St. Robert Bellarmine, De Romano Pontifice, II, 30: "A pope who is a manifest heretic automatically (per se) ceases to be pope and head, just as he ceases automatically to be a Christian and a member of the Church. Wherefore, he can be judged and punished by the Church. This is the teaching of all the ancient Fathers who teach that manifest heretics immediately lose all jurisdiction."

St. Antoninus (1459): "In the case in which the pope would become a heretic, he would find himself, by that fact alone and without any other sentence, separated from the Church. A head separated from a body cannot, as long as it remains separated, be head of the same body from which it was cut off. A pope who would be separated from the Church by heresy, therefore, would by that very fact itself cease to be head of the Church.
He could not be a heretic and remain pope, because, since he is outside of the Church, he cannot possess the keys of the Church." (Summa Theologica, cited in Actes de Vatican I. V. Frond pub.)

St. Irenaeus, Against Heresies, c. 185: “And the heretics, indeed, who bring strange fire to the altar of God – namely, strange doctrines – shall be burned up by the fire from heaven, as were Nadab and Abiud. But such as rise in opposition to the truth, and exhort others against the Church of God, [shall] remain among those in hell, being swallowed up by an earthquake, even as those who were with Core, Dathan, and Abiron.”

* A Heretic is a baptized person who rejects an authoritative teaching of the Roman Catholic Church. A schismatic is a person who refuses communion with a true Pope or refuses communion with true Catholics. An apostate is a person who rejects the Christian faith completely. All heretics, schismatics and apostates sever themselves from the Catholic Church automatically (Pius XII, Mystici Corporis, June 29, 1943). Therefore, if one is a heretic he is not a Catholic (Pope Leo XIII, Satis Cognitum June 29, 1896). And most heretics convince themselves that they are not denying any dogma when they actually are.