20t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b @ V0c @ V20t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V20t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V22t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V22t ) ) )
= ( ^ [V23t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V24t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V24t ) ) )
@ V23t )
@ ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1b @ V0c @ V23t )
@ ( c_2ETemporal__Logic_2ENEXT
@ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V25t ) @ ( V1b @ V25t ) )
@ V23t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESEPARATE__SUNTIL__THM,axiom,
! [V0d: tyop_2Enum_2Enum > $o,V1c: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o,V3a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V4t ) @ ( V1c @ V4t ) ) )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V2b @ V5t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1c @ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V6t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V6t ) ) )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V7t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V7t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V8t ) @ ( c_2Ebool_2E_2F_5C @ ( V1c @ V8t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V8t ) ) )
@ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V9t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V9t ) ) )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V10t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V10t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V11t ) @ ( c_2Ebool_2E_2F_5C @ ( V1c @ V11t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V11t ) ) )
@ V10t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1c @ V0d @ V12t ) ) )
= ( ^ [V13t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1c @ V0d @ V13t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V14t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V14t ) )
@ V2b
@ V13t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V15t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V0d @ V15t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V16t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V16t ) )
@ V2b
@ V15t ) )
@ V13t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V17t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1c @ V0d @ V17t ) ) )
= ( ^ [V18t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1c @ V0d @ V18t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V19t ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V19t ) ) )
@ V2b
@ V18t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL @ V3a
@ ^ [V20t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V1c @ V20t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V20t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V21t ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V21t ) ) )
@ V2b
@ V20t ) ) )
@ V18t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V22t ) @ ( V2b @ V22t ) )
@ V1c )
= ( ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1c @ V23t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2b @ V1c @ V23t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V24t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V24t ) )
@ V1c )
= ( ^ [V25t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( V1c @ V25t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V25t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V25t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V26t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V26t ) )
@ ( c_2ETemporal__Logic_2ENEXT @ V1c )
@ V25t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V27t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V27t ) )
@ V1c )
= ( ^ [V28t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( V1c @ V28t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V28t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V28t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V29t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V29t ) )
@ ( c_2ETemporal__Logic_2ENEXT @ V1c )
@ V28t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V30t ) )
@ V0d )
= ( ^ [V31t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V31t )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V32t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V32t ) )
@ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V33t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V33t ) ) )
@ V31t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V34t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( V2b @ V34t )
@ ( c_2Ebool_2E_5C_2F @ ( V1c @ V34t )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V35t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V35t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V35t ) )
@ ^ [V36t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V36t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V36t ) ) )
@ V34t ) ) )
@ V0d
@ V31t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V37t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V37t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V37t ) )
@ V0d )
= ( ^ [V38t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V38t )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V39t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V39t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V39t ) )
@ ^ [V40t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V40t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V40t ) ) )
@ V38t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V41t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1c @ V41t ) )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V42t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V42t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V42t ) )
@ ^ [V43t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V43t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V43t ) ) )
@ V41t ) )
@ V0d
@ V38t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESEPARATE__BEFORE__THM,axiom,
! [V0d: tyop_2Enum_2Enum > $o,V1c: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o,V3a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V4t ) @ ( V1c @ V4t ) ) )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V3a @ V2b @ V5t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V3a @ V1c @ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V6t ) @ ( V2b @ V6t ) )
@ V1c )
= ( ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V3a @ V1c @ V7t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V2b @ V1c @ V7t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V8t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V8t ) ) )
= ( ^ [V9t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V9t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V9t ) ) )
@ ( c_2Ebool_2E_5C_2F @ ( V3a @ V9t )
@ ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V3a )
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1c @ V10t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V10t ) )
@ V9t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V11t ) ) )
= ( ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V12t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c @ V12t ) ) )
@ ( c_2Ebool_2E_5C_2F @ ( V3a @ V12t )
@ ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V3a )
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1c @ V13t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V13t ) )
@ V12t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V1c @ V0d @ V14t ) ) )
= ( ^ [V15t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_5C_2F
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1c @ V16t ) )
@ V0d
@ V15t )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V17t ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V17t ) ) )
@ V2b
@ V15t ) )
@ ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V18t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V0d @ V18t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V19t ) ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V19t ) )
@ V2b
@ V18t ) )
@ V15t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V1c @ V0d @ V20t ) ) )
= ( ^ [V21t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_5C_2F
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V22t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1c @ V22t ) )
@ V0d
@ V21t )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V23t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V23t ) )
@ V2b
@ V21t ) )
@ ( c_2ETemporal__Logic_2EBEFORE @ V3a
@ ^ [V24t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V1c @ V24t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V24t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V25t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V25t ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0d @ V25t ) ) )
@ V2b
@ V24t ) ) )
@ V21t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V26t ) )
@ V1c )
= ( ^ [V27t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V27t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V3a @ V27t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2b @ V27t ) ) )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V27t ) )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V28t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V28t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V28t ) )
@ ( c_2ETemporal__Logic_2ENEXT @ V1c )
@ V27t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V29t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V29t ) )
@ V1c )
= ( ^ [V30t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V30t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V3a @ V30t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V30t ) ) )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V30t ) )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V31t ) @ ( c_2ETemporal__Logic_2ENEXT @ V3a @ V31t ) )
@ ( c_2ETemporal__Logic_2ENEXT @ V1c )
@ V30t ) ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V32t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V32t ) @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V32t ) )
@ V0d )
= ( ^ [V33t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2b @ V1c @ V33t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V34t ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V34t ) ) )
@ ^ [V35t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V35t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V35t ) ) )
@ V33t ) )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V36t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V2b @ V36t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1c @ V36t ) )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V37t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V37t ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V37t ) ) )
@ ^ [V38t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V38t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V38t ) ) )
@ V36t ) ) )
@ V0d
@ V33t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V39t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V39t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V39t ) )
@ V0d )
= ( ^ [V40t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V40t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V41t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V41t ) ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V41t ) )
@ ^ [V42t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V42t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V42t ) ) )
@ V40t ) )
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V43t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V1c @ V43t )
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V44t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V44t ) ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V44t ) )
@ ^ [V45t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V45t ) @ ( c_2Ebool_2E_7E @ ( V0d @ V45t ) ) )
@ V43t ) )
@ V0d
@ V40t ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESEPARATE__PNEXT__THM,axiom,
! [V0c: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V3t ) ) )
= ( ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EInitPoint @ V4t ) @ ( c_2Ebool_2E_2F_5C @ ( V1b @ V4t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V4t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V5t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V5t ) ) )
= ( ^ [V6t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V7t ) @ ( V0c @ V7t ) )
@ V6t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V6t )
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V8t ) @ ( V1b @ V8t ) )
@ V6t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V9t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V9t ) ) )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V11t ) @ ( c_2Ebool_2E_2F_5C @ ( V1b @ V11t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V11t ) ) ) )
@ V10t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V10t )
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V12t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2a @ V12t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V12t ) ) )
@ V10t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V13t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b @ V13t ) ) )
= ( ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1b @ V14t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a @ V14t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V15t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V15t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V15t ) ) )
= ( ^ [V16t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V17t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V17t ) @ ( V0c @ V17t ) )
@ V16t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V1b @ V0c @ V16t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1b @ V16t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V18t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V18t ) ) )
= ( ^ [V19t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V20t ) @ ( c_2Ebool_2E_7E @ ( V0c @ V20t ) ) )
@ V19t )
@ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V1b @ V0c @ V19t )
@ ( c_2EPast__Temporal__Logic_2EPNEXT
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2a @ V21t ) @ ( V1b @ V21t ) )
@ V19t ) ) ) ) ) ) ).
thf(thm_2EPast__Temporal__Logic_2ESEPARATE__PSUNTIL__THM,axiom,
! [V0d: tyop_2Enum_2Enum > $o,V1c: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o,V3a: tyop_2Enum_2Enum > $o] :
( ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V4t ) @ ( V1c @ V4t ) ) )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a @ V2b @ V5t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a @ V1c @ V5t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V6t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V6t ) ) )
= ( ^ [V7t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_2F_5C @ ( V2b @ V7t ) @ ( c_2ETemporal__Logic_2ENEXT @ V1c @ V7t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V8t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V8t ) @ ( c_2Ebool_2E_2F_5C @ ( V1c @ V8t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V8t ) ) )
@ V7t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V9t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V9t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V1c @ V0d @ V9t ) ) )
= ( ^ [V10t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ESUNTIL @ V1c @ V0d @ V10t )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V11t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V11t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V11t ) )
@ V2b
@ V10t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V12t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V0d @ V12t )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V13t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V13t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V13t ) )
@ V2b
@ V12t ) )
@ V10t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V14t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V2b @ V14t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V1c @ V0d @ V14t ) ) )
= ( ^ [V15t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V1c @ V0d @ V15t )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V16t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V16t ) @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0d @ V16t ) ) )
@ V2b
@ V15t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a
@ ^ [V17t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C @ ( V1c @ V17t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0d @ V17t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V18t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V18t ) @ ( c_2Ebool_2E_7E @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0d @ V18t ) ) )
@ V2b
@ V17t ) ) )
@ V15t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V19t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V3a @ V19t ) @ ( V2b @ V19t ) )
@ V1c )
= ( ^ [V20t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V3a @ V1c @ V20t ) @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2b @ V1c @ V20t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V21t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V21t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V21t ) )
@ V1c )
= ( ^ [V22t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( V1c @ V22t )
@ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_5C_2F @ ( V3a @ V22t ) @ ( c_2ETemporal__Logic_2ENEXT @ V2b @ V22t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V23t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V2b @ V23t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V3a @ V23t ) )
@ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V1c )
@ V22t ) ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V24t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V24t ) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2b @ V1c @ V24t ) )
@ V0d )
= ( ^ [V25t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V2b @ V1c @ V25t )
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V26t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V26t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V26t ) )
@ ^ [V27t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V27t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V27t ) ) )
@ V25t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V28t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( V2b @ V28t )
@ ( c_2Ebool_2E_5C_2F @ ( V1c @ V28t )
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V29t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V29t ) @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V1c @ V29t ) )
@ ^ [V30t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V30t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V30t ) ) )
@ V28t ) ) )
@ V0d
@ V25t ) ) ) )
& ( ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V31t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V3a @ V31t ) @ ( c_2ETemporal__Logic_2EBEFORE @ V2b @ V1c @ V31t ) )
@ V0d )
= ( ^ [V32t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2EBEFORE @ V2b @ V1c @ V32t )
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V33t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V33t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V33t ) )
@ ^ [V34t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V34t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V34t ) ) )
@ V32t ) )
@ ( c_2EPast__Temporal__Logic_2EPSUNTIL
@ ^ [V35t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2Ebool_2E_7E @ ( V1c @ V35t ) )
@ ( c_2EPast__Temporal__Logic_2EPBEFORE
@ ^ [V36t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V0d @ V36t ) @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2b @ V36t ) )
@ ^ [V37t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V3a @ V37t ) ) @ ( c_2Ebool_2E_7E @ ( V0d @ V37t ) ) )
@ V35t ) )
@ V0d
@ V32t ) ) ) ) ) ).
%------------------------------------------------------------------------------