ITP001 Axioms: ITP080^5.ax
%------------------------------------------------------------------------------
% File : ITP080^5 : 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 : Omega_Automata^2.ax [Gau20]
% : HL4080^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 40 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 7906 ( 60 equ; 0 cnn)
% Maximal formula atoms : 505 ( 197 avg)
% Number of connectives : 11183 ( 173 ~; 97 |; 624 &;9959 @)
% ( 153 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 30 avg;9959 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 47 con; 0-2 aty)
% Number of variables : 629 ( 39 ^ 388 !; 202 ?; 629 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(conj_thm_2EOmega__Automata_2EDET__OMEGA__EXISTS__FORALL__THEOREM,axiom,
! [A_27input: del,A_27state: del,V0t0: tp__ty_2Enum_2Enum,V1InitVal: $i] :
( ( mem @ V1InitVal @ A_27state )
=> ! [V2TransRel: $i] :
( ( mem @ V2TransRel @ ( arr @ ( ty_2Epair_2Eprod @ A_27input @ A_27state ) @ A_27state ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27input ) )
=> ! [V4Accept: $i] :
( ( mem @ V4Accept @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27input ) @ ( arr @ ty_2Enum_2Enum @ A_27state ) ) @ bool ) )
=> ( ? [V5q: $i] :
( ( mem @ V5q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( ( ap @ V5q @ ( inj__ty_2Enum_2Enum @ V0t0 ) )
= V1InitVal )
& ! [V6t: tp__ty_2Enum_2Enum] :
( ( ap @ V5q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ V2TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27input @ A_27state ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) @ ( ap @ V5q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) )
& ( p
@ ( ap @ V4Accept
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27input ) @ ( arr @ ty_2Enum_2Enum @ A_27state ) ) @ V3i )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ V5q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V7t ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) )
<=> ! [V8q: $i] :
( ( mem @ V8q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
=> ( ( ( ( ap @ V8q @ ( inj__ty_2Enum_2Enum @ V0t0 ) )
= V1InitVal )
& ! [V9t: tp__ty_2Enum_2Enum] :
( ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ V2TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27input @ A_27state ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
=> ( p
@ ( ap @ V4Accept
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27input ) @ ( arr @ ty_2Enum_2Enum @ A_27state ) ) @ V3i )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ENEG__DET__AUTOMATA,axiom,
! [A_27input: del,A_27state: del,V0t0: tp__ty_2Enum_2Enum,V1InitVal: $i] :
( ( mem @ V1InitVal @ A_27state )
=> ! [V2TransRel: $i] :
( ( mem @ V2TransRel @ ( arr @ ( ty_2Epair_2Eprod @ A_27input @ A_27state ) @ A_27state ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27input ) )
=> ! [V4Accept: $i] :
( ( mem @ V4Accept @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27input ) @ ( arr @ ty_2Enum_2Enum @ A_27state ) ) @ bool ) )
=> ( ~ ? [V5q: $i] :
( ( mem @ V5q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( ( ap @ V5q @ ( inj__ty_2Enum_2Enum @ V0t0 ) )
= V1InitVal )
& ! [V6t: tp__ty_2Enum_2Enum] :
( ( ap @ V5q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ V2TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27input @ A_27state ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) @ ( ap @ V5q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) )
& ( p
@ ( ap @ V4Accept
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27input ) @ ( arr @ ty_2Enum_2Enum @ A_27state ) ) @ V3i )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ V5q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V7t ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) )
<=> ? [V8q: $i] :
( ( mem @ V8q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( ( ap @ V8q @ ( inj__ty_2Enum_2Enum @ V0t0 ) )
= V1InitVal )
& ! [V9t: tp__ty_2Enum_2Enum] :
( ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ V2TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27input @ A_27state ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) )
& ~ ( p
@ ( ap @ V4Accept
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27input ) @ ( arr @ ty_2Enum_2Enum @ A_27state ) ) @ V3i )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EOMEGA__CONJ__CLOSURE,axiom,
! [A_27a: del,A_27b1: del,A_27b2: del,V0Phi__I1: $i] :
( ( mem @ V0Phi__I1 @ ( arr @ A_27b1 @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2Phi__R1: $i] :
( ( mem @ V2Phi__R1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b1 ) @ bool ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V4Psi1: $i] :
( ( mem @ V4Psi1 @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) ) @ bool ) )
=> ! [V5Phi__I2: $i] :
( ( mem @ V5Phi__I2 @ ( arr @ A_27b2 @ bool ) )
=> ! [V6Phi__R2: $i] :
( ( mem @ V6Phi__R2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b2 ) @ bool ) )
=> ! [V7Psi2: $i] :
( ( mem @ V7Psi2 @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) ) @ bool ) )
=> ( ( ? [V8q1: $i] :
( ( mem @ V8q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V8q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V9t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V8q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) ) @ V3i ) @ V8q1 ) ) ) )
& ? [V10q2: $i] :
( ( mem @ V10q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V10q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V11t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V10q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) ) @ V3i ) @ V10q2 ) ) ) ) )
<=> ? [V12q1: $i] :
( ( mem @ V12q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ? [V13q2: $i] :
( ( mem @ V13q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V12q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V13q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V14t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V12q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V13q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) ) @ V3i ) @ V12q1 ) ) )
& ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) ) @ V3i ) @ V13q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EOMEGA__DISJ__CLOSURE,axiom,
! [A_27a: del,A_27b1: del,A_27b2: del,V0Phi__I1: $i] :
( ( mem @ V0Phi__I1 @ ( arr @ A_27b1 @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2Phi__R1: $i] :
( ( mem @ V2Phi__R1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b1 ) @ bool ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V4Psi1: $i] :
( ( mem @ V4Psi1 @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) ) @ bool ) )
=> ! [V5Phi__I2: $i] :
( ( mem @ V5Phi__I2 @ ( arr @ A_27b2 @ bool ) )
=> ! [V6Phi__R2: $i] :
( ( mem @ V6Phi__R2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b2 ) @ bool ) )
=> ! [V7Psi2: $i] :
( ( mem @ V7Psi2 @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) ) @ bool ) )
=> ( ( ? [V8q1: $i] :
( ( mem @ V8q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V8q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V9t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V8q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) ) @ V3i ) @ V8q1 ) ) ) )
| ? [V10q2: $i] :
( ( mem @ V10q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V10q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V11t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V10q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) ) @ V3i ) @ V10q2 ) ) ) ) )
<=> ? [V12p: $i] :
( ( mem @ V12p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13q1: $i] :
( ( mem @ V13q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ? [V14q2: $i] :
( ( mem @ V14q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( ( ~ ( p @ ( ap @ V12p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V13q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ( ( p @ ( ap @ V12p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V14q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V13q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V14q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ( ~ ( p @ ( ap @ V12p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) ) @ V3i ) @ V13q1 ) ) ) )
| ( ( p @ ( ap @ V12p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) ) @ V3i ) @ V14q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__G,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ~ ! [V3t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ? [V4t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( ( ! [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V6t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ! [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( ! [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ! [V9t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ? [V10p: $i] :
( ( mem @ V10p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V11q: $i] :
( ( mem @ V11q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V10p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ~ ( p @ ( ap @ V11q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V12t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V10p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( p @ ( ap @ V10p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ~ ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ! [V13t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V10p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ~ ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__F,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ~ ? [V3t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ! [V4t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( ( ? [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ? [V6t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ? [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( ? [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ? [V9t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ? [V10p: $i] :
( ( mem @ V10p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V11q: $i] :
( ( mem @ V11q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V10p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ~ ( p @ ( ap @ V11q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V12t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V10p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( p @ ( ap @ V10p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ? [V13t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V10p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__FG,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ~ ? [V3t1: tp__ty_2Enum_2Enum] :
! [V4t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ! [V5t1: tp__ty_2Enum_2Enum] :
? [V6t2: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( ? [V7t1: tp__ty_2Enum_2Enum] :
! [V8t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ? [V9t1: tp__ty_2Enum_2Enum] :
! [V10t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
<=> ? [V11t1: tp__ty_2Enum_2Enum] :
! [V12t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ( ( ? [V13t1: tp__ty_2Enum_2Enum] :
! [V14t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ? [V15t1: tp__ty_2Enum_2Enum] :
! [V16t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
<=> ? [V17q: $i] :
( ( mem @ V17q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V17q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V18t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V17q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V17q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ? [V19t1: tp__ty_2Enum_2Enum] :
! [V20t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V17q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__GF,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ~ ! [V3t1: tp__ty_2Enum_2Enum] :
? [V4t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( ! [V7t1: tp__ty_2Enum_2Enum] :
? [V8t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ! [V9t1: tp__ty_2Enum_2Enum] :
? [V10t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
<=> ! [V11t1: tp__ty_2Enum_2Enum] :
? [V12t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ( ( ! [V13t1: tp__ty_2Enum_2Enum] :
? [V14t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ! [V15t1: tp__ty_2Enum_2Enum] :
? [V16t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
<=> ? [V17q: $i] :
( ( mem @ V17q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V17q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V18t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V17q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V17q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ! [V19t1: tp__ty_2Enum_2Enum] :
? [V20t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V17q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOREL__HIERARCHY__G,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( ! [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ! [V6t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ? [V7q: $i] :
( ( mem @ V7q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V8t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V7q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ( ( p @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V9t1: tp__ty_2Enum_2Enum] :
! [V10t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ( ! [V11t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ? [V12q: $i] :
( ( mem @ V12q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V12q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V13t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V12q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ( ( p @ ( ap @ V12q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ! [V14t1: tp__ty_2Enum_2Enum] :
? [V15t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V12q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOREL__HIERARCHY__F,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( ? [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ( ? [V7t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
<=> ? [V8q: $i] :
( ( mem @ V8q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V8q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V9t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V8q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ( ( p @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ! [V10t1: tp__ty_2Enum_2Enum] :
? [V11t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBOREL__HIERARCHY__FG,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( ? [V2t1: tp__ty_2Enum_2Enum] :
! [V3t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ? [V4q: $i] :
( ( mem @ V4q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V4q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V5t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V4q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
=> ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V4q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ? [V6t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V4q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ? [V7t1: tp__ty_2Enum_2Enum] :
! [V8t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ? [V9p: $i] :
( ( mem @ V9p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V10q: $i] :
( ( mem @ V10q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V9p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ~ ( p @ ( ap @ V10q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V11t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V9p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
=> ( p @ ( ap @ V9p @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ V9p @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
=> ( ( p @ ( ap @ V9p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
| ~ ( p @ ( ap @ V10q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ V10q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
<=> ( ( ( p @ ( ap @ V9p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ~ ( p @ ( ap @ V10q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ( ( p @ ( ap @ V9p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V10q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) )
& ! [V12t1: tp__ty_2Enum_2Enum] :
? [V13t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V9p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ~ ( p @ ( ap @ V10q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ETEMP__OPS__DEFS__TO__OMEGA,axiom,
! [V0l: $i] :
( ( mem @ V0l @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( V0l
= ( ap @ c_2ETemporal__Logic_2ENEXT @ V1a ) )
<=> ( $true
& ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V3t ) ) )
<=> ( p @ ( ap @ V1a @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
<=> ( $true
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V4t ) ) )
<=> ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V4t ) ) )
& ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4t ) ) ) ) ) )
& ! [V5t1: tp__ty_2Enum_2Enum] :
? [V6t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V1a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) ) )
=> ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
<=> ( $true
& ! [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V7t ) ) )
<=> ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V7t ) ) )
| ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V7t ) ) ) ) ) )
& ! [V8t1: tp__ty_2Enum_2Enum] :
? [V9t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t1 ) ) @ ( inj__ty_2Enum_2Enum @ V9t2 ) ) ) )
=> ( p @ ( ap @ V1a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t1 ) ) @ ( inj__ty_2Enum_2Enum @ V9t2 ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a ) @ V2b ) )
<=> ( $true
& ! [V10t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V10t ) ) )
<=> ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V10t ) ) )
=> ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V10t ) ) )
& ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V10t ) ) ) ) ) ) )
& ! [V11t1: tp__ty_2Enum_2Enum] :
? [V12t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) ) )
=> ( ~ ( p @ ( ap @ V1a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V2b ) )
<=> ( $true
& ! [V13t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V13t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V13t ) ) ) @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V13t ) ) ) @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V13t ) ) ) ) ) )
& ! [V14t1: tp__ty_2Enum_2Enum] :
? [V15t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) ) )
=> ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V2b ) )
<=> ( $true
& ! [V16t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V16t ) ) )
<=> ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V16t ) ) )
& ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V16t ) ) )
| ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V16t ) ) ) ) ) ) )
& ! [V17t1: tp__ty_2Enum_2Enum] :
? [V18t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t1 ) ) @ ( inj__ty_2Enum_2Enum @ V18t2 ) ) ) )
=> ( ( p @ ( ap @ V1a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t1 ) ) @ ( inj__ty_2Enum_2Enum @ V18t2 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t1 ) ) @ ( inj__ty_2Enum_2Enum @ V18t2 ) ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a ) @ V2b ) )
<=> ( $true
& ! [V19t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V19t ) ) )
<=> ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V19t ) ) )
=> ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V19t ) ) )
& ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V19t ) ) ) ) ) ) )
& ! [V20t1: tp__ty_2Enum_2Enum] :
? [V21t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t1 ) ) @ ( inj__ty_2Enum_2Enum @ V21t2 ) ) ) )
=> ( ~ ( p @ ( ap @ V1a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t1 ) ) @ ( inj__ty_2Enum_2Enum @ V21t2 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t1 ) ) @ ( inj__ty_2Enum_2Enum @ V21t2 ) ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V2b ) )
<=> ( $true
& ! [V22t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V22t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V22t ) ) ) @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V22t ) ) ) @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V22t ) ) ) ) ) )
& ! [V23t1: tp__ty_2Enum_2Enum] :
? [V24t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V23t1 ) ) @ ( inj__ty_2Enum_2Enum @ V24t2 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V23t1 ) ) @ ( inj__ty_2Enum_2Enum @ V24t2 ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V2b ) )
<=> ( $true
& ! [V25t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V25t ) ) )
<=> ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V25t ) ) )
& ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V25t ) ) )
| ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V25t ) ) ) ) ) ) )
& ! [V26t1: tp__ty_2Enum_2Enum] :
? [V27t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V0l @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V26t1 ) ) @ ( inj__ty_2Enum_2Enum @ V27t2 ) ) ) )
=> ( ( p @ ( ap @ V1a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V26t1 ) ) @ ( inj__ty_2Enum_2Enum @ V27t2 ) ) ) )
| ( p @ ( ap @ V2b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V26t1 ) ) @ ( inj__ty_2Enum_2Enum @ V27t2 ) ) ) ) ) ) ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V1a ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ! [V28t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V28t ) ) ) )
<=> ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V28t ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V1a ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ! [V29t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V29t ) ) ) )
<=> ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V29t ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V1a ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ! [V30t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V30t ) ) ) )
<=> ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V30t ) ) )
& ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V30t ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V1a ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ! [V31t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V31t ) ) ) )
<=> ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V31t ) ) )
| ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V31t ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V1a ) @ V2b ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ! [V32t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V32t ) ) ) )
<=> ( ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V32t ) ) )
| ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V32t ) ) )
& ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V32t ) ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V1a ) @ V2b ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ! [V33t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V33t ) ) ) )
<=> ( ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V33t ) ) )
& ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V33t ) ) ) )
| ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V33t ) ) )
& ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V33t ) ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V1a ) @ V2b ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $false )
& ! [V34t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V34t ) ) ) )
<=> ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V34t ) ) )
& ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V34t ) ) )
| ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V34t ) ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V1a ) @ V2b ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ! [V35t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V35t ) ) ) )
<=> ( ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V35t ) ) )
| ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V35t ) ) )
& ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V35t ) ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V1a ) @ V2b ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ! [V36t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V36t ) ) ) )
<=> ( ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V36t ) ) )
& ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V36t ) ) ) )
| ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V36t ) ) )
& ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V36t ) ) ) ) ) )
& $true ) )
& ( ( V0l
= ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V1a ) @ V2b ) ) )
<=> ( ( ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> $true )
& ! [V37t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0l @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V37t ) ) ) )
<=> ( ~ ( p @ ( ap @ V2b @ ( inj__ty_2Enum_2Enum @ V37t ) ) )
& ( ( p @ ( ap @ V1a @ ( inj__ty_2Enum_2Enum @ V37t ) ) )
| ( p @ ( ap @ V0l @ ( inj__ty_2Enum_2Enum @ V37t ) ) ) ) ) )
& $true ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EAUTOMATON__TEMP__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0Phi__I1: $i] :
( ( mem @ V0Phi__I1 @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ bool ) )
=> ! [V1Phi__R1: $i] :
( ( mem @ V1Phi__R1 @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ bool ) )
=> ! [V2Phi__I2: $i] :
( ( mem @ V2Phi__I2 @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27b ) @ bool ) )
=> ! [V3Phi__R2: $i] :
( ( mem @ V3Phi__R2 @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27b ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) @ bool ) )
=> ! [V4Phi__F: $i] :
( ( mem @ V4Phi__F @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b ) ) @ bool ) )
=> ! [V5Phi: $i] :
( ( mem @ V5Phi @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ bool ) )
=> ! [V6phi: $i] :
( ( mem @ V6phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V7a: $i] :
( ( mem @ V7a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V8b: $i] :
( ( mem @ V8b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ? [V9q1: $i] :
( ( mem @ V9q1 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ( p @ ( ap @ V0Phi__I1 @ V9q1 ) )
& ( p @ ( ap @ V1Phi__R1 @ V9q1 ) )
& ? [V10q2: $i] :
( ( mem @ V10q2 @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( p @ ( ap @ V2Phi__I2 @ V10q2 ) )
& ( p @ ( ap @ V3Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27b ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) @ V10q2 ) @ V9q1 ) ) )
& ( p @ ( ap @ V4Phi__F @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b ) ) @ V9q1 ) @ V10q2 ) ) ) ) )
<=> ? [V11q1: $i] :
( ( mem @ V11q1 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V12q2: $i] :
( ( mem @ V12q2 @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( p @ ( ap @ V0Phi__I1 @ V11q1 ) )
& ( p @ ( ap @ V2Phi__I2 @ V12q2 ) )
& ( p @ ( ap @ V1Phi__R1 @ V11q1 ) )
& ( p @ ( ap @ V3Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27b ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) @ V12q2 ) @ V11q1 ) ) )
& ( p @ ( ap @ V4Phi__F @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27b ) ) @ V11q1 ) @ V12q2 ) ) ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V6phi ) ) )
<=> ? [V13q0: $i] :
( ( mem @ V13q0 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V14q1: $i] :
( ( mem @ V14q1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V13q0 @ ( inj__ty_2Enum_2Enum @ V15t ) ) )
<=> ( p @ ( ap @ V6phi @ ( inj__ty_2Enum_2Enum @ V15t ) ) ) )
& ( ( p @ ( ap @ V14q1 @ ( inj__ty_2Enum_2Enum @ V15t ) ) )
<=> ( p @ ( ap @ V13q0 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V14q1 ) ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ V6phi ) ) )
<=> ? [V16q: $i] :
( ( mem @ V16q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V16q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V17t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V16q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( p @ ( ap @ V6phi @ ( inj__ty_2Enum_2Enum @ V17t ) ) ) )
& ( p @ ( ap @ V5Phi @ V16q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ V6phi ) ) )
<=> ? [V18q: $i] :
( ( mem @ V18q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V18q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V19t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V18q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( p @ ( ap @ V6phi @ ( inj__ty_2Enum_2Enum @ V19t ) ) ) )
& ( p @ ( ap @ V5Phi @ V18q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPALWAYS @ V7a ) ) ) )
<=> ? [V20q: $i] :
( ( mem @ V20q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V20q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V21t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V20q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V21t ) ) )
& ( p @ ( ap @ V20q @ ( inj__ty_2Enum_2Enum @ V21t ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V20q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ c_2EPast__Temporal__Logic_2EPEVENTUAL @ V7a ) ) ) )
<=> ? [V22q: $i] :
( ( mem @ V22q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V22q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V23t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V22q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V23t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V23t ) ) )
| ( p @ ( ap @ V22q @ ( inj__ty_2Enum_2Enum @ V23t ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V22q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSUNTIL @ V7a ) @ V8b ) ) ) )
<=> ? [V24q: $i] :
( ( mem @ V24q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V24q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V25t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V24q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V25t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V25t ) ) )
| ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V25t ) ) )
& ( p @ ( ap @ V24q @ ( inj__ty_2Enum_2Enum @ V25t ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V24q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSWHEN @ V7a ) @ V8b ) ) ) )
<=> ? [V26q: $i] :
( ( mem @ V26q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V26q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V27t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V26q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V27t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V27t ) ) )
& ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V27t ) ) ) )
| ( ~ ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V27t ) ) )
& ( p @ ( ap @ V26q @ ( inj__ty_2Enum_2Enum @ V27t ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V26q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPSNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPSBEFORE @ V7a ) @ V8b ) ) ) )
<=> ? [V28q: $i] :
( ( mem @ V28q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V28q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V29t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V28q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V29t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ~ ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V29t ) ) )
& ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V29t ) ) )
| ( p @ ( ap @ V28q @ ( inj__ty_2Enum_2Enum @ V29t ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V28q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPUNTIL @ V7a ) @ V8b ) ) ) )
<=> ? [V30q: $i] :
( ( mem @ V30q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V30q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V31t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V30q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V31t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V31t ) ) )
| ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V31t ) ) )
& ( p @ ( ap @ V30q @ ( inj__ty_2Enum_2Enum @ V31t ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V30q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPWHEN @ V7a ) @ V8b ) ) ) )
<=> ? [V32q: $i] :
( ( mem @ V32q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V32q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V33t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V32q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V33t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V33t ) ) )
& ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V33t ) ) ) )
| ( ~ ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V33t ) ) )
& ( p @ ( ap @ V32q @ ( inj__ty_2Enum_2Enum @ V33t ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V32q ) ) ) )
& ( ( p @ ( ap @ V5Phi @ ( ap @ c_2EPast__Temporal__Logic_2EPNEXT @ ( ap @ ( ap @ c_2EPast__Temporal__Logic_2EPBEFORE @ V7a ) @ V8b ) ) ) )
<=> ? [V34q: $i] :
( ( mem @ V34q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V34q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V35t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V34q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V35t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( ~ ( p @ ( ap @ V8b @ ( inj__ty_2Enum_2Enum @ V35t ) ) )
& ( ( p @ ( ap @ V7a @ ( inj__ty_2Enum_2Enum @ V35t ) ) )
| ( p @ ( ap @ V34q @ ( inj__ty_2Enum_2Enum @ V35t ) ) ) ) ) )
& ( p @ ( ap @ V5Phi @ V34q ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBUECHI__TRANSLATION,axiom,
! [V0Phi: $i] :
( ( mem @ V0Phi @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ bool ) )
=> ! [V1phi: $i] :
( ( mem @ V1phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( p @ ( ap @ V0Phi @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1phi ) ) )
<=> ? [V4q0: $i] :
( ( mem @ V4q0 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V5q1: $i] :
( ( mem @ V5q1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V6t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V4q0 @ ( inj__ty_2Enum_2Enum @ V6t ) ) )
<=> ( p @ ( ap @ V1phi @ ( inj__ty_2Enum_2Enum @ V6t ) ) ) )
& ( ( p @ ( ap @ V5q1 @ ( inj__ty_2Enum_2Enum @ V6t ) ) )
<=> ( p @ ( ap @ V4q0 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V5q1 ) ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V2a ) ) )
<=> ? [V7q: $i] :
( ( mem @ V7q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V8t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ V8t ) ) )
<=> ( ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V8t ) ) )
& ( p @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V9t1: tp__ty_2Enum_2Enum] :
? [V10t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V2a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) ) )
=> ( p @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V7q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V2a ) ) )
<=> ? [V11q: $i] :
( ( mem @ V11q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V12t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V11q @ ( inj__ty_2Enum_2Enum @ V12t ) ) )
<=> ( ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V12t ) ) )
| ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V13t1: tp__ty_2Enum_2Enum] :
? [V14t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V11q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t1 ) ) @ ( inj__ty_2Enum_2Enum @ V14t2 ) ) ) )
=> ( p @ ( ap @ V2a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t1 ) ) @ ( inj__ty_2Enum_2Enum @ V14t2 ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V11q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V2a ) @ V3b ) ) )
<=> ? [V15q: $i] :
( ( mem @ V15q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V16t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V15q @ ( inj__ty_2Enum_2Enum @ V16t ) ) )
<=> ( ( p @ ( ap @ V3b @ ( inj__ty_2Enum_2Enum @ V16t ) ) )
| ( ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V16t ) ) )
& ( p @ ( ap @ V15q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V17t1: tp__ty_2Enum_2Enum] :
? [V18t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V15q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t1 ) ) @ ( inj__ty_2Enum_2Enum @ V18t2 ) ) ) )
=> ( ~ ( p @ ( ap @ V2a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t1 ) ) @ ( inj__ty_2Enum_2Enum @ V18t2 ) ) ) )
| ( p @ ( ap @ V3b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t1 ) ) @ ( inj__ty_2Enum_2Enum @ V18t2 ) ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V15q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V2a ) @ V3b ) ) )
<=> ? [V19q: $i] :
( ( mem @ V19q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V20t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V19q @ ( inj__ty_2Enum_2Enum @ V20t ) ) )
<=> ( ( p @ ( ap @ V3b @ ( inj__ty_2Enum_2Enum @ V20t ) ) )
| ( ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V20t ) ) )
& ( p @ ( ap @ V19q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V21t1: tp__ty_2Enum_2Enum] :
? [V22t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V19q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) ) )
=> ( ~ ( p @ ( ap @ V2a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) ) )
| ( p @ ( ap @ V3b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V19q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V3b ) ) )
<=> ? [V23q: $i] :
( ( mem @ V23q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V24t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V23q @ ( inj__ty_2Enum_2Enum @ V24t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V3b @ ( inj__ty_2Enum_2Enum @ V24t ) ) ) @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V24t ) ) ) @ ( ap @ V23q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V24t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V25t1: tp__ty_2Enum_2Enum] :
? [V26t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V23q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V25t1 ) ) @ ( inj__ty_2Enum_2Enum @ V26t2 ) ) ) )
=> ( p @ ( ap @ V3b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V25t1 ) ) @ ( inj__ty_2Enum_2Enum @ V26t2 ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V23q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V3b ) ) )
<=> ? [V27q: $i] :
( ( mem @ V27q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V28t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V27q @ ( inj__ty_2Enum_2Enum @ V28t ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V3b @ ( inj__ty_2Enum_2Enum @ V28t ) ) ) @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V28t ) ) ) @ ( ap @ V27q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V28t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V29t1: tp__ty_2Enum_2Enum] :
? [V30t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V27q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V29t1 ) ) @ ( inj__ty_2Enum_2Enum @ V30t2 ) ) ) )
| ( p @ ( ap @ V3b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V29t1 ) ) @ ( inj__ty_2Enum_2Enum @ V30t2 ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V27q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V2a ) @ V3b ) ) )
<=> ? [V31q: $i] :
( ( mem @ V31q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V32t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V31q @ ( inj__ty_2Enum_2Enum @ V32t ) ) )
<=> ( ~ ( p @ ( ap @ V3b @ ( inj__ty_2Enum_2Enum @ V32t ) ) )
& ( ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V32t ) ) )
| ( p @ ( ap @ V31q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V32t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V33t1: tp__ty_2Enum_2Enum] :
? [V34t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V31q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V33t1 ) ) @ ( inj__ty_2Enum_2Enum @ V34t2 ) ) ) )
=> ( ( p @ ( ap @ V2a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V33t1 ) ) @ ( inj__ty_2Enum_2Enum @ V34t2 ) ) ) )
| ( p @ ( ap @ V3b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V33t1 ) ) @ ( inj__ty_2Enum_2Enum @ V34t2 ) ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V31q ) ) ) )
& ( ( p @ ( ap @ V0Phi @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V2a ) @ V3b ) ) )
<=> ? [V35q: $i] :
( ( mem @ V35q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& $true
& ! [V36t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V35q @ ( inj__ty_2Enum_2Enum @ V36t ) ) )
<=> ( ~ ( p @ ( ap @ V3b @ ( inj__ty_2Enum_2Enum @ V36t ) ) )
& ( ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V36t ) ) )
| ( p @ ( ap @ V35q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V36t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V37t1: tp__ty_2Enum_2Enum] :
? [V38t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V35q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V37t1 ) ) @ ( inj__ty_2Enum_2Enum @ V38t2 ) ) ) )
=> ( ( p @ ( ap @ V2a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V37t1 ) ) @ ( inj__ty_2Enum_2Enum @ V38t2 ) ) ) )
| ( p @ ( ap @ V3b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V37t1 ) ) @ ( inj__ty_2Enum_2Enum @ V38t2 ) ) ) ) ) )
& ( p @ ( ap @ V0Phi @ V35q ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__CONJ__CLOSURE,axiom,
! [A_27a: del,A_27b1: del,A_27b2: del,V0Phi__I1: $i] :
( ( mem @ V0Phi__I1 @ ( arr @ A_27b1 @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2Phi__R1: $i] :
( ( mem @ V2Phi__R1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b1 ) @ bool ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V4Psi1: $i] :
( ( mem @ V4Psi1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b1 ) @ bool ) )
=> ! [V5Phi__I2: $i] :
( ( mem @ V5Phi__I2 @ ( arr @ A_27b2 @ bool ) )
=> ! [V6Phi__R2: $i] :
( ( mem @ V6Phi__R2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b2 ) @ bool ) )
=> ! [V7Psi2: $i] :
( ( mem @ V7Psi2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b2 ) @ bool ) )
=> ( ( ? [V8q1: $i] :
( ( mem @ V8q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V8q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V9t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V8q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V10t1: tp__ty_2Enum_2Enum] :
! [V11t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V8q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) )
& ? [V12q2: $i] :
( ( mem @ V12q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V12q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V13t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V12q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V14t1: tp__ty_2Enum_2Enum] :
! [V15t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V12q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) )
<=> ? [V16q1: $i] :
( ( mem @ V16q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ? [V17q2: $i] :
( ( mem @ V17q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V16q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V17q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V18t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V16q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V17q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ? [V19t1: tp__ty_2Enum_2Enum] :
! [V20t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V16q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V17q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V19t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__DISJ__CLOSURE,axiom,
! [A_27a: del,A_27b1: del,A_27b2: del,V0Phi__I1: $i] :
( ( mem @ V0Phi__I1 @ ( arr @ A_27b1 @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum,V2Phi__R1: $i] :
( ( mem @ V2Phi__R1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b1 ) @ bool ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V4Psi1: $i] :
( ( mem @ V4Psi1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b1 ) @ bool ) )
=> ! [V5Phi__I2: $i] :
( ( mem @ V5Phi__I2 @ ( arr @ A_27b2 @ bool ) )
=> ! [V6Phi__R2: $i] :
( ( mem @ V6Phi__R2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b2 ) @ bool ) )
=> ! [V7Psi2: $i] :
( ( mem @ V7Psi2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b2 ) @ bool ) )
=> ! [V8t: tp__ty_2Enum_2Enum] :
( ( ? [V9q1: $i] :
( ( mem @ V9q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V9q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V10t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V9q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V10t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V11t1: tp__ty_2Enum_2Enum] :
! [V12t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V9q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) )
| ? [V13q2: $i] :
( ( mem @ V13q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V13q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V14t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V13q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ? [V15t1: tp__ty_2Enum_2Enum] :
! [V16t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V13q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) )
<=> ? [V17p: $i] :
( ( mem @ V17p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V18q1: $i] :
( ( mem @ V18q1 @ ( arr @ ty_2Enum_2Enum @ A_27b1 ) )
& ? [V19q2: $i] :
( ( mem @ V19q2 @ ( arr @ ty_2Enum_2Enum @ A_27b2 ) )
& ( ( ~ ( p @ ( ap @ V17p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V0Phi__I1 @ ( ap @ V18q1 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ( ( p @ ( ap @ V17p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ V5Phi__I2 @ ( ap @ V19q2 @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ! [V20t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V17p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2Phi__R1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V18q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ~ ( p @ ( ap @ V17p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V17p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V6Phi__R2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) @ ( ap @ V19q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( p @ ( ap @ V17p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V20t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V21t1: tp__ty_2Enum_2Enum] :
! [V22t2: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V17p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V4Psi1 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V18q1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V17p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V7Psi2 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V19q2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V21t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V22t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__NEXT__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0Phi__I: $i] :
( ( mem @ V0Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V1Phi__R: $i] :
( ( mem @ V1Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V2i: $i] :
( ( mem @ V2i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V3Psi: $i] :
( ( mem @ V3Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V4t0: tp__ty_2Enum_2Enum,V5c: $i] :
( ( mem @ V5c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V7q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0Phi__I @ ( ap @ V7q @ V6t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V8t ) @ V6t0 ) ) ) @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V8t ) @ V6t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t2: $i] : ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t2 ) @ V6t0 ) ) ) ) @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t2 ) @ V6t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V4t0 ) ) )
<=> ? [V11p: $i] :
( ( mem @ V11p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V12q: $i] :
( ( mem @ V12q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( ( p @ ( ap @ V11p @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) )
<=> $false )
& ( ( ap @ V12q @ ( inj__ty_2Enum_2Enum @ V4t0 ) )
= V5c )
& ! [V13t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V11p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) ) )
& ( ( ap @ V12q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) )
= V5c )
& ( p @ ( ap @ V11p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V12q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V11p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) ) ) @ ( ap @ V12q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) ) ) ) )
& ( p @ ( ap @ V11p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V13t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V14t1: tp__ty_2Enum_2Enum] :
! [V15t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) ) ) ) @ ( ap @ V12q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V4t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__SUNTIL__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0phi: $i] :
( ( mem @ V0phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1Phi__I: $i] :
( ( mem @ V1Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V2Phi__R: $i] :
( ( mem @ V2Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V4Psi: $i] :
( ( mem @ V4Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V5t0: tp__ty_2Enum_2Enum,V6c: $i] :
( ( mem @ V6c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0phi )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V8q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1Phi__I @ ( ap @ V8q @ V7t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V2Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t2: $i] : ( ap @ V4Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
<=> ? [V12p: $i] :
( ( mem @ V12p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13q: $i] :
( ( mem @ V13q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V12p @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) @ ( ap @ V1Phi__I @ ( ap @ V13q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V13q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) @ V6c ) ) )
& ! [V14t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ( p @ ( ap @ V0phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= V6c ) )
| ( ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ( p @ ( ap @ V0phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V1Phi__I @ ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V2Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V15t1: tp__ty_2Enum_2Enum] :
! [V16t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V4Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) @ ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__UNTIL__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0phi: $i] :
( ( mem @ V0phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1Phi__I: $i] :
( ( mem @ V1Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V2Phi__R: $i] :
( ( mem @ V2Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V4Psi: $i] :
( ( mem @ V4Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V5t0: tp__ty_2Enum_2Enum,V6c: $i] :
( ( mem @ V6c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0phi )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V8q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1Phi__I @ ( ap @ V8q @ V7t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V2Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t2: $i] : ( ap @ V4Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
<=> ? [V12p: $i] :
( ( mem @ V12p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13q: $i] :
( ( mem @ V13q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V12p @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) @ ( ap @ V1Phi__I @ ( ap @ V13q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V13q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) @ V6c ) ) )
& ! [V14t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ( p @ ( ap @ V0phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= V6c ) )
| ( ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ( p @ ( ap @ V0phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V1Phi__I @ ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V2Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V14t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V15t1: tp__ty_2Enum_2Enum] :
! [V16t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V12p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
| ( p @ ( ap @ V4Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V3i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) @ ( ap @ V13q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__SBEFORE__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0Phi__I: $i] :
( ( mem @ V0Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V1Phi__R: $i] :
( ( mem @ V1Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V2i: $i] :
( ( mem @ V2i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V3Psi: $i] :
( ( mem @ V3Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V4phi: $i] :
( ( mem @ V4phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V5t0: tp__ty_2Enum_2Enum,V6c: $i] :
( ( mem @ V6c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V8q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0Phi__I @ ( ap @ V8q @ V7t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t2: $i] : ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ V4phi )
@ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
<=> ? [V12p1: $i] :
( ( mem @ V12p1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13p2: $i] :
( ( mem @ V13p2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V14q: $i] :
( ( mem @ V14q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( ( ~ ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) )
= V6c ) )
| ( ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= V6c ) )
| ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V16t1: tp__ty_2Enum_2Enum] :
! [V17t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__BEFORE__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0Phi__I: $i] :
( ( mem @ V0Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V1Phi__R: $i] :
( ( mem @ V1Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V2i: $i] :
( ( mem @ V2i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V3Psi: $i] :
( ( mem @ V3Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V4phi: $i] :
( ( mem @ V4phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V5t0: tp__ty_2Enum_2Enum,V6c: $i] :
( ( mem @ V6c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V8q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0Phi__I @ ( ap @ V8q @ V7t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t2: $i] : ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ V4phi )
@ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
<=> ? [V12p1: $i] :
( ( mem @ V12p1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13p2: $i] :
( ( mem @ V13p2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V14q: $i] :
( ( mem @ V14q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( ( ~ ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) )
= V6c ) )
| ( ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= V6c ) )
| ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V16t1: tp__ty_2Enum_2Enum] :
! [V17t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
| ( p @ ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__SWHEN__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0Phi__I: $i] :
( ( mem @ V0Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V1Phi__R: $i] :
( ( mem @ V1Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V2i: $i] :
( ( mem @ V2i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V3Psi: $i] :
( ( mem @ V3Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V4phi: $i] :
( ( mem @ V4phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V5t0: tp__ty_2Enum_2Enum,V6c: $i] :
( ( mem @ V6c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V8q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0Phi__I @ ( ap @ V8q @ V7t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t2: $i] : ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ V4phi )
@ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
<=> ? [V12p1: $i] :
( ( mem @ V12p1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13p2: $i] :
( ( mem @ V13p2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V14q: $i] :
( ( mem @ V14q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( ( ~ ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) )
= V6c ) )
| ( ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= V6c ) )
| ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V16t1: tp__ty_2Enum_2Enum] :
! [V17t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ECO__BUECHI__WHEN__CLOSURE,axiom,
! [A_27a: del,A_27b: del,V0Phi__I: $i] :
( ( mem @ V0Phi__I @ ( arr @ A_27b @ bool ) )
=> ! [V1Phi__R: $i] :
( ( mem @ V1Phi__R @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V2i: $i] :
( ( mem @ V2i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V3Psi: $i] :
( ( mem @ V3Psi @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V4phi: $i] :
( ( mem @ V4phi @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V5t0: tp__ty_2Enum_2Enum,V6c: $i] :
( ( mem @ V6c @ A_27b )
=> ( ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27b )
@ ^ [V8q: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0Phi__I @ ( ap @ V8q @ V7t0 ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V9t ) @ V7t0 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11t2: $i] : ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) @ ( ap @ V8q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V10t1 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V11t2 ) @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ V4phi )
@ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
<=> ? [V12p1: $i] :
( ( mem @ V12p1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V13p2: $i] :
( ( mem @ V13p2 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V14q: $i] :
( ( mem @ V14q @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
& ( ( ~ ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) )
= V6c ) )
| ( ( p @ ( ap @ V12p1 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= V6c ) )
| ( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) )
= V6c )
& ~ ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ~ ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V4phi @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V0Phi__I @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
| ( ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) )
& ( p @ ( ap @ V1Phi__R @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) )
& ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ V13p2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ? [V16t1: tp__ty_2Enum_2Enum] :
! [V17t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V12p1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) )
| ( p @ ( ap @ V3Psi @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ V2i @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) @ ( ap @ V14q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V16t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t2 ) ) @ ( inj__ty_2Enum_2Enum @ V5t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ENEXT__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2p: $i] :
( ( mem @ V2p @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V2p @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V2p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V2p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V2p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ESUNTIL__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EUNTIL__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ESBEFORE__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBEFORE__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ESWHEN__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EWHEN__AS__CO__BUECHI,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ~ ( p @ ( ap @ V3q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
| ( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) )
& ? [V5t1: tp__ty_2Enum_2Enum] :
! [V6t2: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t2 ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBUECHI__PERIODIC__MODEL,axiom,
! [A_27a: del,A_27state: del,V0InitState: $i] :
( ( mem @ V0InitState @ ( arr @ A_27state @ bool ) )
=> ! [V1TransRel: $i] :
( ( mem @ V1TransRel @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ bool ) )
=> ! [V2Accept: $i] :
( ( mem @ V2Accept @ ( arr @ A_27state @ bool ) )
=> ( ! [V3s: $i] :
( ( mem @ V3s @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
=> ? [V4x0: tp__ty_2Enum_2Enum,V5l: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) )
& ( ( ap @ V3s @ ( inj__ty_2Enum_2Enum @ V4x0 ) )
= ( ap @ V3s @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4x0 ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) ) ) ) )
=> ( ? [V6i: $i] :
( ( mem @ V6i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V7q: $i] :
( ( mem @ V7q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( p @ ( ap @ V0InitState @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( ap @ V6i @ ( inj__ty_2Enum_2Enum @ V8t ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27state @ A_27state ) @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ V8t ) ) ) @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V9t1: tp__ty_2Enum_2Enum] :
? [V10t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Accept @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) ) ) ) ) )
<=> ? [V11x0: tp__ty_2Enum_2Enum,V12l: tp__ty_2Enum_2Enum,V13j: $i] :
( ( mem @ V13j @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V14p: $i] :
( ( mem @ V14p @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) )
& ! [V15t2: tp__ty_2Enum_2Enum] :
( ( ap @ V13j @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) )
= ( ap @ V13j @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) ) )
& ! [V16t2: tp__ty_2Enum_2Enum] :
( ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) )
= ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) ) )
& ( p @ ( ap @ V0InitState @ ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V17t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( ap @ V13j @ ( inj__ty_2Enum_2Enum @ V17t ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27state @ A_27state ) @ ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ V17t ) ) ) @ ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V18t1: tp__ty_2Enum_2Enum] :
? [V19t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Accept @ ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18t1 ) ) @ ( inj__ty_2Enum_2Enum @ V19t2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBUECHI__PERIODIC__REDUCTION__THM,axiom,
! [A_27a: del,A_27state: del,V0InitState: $i] :
( ( mem @ V0InitState @ ( arr @ A_27state @ bool ) )
=> ! [V1TransRel: $i] :
( ( mem @ V1TransRel @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ bool ) )
=> ! [V2Accept: $i] :
( ( mem @ V2Accept @ ( arr @ A_27state @ bool ) )
=> ( ! [V3s: $i] :
( ( mem @ V3s @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
=> ? [V4x0: tp__ty_2Enum_2Enum,V5l: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) )
& ( ( ap @ V3s @ ( inj__ty_2Enum_2Enum @ V4x0 ) )
= ( ap @ V3s @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4x0 ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) ) ) ) )
=> ( ? [V6i: $i] :
( ( mem @ V6i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V7q: $i] :
( ( mem @ V7q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( p @ ( ap @ V0InitState @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( ap @ V6i @ ( inj__ty_2Enum_2Enum @ V8t ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27state @ A_27state ) @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ V8t ) ) ) @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V9t1: tp__ty_2Enum_2Enum] :
? [V10t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Accept @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) ) ) ) ) )
<=> ? [V11x0: tp__ty_2Enum_2Enum,V12l: tp__ty_2Enum_2Enum,V13j: $i] :
( ( mem @ V13j @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V14p: $i] :
( ( mem @ V14p @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) )
& ! [V15t2: tp__ty_2Enum_2Enum] :
( ( ap @ V13j @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) )
= ( ap @ V13j @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V15t2 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) ) )
& ! [V16t2: tp__ty_2Enum_2Enum] :
( ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) )
= ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V16t2 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) ) )
& ( p @ ( ap @ V0InitState @ ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V17t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V17t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) )
=> ( p @ ( ap @ V1TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( ap @ V13j @ ( inj__ty_2Enum_2Enum @ V17t ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27state @ A_27state ) @ ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ V17t ) ) ) @ ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V17t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ? [V18t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V18t ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) )
& ( p @ ( ap @ V2Accept @ ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V18t ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EBUECHI__PROP__REDUCTION,axiom,
! [A_27a: del,A_27state: del,V0InitState: $i] :
( ( mem @ V0InitState @ ( arr @ A_27state @ bool ) )
=> ! [V1TransRel: $i] :
( ( mem @ V1TransRel @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ bool ) )
=> ! [V2Accept: $i] :
( ( mem @ V2Accept @ ( arr @ A_27state @ bool ) )
=> ( ! [V3s: $i] :
( ( mem @ V3s @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
=> ? [V4x0: tp__ty_2Enum_2Enum,V5l: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) )
& ( ( ap @ V3s @ ( inj__ty_2Enum_2Enum @ V4x0 ) )
= ( ap @ V3s @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4x0 ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) ) ) ) )
=> ( ? [V6i: $i] :
( ( mem @ V6i @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V7q: $i] :
( ( mem @ V7q @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( p @ ( ap @ V0InitState @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( ap @ V6i @ ( inj__ty_2Enum_2Enum @ V8t ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27state @ A_27state ) @ ( ap @ V7q @ ( inj__ty_2Enum_2Enum @ V8t ) ) ) @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ! [V9t1: tp__ty_2Enum_2Enum] :
? [V10t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V2Accept @ ( ap @ V7q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9t1 ) ) @ ( inj__ty_2Enum_2Enum @ V10t2 ) ) ) ) ) ) )
<=> ? [V11x0: tp__ty_2Enum_2Enum,V12l: tp__ty_2Enum_2Enum,V13j: $i] :
( ( mem @ V13j @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
& ? [V14p: $i] :
( ( mem @ V14p @ ( arr @ ty_2Enum_2Enum @ A_27state ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) )
& ( p @ ( ap @ V0InitState @ ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V15t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) )
=> ( p @ ( ap @ V1TransRel @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( ap @ V13j @ ( inj__ty_2Enum_2Enum @ V15t ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27state @ A_27state ) @ ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ V15t ) ) ) @ ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V15t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ? [V16t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V16t ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) )
& ( p @ ( ap @ V2Accept @ ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V16t ) ) ) ) ) )
& ( ( ap @ V14p @ ( inj__ty_2Enum_2Enum @ V11x0 ) )
= ( ap @ V14p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V11x0 ) ) @ ( inj__ty_2Enum_2Enum @ V12l ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EEQUALITY__THM,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( V0x = V1y )
<=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ V2P @ V0x ) )
<=> ( p @ ( ap @ V2P @ V1y ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2ELESS__THM,axiom,
! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
<=> ? [V2P: $i] :
( ( mem @ V2P @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
& ~ ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
& ! [V3z: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V2P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3z ) ) ) )
=> ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V3z ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EFORALL__EXISTS__THM,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ! [V1t1: tp__ty_2Enum_2Enum] :
? [V2t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t1 ) ) @ ( inj__ty_2Enum_2Enum @ V2t2 ) ) ) )
<=> ! [V3t1: tp__ty_2Enum_2Enum] :
? [V4t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) @ ( inj__ty_2Enum_2Enum @ V4t2 ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4t2 ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EEXISTS__FORALL__THM,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ? [V1t1: tp__ty_2Enum_2Enum] :
! [V2t2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t1 ) ) @ ( inj__ty_2Enum_2Enum @ V2t2 ) ) ) )
<=> ? [V3t1: tp__ty_2Enum_2Enum] :
! [V4t2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) @ ( inj__ty_2Enum_2Enum @ V4t2 ) ) )
=> ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4t2 ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EELGOT__LEMMA,axiom,
! [A_27a: del,V0PHI: $i] :
( ( mem @ V0PHI @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
=> ( ? [V1x: $i] :
( ( mem @ V1x @ A_27a )
& ! [V2p: $i] :
( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
=> ( p @ ( ap @ ( ap @ V0PHI @ V2p ) @ V1x ) ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ A_27a @ bool ) )
& ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ( ( p @ ( ap @ V3q @ V4x ) )
=> ! [V5p: $i] :
( ( mem @ V5p @ ( arr @ A_27a @ bool ) )
=> ( p @ ( ap @ ( ap @ V0PHI @ V5p ) @ V4x ) ) ) ) )
& ? [V6z: $i] :
( ( mem @ V6z @ A_27a )
& ( p @ ( ap @ V3q @ V6z ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EELGOT1__THM,axiom,
! [A_27a: del,V0PHI: $i] :
( ( mem @ V0PHI @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
=> ( ? [V1x: $i] :
( ( mem @ V1x @ A_27a )
& ! [V2p: $i] :
( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
=> ( p @ ( ap @ ( ap @ V0PHI @ V2p ) @ V1x ) ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ A_27a @ bool ) )
& ! [V4p: $i] :
( ( mem @ V4p @ ( arr @ A_27a @ bool ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ? [V6z: $i] :
( ( mem @ V6z @ A_27a )
& ( ( p @ ( ap @ V3q @ V5x ) )
=> ( p @ ( ap @ ( ap @ V0PHI @ V4p ) @ V5x ) ) )
& ( p @ ( ap @ V3q @ V6z ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EOmega__Automata_2EELGOT2__THM,axiom,
! [A_27a: del,V0PHI: $i] :
( ( mem @ V0PHI @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
=> ( ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ? [V2p: $i] :
( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
& ( p @ ( ap @ ( ap @ V0PHI @ V2p ) @ V1x ) ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ A_27a @ bool ) )
=> ? [V4p: $i] :
( ( mem @ V4p @ ( arr @ A_27a @ bool ) )
& ? [V5x: $i] :
( ( mem @ V5x @ A_27a )
& ! [V6z: $i] :
( ( mem @ V6z @ A_27a )
=> ( ( p @ ( ap @ V3q @ V6z ) )
=> ( ( p @ ( ap @ ( ap @ V0PHI @ V4p ) @ V5x ) )
& ( p @ ( ap @ V3q @ V5x ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------