Trivia question;
What do end time popes have to do with popeless catholics?
Answer that question and you are still on topic.
Answer differently and you have derailed the thread.
There are several groups that use the name Catholic and that have "fathers".
But I will assume that you are referring to the ROMAN Catholics and the Vatican..
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Several times the RCC, Methodists, and other have tried to settle questions that have divided them.
But in in every case that I know of, the last obstacle to unification is always the authority of the Vatican over everyone else.
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So I would say that you can't have a ROMAN Catholic "Church",
Without the Vatican and a "holy father", (Caesar woship, man is god, worship the creation, Babylon, Babel,confusion, mystery).
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The 4th beast of Dan 7, and the iron legs of Dan 2, Rome, are still with us today.
But not the original Roman Empire, only the "image", the spiritual image of Caesar worship.
Caesar worship is one facet of a greater lie which is Satan's words,
Worship Satan, the creation, rather than God the Creator.
This is shown to begin at the sin of Adam and Eve,
And continued until the earth was "cleansed" in the flood of Noah's time.
After the first cleansing, the lie reappeared at the tower of Babel in various forms of creation worship,
Sun, Moon, numbers, Zodiac, Creatures, elements, and other imaginings,
And people, ancestor worship, the conjuring of spirits of the dead, idolizing the living, etc.
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This "mystery" religion of Babel/Babylon is here with us still,
Sometimes disguised, RCC, Spiritualist Churches (speak to familiar spirits), witchcraft.
Sometimes not disguised, Zodiac believers, Satan worshipers.
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I pray that all Catholics find salvation.
All Jews, Islam, all people, turn to Jesus as the Messiah, obey the gospel and make it to heaven.
But it is not our part to separate the wheat from the chaff.
We must preach and teach,
Provide food and water to others, show that God is love.
I am for the people.
But against the system which is the spirit of Satan.
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The beast of Rome is only the image of the Roman Empire now.
But his goal is still the same,
Kill Israel and God's people, destroy God's love.
The only thing left that he can do now to destroy Israel, is to deceive the Kings of the East (Iran) into conquering Jerusalem.