I take it by this answer that you believe the souls of the wicked are annihilated after this life; is that correct? What happens to them?
If you want ANOTHER church father I would suggest A Treatise on the Soul by Tertullian where he states:
For in this philosophy lie both their Æons and their genealogies. Thus, too, do they divide sensation, both into the intellectual powers from their spiritual seed, and the sensuous faculties from the animal, which cannot by any means comprehend spiritual things.
The truth is, the soul is indivisible, because it is immortal; (and this fact) compels us to believe that death itself is an indivisible process, accruing indivisibly to the soul, not indeed because it is immortal, but because it is indivisible.
Tertullian was a heretic and the Latins, as in other matters, are simply wrong. The quoted position is from the Middle Ages after Rome broke from the other Patriarchates. Rome picked up a lot of odd stuff after the Great Schism. Some of those oddities lead to the Reformation. More later; off to an Armenian dance where I can say all the bad things about Turks I want!
Tertullian is not a Church Father and more than Martin Luther is.
The mortality of the soul is scriptural: Ezekiel 18:4 "the soul that sinneth, it shall die." Those who will remain separated from God for all eternity, due to unrepentant sins, hall be dead. Sin is death.