According to the Bible (which doesn't seem to matter at all to you) the wicked will be punished BY being destroyed.
Isaiah 33:1 ESV
Ah, you destroyer,
who yourself have not been destroyed,
you traitor,
whom none has betrayed!
When you have ceased to destroy,
you will be destroyed;
and when you have finished betraying,
they will betray you.
Psalm 37:20
But the wicked will perish;
the enemies of the Lord are like the glory of the pastures;
they vanish—like smoke they vanish away.
Psalm 37:38
But transgressors shall be altogether destroyed;
the future of the wicked shall be cut off.
I don't know how you can read this and then continue to deny what it says. Look up John 3:16 in your Bible. Tell me what it says. I'm serious, do this. It contradicts your false doctrine!
Isa 33:1 accuses the heathen king of "destroying," but its only physical bodies he was destroying, not the immaterial souls, because Jesus says they (people like this destroyer in Isa 33:1) can kill the body but not the soul. While the word soul does at times mean the body, at other times it definitely refers to another part of us that does not get destroyed when the body dies.
Further, Bible passages that talk about the destruction of the wicked only talk about the ruin of the person, not putting them out of existence. Here is what Greek scholars says about the Greek word for "destroy" in the NT:
"apollumi..."to destroy utterly"; in middle voice, "to perish." The idea is NOT EXTINCTION but ruin, loss, NOT OF BEING, but of wellbeing. This is clear from its use, as, e.g., of the
marring of wine skins, Luke 5:37; of
lost sheep, i.e., lost to the shepherd, metaphorical of spiritual destitution, Luke 15:4,6, etc.; the
lost son, 15:24; of the perishing of food, John 6:27; of gold, 1 Pet 1:7." (W.E. Vine's Complete Expository Dictionary of Old and New Testament Words, p.164)
So in other words, the wine skins were apollumi (marred) but they still existed. They simply could not fully function the way they were meant to. The sheep and the son are said to be apollumi (lost) but they were still in conscious existence. Food can perish in the sense that it has gone stale, but it still exists, just as gold can perish (apollumi) by being tainted even though it still exists. So when the wicked are apollumi, they are simply ruined in the hereafter, but that doesn't mean they cease to exist.