Keep reading. In Revelation 20:14-15, anyone not found in the book of life is given the second death.
14And death and hell were cast into the lake of fire. This is the second death.
15And whosoever was not found written in the book of life was cast into the lake of fire.
The devil, beast, false prophet, the rich man, and everyone else will be put to death if they are not found in the book of life. I think where you're getting hung up is you're reading things like "eternal fire" and believing that means eternal torment.
You would need to prove that the soul is indestructible, which it isn't. God can destroy both soul and body on hell.
There is a big case to make for cessation of life in hell. Annihilation cures many biblical contradictions that those who espouse eternal torment hold, such as receiving eternal life in hell
Jesus said only the righteous receive eternal life, pro-eternal torment people say everyone in hell lives forever. Clearly Jesus is correct so this isn't debatable.
Did you know that "eternal" and "forever" are sometimes used in non-literal ways in the Bible? There are some excellent posts about that somewhere in this thread.