May I also remind you that you are not one of the authors of the Bible, dear JRightly? The infallible Bible does say that only the righteous receive eternal life, but that the fate of the wicked is eternal punishment, to perish and be burnt up and to be no more. Johnathan Edwards is an example that even a hostile witness recognizes that "being snuffed out" does constitute eternal punishment according to scripture.
Eternal punishment does include being snuffed out of existence in a brief moment of judgment, but if the snuffing out was temporary then the punishment wouldn't be eternal or everlasting. See Jonathan Edwards above.
So where is the point of confusion (disagreement?) Are you perhaps confusing the words "punishment" and "judgment?" The punishment of sin is the wages of sin, also known as death. The punishment of death is everlasting. The gift of God is eternal life. The gift of life is everlasting.
Or are you somehow proceeding on an assumption that being cast into a fire grants life? That sounds somewhat crazy, yet somehow I have the impression that's what's going on here.
I'm simply following what scripture says, which describes a different definition of "life," which you seem to have confused with something else
We are currently alive, here on this earth. We have life in our bodies.
When we die, however, we are both dead and alive. Our bodies, which are part of us, are dead, yet we are still alive, because we are more than just our bodies. Our soul/spirit is alive, yet our body is dead.
Death is just separation.
Physical death is separation of our body and soul/spirit. So, in a sense, those who are in hell currently (and they are indeed in hell, not in "soul-sleep") are dead, as they are physically dead, But they are also still living (as Jesus described those who were in Abraham's bosom which is one of the places in hell, separated from what we call Hades, where the righteous would go upon death to await the death of the High Priest (note: a place of refuge, see cities of refuge in The Law in the Old Testament)), very much aware of their situation.
Spiritual death, on the other hand, is separation from God. If someone is dead spiritually, they have been separated from God (this is driven home by the wording used to described what Christ's DBR accomplished, a "reconciling" of the world, which means to restore friendly relations between).
God told Adam that he was not to eat of the Tree of the Knowledge of Good and Evil (hereafter called simply, "the Tree", for simplicity's sake), "for in the day that you eat of it you shall surely die." No, the day they ate of it, Adam and Eve didn't die (physically, at least), they didn't cease to exist, they weren't snuffed out. They WERE, however, removed from God's presence. This is why death is separation, and not a cessation of existence.
If we use THAT standard, that "for in the day that you eat of it you shall surely die" means separation from God, reading the Bible becomes easier, and it is easier to understand.
So now that we understand that death is only separation, and not cessation of existence or soul-sleep, let's look at the Biblical claim that the wicked receive eternal punishment, while the righteous receive eternal life. The punishment here is eternal separation from God, death.
The alternative is eternal life, life meaning an association or union (to God).
So no, I may not be inspired, nor do I claim to be, but I am only putting forth what the Bible says.
I let the Bible speak for itself, rather than relying on man's interpretation.