The beast and FP are cast into the fire in Rev 19 but satan isn't. instead, he is bound and imprisoned for a thousand years. Afterward, satan will be cast into the fire where the other two had previously be cast. It's contextually clear the two go there first, and much later satan goes to the same place. The events of Armageddon etc do take place BEFORE the events of Rev 20.
Rev 19:17-20
(17) And I saw an angel standing in the sun; and he cried with a loud voice, saying to all the fowls that fly in the midst of heaven, Come and gather yourselves together unto the supper of the great God;
(18) That ye may eat the flesh of kings, and the flesh of captains, and the flesh of mighty men, and the flesh of horses, and of them that sit on them, and the flesh of all men, both free and bond, both small and great.
(19) And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against him that sat on the horse, and against his army.
(20) And the
beast was taken, and
with him the false prophet that wrought miracles before him, with
which he deceived them that had received the mark of the beast, and them that worshipped his image.
These both were cast alive into a lake of fire burning with brimstone.
Rev 20:6-11
(6) Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and
of Christ, and shall reign with him a thousand years.
(7) And when the thousand years are expired,
Satan shall be loosed out of his prison,
(8) And
shall go out to deceive the nations which are in the four quarters of the earth, Gog and Magog, to
gather them together to battle: the number of whom is as the sand of the sea.
(9) And they went up on the breadth of the earth, and
compassed the camp of the saints about, and the beloved city: and
fire came down from God out of heaven, and devoured them.
(10) And the
devil that deceived them was
cast into the lake of fire and brimstone, where the
beast and the false prophet are, and shall be tormented day and night for ever and ever.
(11) And
I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.
Each verse is talking about something else, not continuing the same episode as the previous one. The verse 6 is talking about the reign through the New Covenant era. The verse 7 talks about Satan being loosed afterward. The verse 8 talks about how he then goes out to deceive the nations The verse 9 talks about how they attacked the Church. The verse 10 talks about their judgment. The verse 11 then talks about the white throne judgment "
after" that. So I don't think you can dogmatically say this shows it is Judgment Day as indicated by the verses that follow. I would need more proof or evidence than that, because the whole chapter goes from Christ's first advent, death, church, the judgment of the Church, and white throne judgment. I'm assuming we agree that God sent them against the camp of the saints as judgment?
Rev 17:16-17
(16) And the ten horns which thou sawest upon the beast, these shall
hate the whore, and shall make her desolate and naked, and shall eat her flesh, and burn her with fire.
(17) For
God hath put in their hearts to fulfil his will, and
to agree, and
give their kingdom unto the beast, until the words of God shall be fulfilled.
Also, keep in mind God said:
Rev 20:9
(9) And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and
fire came down from God out of heaven, and devoured them.
This fire from God devoured "
them" and then afterward, the devil that deceived "
them" was cast into the lake of fire, and then the books were opened and the people were judged. Nothing is said about Satan and the beast/false prophet each being cast into lake of fire by 1,000 years apart.