ITP001 Axioms: ITP061^5.ax
%------------------------------------------------------------------------------
% File : ITP061^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : Past_Temporal_Logic^2.ax [Gau20]
% : HL4061^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 66 ( 1 unt; 11 typ; 0 def)
% Number of atoms : 8092 ( 365 equ; 0 cnn)
% Maximal formula atoms : 297 ( 122 avg)
% Number of connectives : 10977 ( 35 ~; 12 |; 408 &;10313 @)
% ( 95 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 78 ( 16 avg;10313 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 43 con; 0-2 aty)
% Number of variables : 783 ( 649 ^ 127 !; 7 ?; 783 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EPast__Temporal__Logic_2EInitPoint,type,
c_2EPast__Temporal__Logic_2EInitPoint: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EInitPoint,axiom,
mem @ c_2EPast__Temporal__Logic_2EInitPoint @ ( arr @ ty_2Enum_2Enum @ bool ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPALWAYS,type,
c_2EPast__Temporal__Logic_2EPALWAYS: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPALWAYS,axiom,
mem @ c_2EPast__Temporal__Logic_2EPALWAYS @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPBEFORE,type,
c_2EPast__Temporal__Logic_2EPBEFORE: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPBEFORE,axiom,
mem @ c_2EPast__Temporal__Logic_2EPBEFORE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPEVENTUAL,type,
c_2EPast__Temporal__Logic_2EPEVENTUAL: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPEVENTUAL,axiom,
mem @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPNEXT,type,
c_2EPast__Temporal__Logic_2EPNEXT: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPNEXT,axiom,
mem @ c_2EPast__Temporal__Logic_2EPNEXT @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPSBEFORE,type,
c_2EPast__Temporal__Logic_2EPSBEFORE: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPSBEFORE,axiom,
mem @ c_2EPast__Temporal__Logic_2EPSBEFORE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPSNEXT,type,
c_2EPast__Temporal__Logic_2EPSNEXT: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPSNEXT,axiom,
mem @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPSUNTIL,type,
c_2EPast__Temporal__Logic_2EPSUNTIL: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPSUNTIL,axiom,
mem @ c_2EPast__Temporal__Logic_2EPSUNTIL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPSWHEN,type,
c_2EPast__Temporal__Logic_2EPSWHEN: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPSWHEN,axiom,
mem @ c_2EPast__Temporal__Logic_2EPSWHEN @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPUNTIL,type,
c_2EPast__Temporal__Logic_2EPUNTIL: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPUNTIL,axiom,
mem @ c_2EPast__Temporal__Logic_2EPUNTIL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2EPast__Temporal__Logic_2EPWHEN,type,
c_2EPast__Temporal__Logic_2EPWHEN: $i ).
thf(mem_c_2EPast__Temporal__Logic_2EPWHEN,axiom,
mem @ c_2EPast__Temporal__Logic_2EPWHEN @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EInitPoint,axiom,
( c_2EPast__Temporal__Logic_2EInitPoint
= ( lam @ ty_2Enum_2Enum
@ ^ [V0t: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V0t ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPSNEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V0a @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPNEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( ( V1t0 = fo__c_2Enum_2E0 )
| ( p @ ( ap @ V0a @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPALWAYS,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V2t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPEVENTUAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPSWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V4t ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V4t ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPSUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V4t ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V4t ) ) )
& ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V4t ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPSBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V4t ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V4t ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) )
| ? [V4delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V4delta ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V4delta ) ) )
& ! [V5t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4delta ) ) @ ( inj__ty_2Enum_2Enum @ V5t ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V5t ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) )
| ? [V4delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V4delta ) ) )
& ! [V5t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4delta ) ) @ ( inj__ty_2Enum_2Enum @ V5t ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V5t ) ) )
& ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V5t ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EPast__Temporal__Logic_2EPBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) )
| ? [V4delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V4delta ) ) )
& ! [V5t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4delta ) ) @ ( inj__ty_2Enum_2Enum @ V5t ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V5t ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EINITIALISATION,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ERECURSION,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) ) @ V2t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) ) @ V3t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) ) @ V4t ) ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ V5t ) ) @ ( ap @ V0a @ V5t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) ) @ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V6t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V6t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) ) @ V6t ) ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V7t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) ) @ V7t ) ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ V8t ) ) @ ( ap @ V0a @ V8t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) ) @ V8t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V9t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V9t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) ) @ V9t ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V10t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) ) @ V10t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V11t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) ) @ V11t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V12t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) ) @ V12t ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V13t ) ) @ ( ap @ V1b @ V13t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V13t ) ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b ) ) @ V13t ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V14t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V14t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b ) ) @ V14t ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V15t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V15t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) ) @ V15t ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V16t ) ) @ ( ap @ V1b @ V16t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V16t ) ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b ) ) @ V16t ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V17t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b ) ) @ V17t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EFIXPOINTS,axiom,
! [V0y: $i] :
( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0y ) @ V3t ) ) ) )
<=> ( ( V0y
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
| ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2EF ) ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V5t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0y ) @ V5t ) ) ) )
<=> ( ( V0y
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
| ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2ET ) ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ V7t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V7t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0y ) @ V7t ) ) ) ) )
<=> ( ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a ) @ V2b ) )
| ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a ) @ V2b ) ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V2b @ V8t ) ) @ ( ap @ V1a @ V8t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0y ) @ V8t ) ) ) )
<=> ( ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V2b ) )
| ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V2b ) ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ V9t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V9t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0y ) @ V9t ) ) ) ) )
<=> ( ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V2b ) )
| ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V2b ) ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V10t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0y ) @ V10t ) ) ) )
<=> ( V0y
= ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V11t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0y ) @ V11t ) ) ) )
<=> ( V0y
= ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2b @ V12t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V12t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0y ) @ V12t ) ) ) ) )
<=> ( V0y
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a ) @ V2b ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V13t ) ) @ ( ap @ V2b @ V13t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ V13t ) ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0y ) @ V13t ) ) ) ) )
<=> ( V0y
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1a ) @ V2b ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ V14t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V14t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0y ) @ V14t ) ) ) ) )
<=> ( V0y
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a ) @ V2b ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2b @ V15t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V15t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0y ) @ V15t ) ) ) ) )
<=> ( V0y
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V1a ) @ V2b ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V16t ) ) @ ( ap @ V2b @ V16t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ V16t ) ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0y ) @ V16t ) ) ) ) )
<=> ( V0y
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1a ) @ V2b ) ) )
& ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ V17t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V17t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0y ) @ V17t ) ) ) ) )
<=> ( V0y
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1a ) @ V2b ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESUNTIL__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2ET ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2ET ) )
@ V0a )
@ V5t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V9t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V9t ) ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V11t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V11t ) ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V12t ) ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V10t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V14t ) ) ) )
@ V1b )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V16t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V17t ) ) @ ( ap @ V1b @ V17t ) ) ) )
@ V15t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V19t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V20t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V20t ) ) ) ) )
@ V18t ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EUNTIL__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ V2t ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V5t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V4t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V9t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V9t ) ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V11t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V10t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V14t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V14t ) ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V15t ) ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V18t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V18t ) ) ) ) )
@ V16t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V20t ) ) ) )
@ V1b )
@ V19t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EWHEN__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V0a )
@ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V9t ) ) @ ( ap @ V1b @ V9t ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V11t ) ) @ ( ap @ V1b @ V11t ) ) ) )
@ V10t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V13t ) ) ) )
@ V1b )
@ V12t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V15t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V16t ) ) @ ( ap @ V1b @ V16t ) ) ) )
@ V14t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V18t ) ) @ ( ap @ V1b @ V18t ) ) ) )
@ V17t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESWHEN__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2ET ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2ET ) )
@ V0a )
@ V5t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V8t ) ) @ ( ap @ V1b @ V8t ) ) ) )
@ V7t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V10t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V11t ) ) @ ( ap @ V1b @ V11t ) ) ) )
@ V9t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V13t ) ) ) )
@ V1b )
@ V12t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V15t ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V14t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V18t ) ) @ ( ap @ V1b @ V18t ) ) ) )
@ V16t ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EBEFORE__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V0a )
@ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V8t ) ) ) )
@ V1b )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V10t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V10t ) ) ) ) )
@ V9t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V11t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V14t ) ) @ ( ap @ V1b @ V14t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V15t ) ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V13t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V17t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) ) )
@ V16t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESBEFORE__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2EF ) )
@ V2t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V5t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V8t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) ) )
@ V7t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V10t ) ) ) )
@ V1b )
@ V9t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] :
( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V12t ) ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V11t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V14t ) ) @ ( ap @ V1b @ V14t ) ) ) )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V16t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V16t ) ) ) ) )
@ V15t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPSUNTIL__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2ET ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2ET ) )
@ V0a )
@ V5t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V9t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V9t ) ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V11t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V11t ) ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V12t ) ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V10t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V14t ) ) ) )
@ V1b )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V16t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V17t ) ) @ ( ap @ V1b @ V17t ) ) ) )
@ V15t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V19t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V20t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V20t ) ) ) ) )
@ V18t ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPUNTIL__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ V2t ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V5t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V4t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V9t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V9t ) ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V11t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V10t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V14t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V14t ) ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V15t ) ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V18t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V18t ) ) ) ) )
@ V16t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V20t ) ) ) )
@ V1b )
@ V19t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPWHEN__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V0a )
@ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V9t ) ) @ ( ap @ V1b @ V9t ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V11t ) ) @ ( ap @ V1b @ V11t ) ) ) )
@ V10t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V13t ) ) ) )
@ V1b )
@ V12t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V15t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V16t ) ) @ ( ap @ V1b @ V16t ) ) ) )
@ V14t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V18t ) ) @ ( ap @ V1b @ V18t ) ) ) )
@ V17t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPSWHEN__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2ET ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2ET ) )
@ V0a )
@ V5t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V8t ) ) @ ( ap @ V1b @ V8t ) ) ) )
@ V7t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V10t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V11t ) ) @ ( ap @ V1b @ V11t ) ) ) )
@ V9t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V13t ) ) ) )
@ V1b )
@ V12t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V15t ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V14t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V18t ) ) @ ( ap @ V1b @ V18t ) ) ) )
@ V16t ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPBEFORE__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ V2t ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V0a )
@ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V8t ) ) ) )
@ V1b )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V10t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V10t ) ) ) ) )
@ V9t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V11t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V14t ) ) @ ( ap @ V1b @ V14t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V15t ) ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V13t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V17t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V17t ) ) ) ) )
@ V16t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPSBEFORE__EXPRESSIVE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2EF ) )
@ V2t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
@ V5t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V8t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V8t ) ) ) ) )
@ V7t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V10t ) ) ) )
@ V1b )
@ V9t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] :
( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V12t ) ) ) @ ( ap @ V1b @ V12t ) ) ) )
@ V11t ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V14t ) ) @ ( ap @ V1b @ V14t ) ) ) )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V16t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V16t ) ) ) ) )
@ V15t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ENEGATION__NORMAL__FORM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t: tp__ty_2Enum_2Enum,V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V5t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V6t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V7t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V8t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V9t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V10t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V11t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V12t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V13t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V14t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V15t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V16t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V17t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V18t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V19t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V20t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V21t ) ) ) )
@ V2b )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ECONJUNCTIVE__NORMAL__FORM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V4t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V4t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V5t ) ) @ ( ap @ V1b @ V5t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V6t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1b ) @ V6t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ V1b @ V7t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V2c ) @ V8t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b ) @ V2c ) @ V8t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V9t ) ) @ ( ap @ V1b @ V9t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V2c ) @ V10t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b ) @ V2c ) @ V10t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V11t ) ) @ ( ap @ V1b @ V11t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V2c ) @ V12t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1b ) @ V2c ) @ V12t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V13t ) ) @ ( ap @ V1b @ V13t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V2c ) @ V14t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V14t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2c )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V15t ) ) @ ( ap @ V1b @ V15t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2c ) @ V0a ) @ V16t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2c ) @ V1b ) @ V16t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V2c )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V17t ) ) @ ( ap @ V1b @ V17t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V2c ) @ V0a ) @ V18t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V2c ) @ V1b ) @ V18t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V19t ) ) @ ( ap @ V1b @ V19t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V20t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V20t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V21t ) ) @ ( ap @ V1b @ V21t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) @ V22t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V22t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V23t ) ) @ ( ap @ V1b @ V23t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) @ V24t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V1b ) @ V24t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V25t ) ) @ ( ap @ V1b @ V25t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V26t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V2c ) @ V26t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1b ) @ V2c ) @ V26t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V27t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V27t ) ) @ ( ap @ V1b @ V27t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V28t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V2c ) @ V28t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1b ) @ V2c ) @ V28t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V29t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V29t ) ) @ ( ap @ V1b @ V29t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V30t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V2c ) @ V30t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V1b ) @ V2c ) @ V30t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V31t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V31t ) ) @ ( ap @ V1b @ V31t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V32t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V2c ) @ V32t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V32t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2c )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V33t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V33t ) ) @ ( ap @ V1b @ V33t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V34t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2c ) @ V0a ) @ V34t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2c ) @ V1b ) @ V34t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V2c )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V35t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V35t ) ) @ ( ap @ V1b @ V35t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V36t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V2c ) @ V0a ) @ V36t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V2c ) @ V1b ) @ V36t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EDISJUNCTIVE__NORMAL__FORM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V4t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V4t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V5t ) ) @ ( ap @ V1b @ V5t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V6t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V6t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V7t ) ) @ ( ap @ V1b @ V7t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V2c ) @ V8t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b ) @ V2c ) @ V8t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V9t ) ) @ ( ap @ V1b @ V9t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V2c ) @ V10t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b ) @ V2c ) @ V10t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V11t ) ) @ ( ap @ V2c @ V11t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ V12t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V2c ) @ V12t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V13t ) ) @ ( ap @ V2c @ V13t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ V14t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V2c ) @ V14t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V15t ) ) @ ( ap @ V1b @ V15t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V2c ) @ V16t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V16t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V17t ) ) @ ( ap @ V1b @ V17t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V2c ) @ V18t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b ) @ V2c ) @ V18t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V19t ) ) @ ( ap @ V1b @ V19t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V20t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V20t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V21t ) ) @ ( ap @ V1b @ V21t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) @ V22t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1b ) @ V22t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V23t ) ) @ ( ap @ V1b @ V23t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V2c ) @ V24t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1b ) @ V2c ) @ V24t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V25t ) ) @ ( ap @ V1b @ V25t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V26t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V2c ) @ V26t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1b ) @ V2c ) @ V26t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V27t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V27t ) ) @ ( ap @ V2c @ V27t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V28t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) @ V28t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V2c ) @ V28t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V29t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V29t ) ) @ ( ap @ V2c @ V29t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V30t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) @ V30t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V2c ) @ V30t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V31t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V31t ) ) @ ( ap @ V1b @ V31t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V32t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V2c ) @ V32t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V32t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V33t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V33t ) ) @ ( ap @ V1b @ V33t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V34t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V2c ) @ V34t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1b ) @ V2c ) @ V34t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPRENEX__NEXT__NORMAL__FORM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t: tp__ty_2Enum_2Enum,V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
& ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V4t ) ) @ ( ap @ V2b @ V4t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
| ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V5t ) ) @ ( ap @ V2b @ V5t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V6t ) ) @ ( ap @ V0a @ V6t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V7t ) ) ) @ ( ap @ V0a @ V7t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V8t ) ) @ ( ap @ V0a @ V8t ) ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V9t ) ) ) @ ( ap @ V0a @ V9t ) ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V10t ) ) ) @ ( ap @ V2b @ V10t ) ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V11t ) ) ) @ ( ap @ V2b @ V11t ) ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V2b ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V12t ) ) ) @ ( ap @ V2b @ V12t ) ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2b ) )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V13t ) ) ) @ ( ap @ V2b @ V13t ) ) ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V14t ) ) ) @ ( ap @ V0a @ V14t ) ) ) )
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V15t ) ) @ ( ap @ V0a @ V15t ) ) ) )
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2b ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ V2b )
= ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2b ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ENEXT__INWARDS__NORMAL__FORM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V3t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V5t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V5t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V6t ) ) @ ( ap @ V1b @ V6t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V7t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V7t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) )
= V0a )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) )
= V0a )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) @ V8t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V8t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) @ V9t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V9t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V10t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V10t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) @ V10t ) ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V11t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V11t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b ) @ V11t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V12t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V12t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b ) @ V12t ) ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V13t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V13t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) @ V13t ) ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V14t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V14t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b ) @ V14t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V15t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V15t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b ) @ V15t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EPNEXT__INWARDS__NORMAL__FORM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) @ V3t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V5t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V5t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V6t ) ) @ ( ap @ V1b @ V6t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V7t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V7t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V8t ) ) @ ( ap @ V0a @ V8t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V9t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V9t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V10t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ V10t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V0a ) )
= ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V11t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) ) @ V11t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V12t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) @ V12t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V13t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) @ V13t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V14t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) @ V14t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) ) @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESIMPLIFY,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : c_2Ebool_2EF ) )
@ V0b )
= V0b )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a ) @ V1a )
= V1a )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : c_2Ebool_2EF ) )
@ V0b )
= V0b )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] : c_2Ebool_2EF ) )
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a ) @ V1a )
= V1a )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V26t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V27t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V28t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V29t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V30t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V31t: $i] : c_2Ebool_2ET ) )
= V1a )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V1a )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V32t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V33t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V33t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V34t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V35t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V36t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V37t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V38t: $i] : c_2Ebool_2ET ) )
= V1a )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V39t: $i] : c_2Ebool_2ET ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V40t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V41t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V42t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V43t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V43t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V44t: $i] : c_2Ebool_2EF ) )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V45t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V46t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V47t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V48t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V49t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V49t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V50t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V51t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V51t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V52t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V53t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V54t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V55t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V1a )
= ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V56t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1a @ V56t ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V57t: $i] : c_2Ebool_2EF ) )
= c_2EPast__Temporal__Logic_2EInitPoint )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V58t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V59t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V60t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V61t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V62t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V63t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V63t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V64t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V65t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V66t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V67t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V68t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V69t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V70t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V71t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V72t: $i] : c_2Ebool_2EF ) )
@ V0b )
= V0b )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V73t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V74t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V75t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V76t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V77t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a ) @ V1a )
= V1a )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V78t: $i] : c_2Ebool_2EF ) )
@ V0b )
= V0b )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V79t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V80t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V81t: $i] : c_2Ebool_2EF ) )
= ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V82t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V83t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V1a ) @ V1a )
= V1a )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V84t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V85t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V86t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V87t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V88t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V89t: $i] : c_2Ebool_2ET ) )
= V1a )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1a ) @ V1a )
= ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V90t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V91t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V91t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V92t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V93t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V94t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V95t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V96t: $i] : c_2Ebool_2ET ) )
= V1a )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V97t: $i] : c_2Ebool_2ET ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V98t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V99t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V100t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V101t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V101t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V102t: $i] : c_2Ebool_2EF ) )
= ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V103t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V104t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V105t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V106t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V107t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V107t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V108t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V109t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V109t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V110t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V111t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V112t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V113t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1a ) @ V1a )
= ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V114t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1a @ V114t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EMORE__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V5t ) ) @ ( ap @ V1b @ V5t ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V6t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V6t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V7t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V8t ) ) @ ( ap @ V1b @ V8t ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V9t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V9t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V10t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V10t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V11t ) ) @ ( ap @ V1b @ V11t ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V12t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V13t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V13t ) ) ) ) )
@ V1b ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2EIMMEDIATE__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ V0b @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ~ ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ~ ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ~ ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ~ ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ENO__FUTURE__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
=> ( ! [V3a: $i] :
( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $true ) )
& ! [V4a: $i] :
( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V4a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ! [V5a: $i] :
( ( mem @ V5a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V5a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $true ) )
& ! [V6a: $i] :
( ( mem @ V6a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V6a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $false ) )
& ! [V7a: $i] :
( ( mem @ V7a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V7a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $false ) )
& ! [V8a: $i] :
( ( mem @ V8a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V8a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V8a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ENO__PAST__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V2a @ V4t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> $false ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESOME__FUTURE__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V3a: $i] :
( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V4a: $i] :
( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESOME__PAST__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V0b ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESEPARATE__NEXT__THM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V3t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V4t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V4t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V5t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V5t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V6t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V6t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V7t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V9t ) ) @ ( ap @ V2c @ V9t ) ) ) )
@ V8t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V8t ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V10t ) ) @ ( ap @ V1b @ V10t ) ) ) )
@ V8t ) ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V11t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V11t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V13t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V13t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V13t ) ) ) ) ) )
@ V12t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V12t ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V14t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V14t ) ) ) ) )
@ V12t ) ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V15t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V15t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V16t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V16t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V17t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V17t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V18t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V18t ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V19t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V19t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V21t ) ) @ ( ap @ V2c @ V21t ) ) ) )
@ V20t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V20t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V20t ) ) ) ) )
& ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V22t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V22t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V24t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V24t ) ) ) ) )
@ V23t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V23t ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V25t ) ) @ ( ap @ V1b @ V25t ) ) ) )
@ V23t ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESEPARATE__SUNTIL__THM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V3d: $i] :
( ( mem @ V3d @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V4t ) ) @ ( ap @ V2c @ V4t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ V5t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V2c ) @ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V6t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V6t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V7t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V7t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V8t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V8t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V8t ) ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V9t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2c ) @ V9t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V10t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2c ) @ V10t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V11t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V11t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V11t ) ) ) ) )
@ V10t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V12t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V2c ) @ V3d ) @ V12t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V2c ) @ V3d ) @ V13t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V14t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V14t ) ) ) )
@ V1b )
@ V13t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V3d @ V15t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V16t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V16t ) ) ) )
@ V1b )
@ V15t ) ) ) )
@ V13t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V17t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2c ) @ V3d ) @ V17t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2c ) @ V3d ) @ V18t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V19t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V3d ) @ V19t ) ) ) ) )
@ V1b )
@ V18t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V20t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V20t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V21t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V3d ) @ V21t ) ) ) ) )
@ V1b )
@ V20t ) ) ) ) )
@ V18t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V22t ) ) @ ( ap @ V1b @ V22t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V2c ) @ V23t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V23t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V24t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V24t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2c @ V25t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V25t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V25t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V26t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V26t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V26t ) ) ) )
@ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) )
@ V25t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V27t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V27t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V27t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V28t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2c @ V28t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V28t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V28t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V29t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V29t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V29t ) ) ) )
@ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) )
@ V28t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V30t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V30t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V30t ) ) ) )
@ V3d )
= ( lam @ ty_2Enum_2Enum
@ ^ [V31t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V31t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V32t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V32t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V32t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V33t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V33t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V33t ) ) ) ) )
@ V31t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V34t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V34t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2c @ V34t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V35t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V35t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V35t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V36t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V36t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V36t ) ) ) ) )
@ V34t ) ) ) ) )
@ V3d )
@ V31t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V37t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V37t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V37t ) ) ) )
@ V3d )
= ( lam @ ty_2Enum_2Enum
@ ^ [V38t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V38t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V39t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V39t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V39t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V40t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V40t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V40t ) ) ) ) )
@ V38t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V41t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V41t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V42t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V42t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V42t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V43t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V43t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V43t ) ) ) ) )
@ V41t ) ) ) )
@ V3d )
@ V38t ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESEPARATE__BEFORE__THM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V3d: $i] :
( ( mem @ V3d @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V4t ) ) @ ( ap @ V2c @ V4t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ V5t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V2c ) @ V5t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V6t ) ) @ ( ap @ V1b @ V6t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V2c ) @ V7t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V8t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V8t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V9t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V9t ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V9t ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V10t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V10t ) ) ) )
@ V9t ) ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V11t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2c ) @ V11t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V12t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2c ) @ V12t ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V12t ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V13t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V13t ) ) ) )
@ V12t ) ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V14t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V2c ) @ V3d ) @ V14t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V16t ) ) ) )
@ V3d )
@ V15t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V17t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V17t ) ) ) ) )
@ V1b )
@ V15t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V3d @ V18t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V19t ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V19t ) ) ) )
@ V1b )
@ V18t ) ) ) )
@ V15t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V20t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V2c ) @ V3d ) @ V20t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V22t ) ) ) )
@ V3d )
@ V21t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V23t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V3d ) @ V23t ) ) ) )
@ V1b )
@ V21t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V24t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V24t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V25t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V3d ) @ V25t ) ) ) ) )
@ V1b )
@ V24t ) ) ) ) )
@ V21t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V26t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V26t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V26t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V27t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V27t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V27t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V27t ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V27t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V28t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V28t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V28t ) ) ) )
@ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) )
@ V27t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V29t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V29t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V29t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V30t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V30t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V30t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V30t ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V30t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V31t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V31t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ V31t ) ) ) )
@ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) )
@ V30t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V32t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V32t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V32t ) ) ) )
@ V3d )
= ( lam @ ty_2Enum_2Enum
@ ^ [V33t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1b ) @ V2c ) @ V33t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V34t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V34t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V34t ) ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V35t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V35t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V35t ) ) ) ) )
@ V33t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V36t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V36t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V36t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V37t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V37t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V37t ) ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V38t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V38t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V38t ) ) ) ) )
@ V36t ) ) ) ) )
@ V3d )
@ V33t ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V39t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V39t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V39t ) ) ) )
@ V3d )
= ( lam @ ty_2Enum_2Enum
@ ^ [V40t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V40t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V41t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V41t ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V41t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V42t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V42t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V42t ) ) ) ) )
@ V40t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V43t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V43t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V44t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V44t ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V44t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V45t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V45t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V45t ) ) ) ) )
@ V43t ) ) ) )
@ V3d )
@ V40t ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESEPARATE__PNEXT__THM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V3t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2EPast__Temporal__Logic_2EInitPoint @ V4t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V4t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V4t ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V5t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V5t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ V2c @ V7t ) ) ) )
@ V6t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V6t ) )
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V8t ) ) @ ( ap @ V1b @ V8t ) ) ) )
@ V6t ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V9t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V9t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V11t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V11t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V11t ) ) ) ) ) )
@ V10t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V10t ) )
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V12t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V12t ) ) ) ) )
@ V10t ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V13t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V13t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V14t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V14t ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V15t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V15t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V17t ) ) @ ( ap @ V2c @ V17t ) ) ) )
@ V16t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V16t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1b ) @ V16t ) ) ) ) )
& ( ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V18t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V18t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V20t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V20t ) ) ) ) )
@ V19t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V19t ) )
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V21t ) ) @ ( ap @ V1b @ V21t ) ) ) )
@ V19t ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EPast__Temporal__Logic_2ESEPARATE__PSUNTIL__THM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V3d: $i] :
( ( mem @ V3d @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V4t ) ) @ ( ap @ V2c @ V4t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V1b ) @ V5t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V2c ) @ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V6t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V6t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V7t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V2c ) @ V7t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V8t ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V8t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V8t ) ) ) ) )
@ V7t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V9t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V2c ) @ V3d ) @ V9t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V2c ) @ V3d ) @ V10t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V11t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V11t ) ) ) )
@ V1b )
@ V10t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V12t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V3d @ V12t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V13t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V13t ) ) ) )
@ V1b )
@ V12t ) ) ) )
@ V10t ) ) ) )
& ( ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V14t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1b @ V14t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2c ) @ V3d ) @ V14t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V15t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2c ) @ V3d ) @ V15t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V16t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V3d ) @ V16t ) ) ) ) )
@ V1b )
@ V15t ) ) )
@ ( ap
@ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V17t: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2c @ V17t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V17t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V18t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V18t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V3d ) @ V18t ) ) ) ) )
@ V1b )
@ V17t ) ) ) ) )
@ V15t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V19t ) ) @ ( ap @ V1b @ V19t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V20t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V0a ) @ V2c ) @ V20t ) ) @ ( ap @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1b ) @ V2c ) @ V20t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V21t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V21t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V21t ) ) ) )
@ V2c )
= ( lam @ ty_2Enum_2Enum
@ ^ [V22t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2c @ V22t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V22t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) @ V22t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V23t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V23t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V0a ) @ V23t ) ) ) )
@ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V2c ) )
@ V22t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V24t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V24t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V24t ) ) ) )
@ V3d )
= ( lam @ ty_2Enum_2Enum
@ ^ [V25t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1b ) @ V2c ) @ V25t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V26t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V26t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V26t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V27t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V27t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V27t ) ) ) ) )
@ V25t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V28t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1b @ V28t ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V2c @ V28t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V29t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V29t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V2c ) @ V29t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V30t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V30t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V30t ) ) ) ) )
@ V28t ) ) ) ) )
@ V3d )
@ V25t ) ) ) )
& ( ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V31t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V31t ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V31t ) ) ) )
@ V3d )
= ( lam @ ty_2Enum_2Enum
@ ^ [V32t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b ) @ V2c ) @ V32t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V33t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V33t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V33t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V34t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V34t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V34t ) ) ) ) )
@ V32t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V35t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2c @ V35t ) ) )
@ ( ap
@ ( ap
@ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V36t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V3d @ V36t ) ) @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1b ) @ V36t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V37t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V37t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3d @ V37t ) ) ) ) )
@ V35t ) ) ) )
@ V3d )
@ V32t ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------