You should know that the verb "
are" is not in the original Greek. It says "Where the beast and the false prophet." The translators supplied the verb and due to their having been influenced by 1100 years of the Roman Church, which dragged in from paganism the doctrine of eternal torment as well as many other pagan ideas, they supplied the verb "
are", which is
purely subjective. In the original, the passage says nothing about their time period in the lake of fire, and we simply can't base our arguments on a word that doesn't even appear in Scripture.
As for "day and night forever and ever", once again, due to the influence of the Roman Church, the translators applied the "
undefined because endless" definition of "aionios" by translating it "forever and ever", an application which is also
purely subjective. They could have just as easily applied the "
undefined but not endless" definition, as other Bibles do, such as a French version of the Textus Receptus which renders it "aux siècles des siècles", or "the age of the age", which does not imply eternity in the least.