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The Eastern Chruch never accepted the false claims of the Roman Church and refused to submit to its insistence that the Bishop of Rome was supreme ruler of the Church.

Not true. Pope Hormisdas demanded that the Eastern bishops sign what is know as the Formula of Hormisdas to end the Acacian schism. In 519 two hundred Eastern bishop came to Constantinople and did so. This is what they signed:

The first condition of salvation is to keep the norm of the true faith and in no way to deviate from the established doctrine of the Fathers. For it is impossible that the words of our Lord Jesus Christ, who said, “Thou art Peter, and upon this rock I will build my Church,” [Matthew 16:18], should not be verified. And their truth has been proved by the course of history, for in the Apostolic See the Catholic religion has always been kept unsullied. From this hope and faith we by no means desire to be separated and, following the doctrine of the Fathers, we declare anathema all heresies, and, especially, the heretic Nestorius, former bishop of Constantinople, who was condemned by the Council of Ephesus, by Blessed Celestine, bishop of Rome, and by the venerable Cyril, bishop of Alexandria. We likewise condemn and declare to be anathema Eutyches and Dioscoros of Alexandria, who were condemned in the holy Council of Chalcedon, which we follow and endorse. This Council followed the holy Council of Nicaea and preached the apostolic faith. And we condemn the assassin Timothy, surnamed Aelurus [”the Cat”] and also Peter [Mongos] of Alexandria, his disciple and follower in everything. We also declare anathema their helper and follower, Acacius of Constantinople, a bishop once condemned by the Apostolic See, and all those who remain in contact and company with them. Because this Acacius joined himself to their communion, he deserved to receive a judgment of condemnation similar to theirs. Furthermore, we condemn Peter [”the Fuller”] of Antioch with all his followers together together with the followers of all those mentioned above.
Following, as we have said before, the Apostolic See in all things and proclaiming all its decisions, we endorse and approve all the letters which Pope St Leo wrote concerning the Christian religion. And so I hope I may deserve to be associated with you in the one communion which the Apostolic See proclaims, in which the whole, true, and perfect security of the Christian religion resides. I promise that from now on those who are separated from the communion of the Catholic Church, that is, who are not in agreement with the Apostolic See, will not have their names read during the sacred mysteries. But if I attempt even the least deviation from my profession, I admit that, according to my own declaration, I am an accomplice to those whom I have condemned. I have signed this, my profession, with my own hand, and I have directed it to you, Hormisdas, the holy and venerable pope of Rome.

The claims of the Orthodox that they never accepted the claims of Rome are not true.