looking for an anime ?

hi i have try a few times to find this i dont know the title, its the future and people live in a domed city thinking outside is dead after the war (like logans run)
this young guy starts to hear a voice and finds a girl asleep conected to a machine with her mind (i think she runs the city) i think she is called eve, and the young lad is a cop of some sorts, he takes her off the machine and then becomes hunted by the cops ect he gets chased and makes his way out of the city and finds it all lush and green ,

That is not dead which can eternal lie, and with strange eons even death may die
H.P.LOVECRAFT