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What infallibility does do is prevent a pope from solemnly and formally teaching as "truth" something that is, in fact, error. It does not help him know what is true, nor does it "inspire" him to teach what is true. He has to learn the truth the way we all do—through study—though, to be sure, he has certain advantages because of his position.
The pope's infallibility (as we understand it) is similar to the infallibility that the Oecumenical Councils have. The Pope's is an extension of this.
His teaching cannot contradict anything the Church has taught officially and previously.
Ecumenical Councils: RC church made numerous Councils that we do not consider Ecumenical. But you will imply that "the Pope cannot make mistakes" so these Ecumenical Councils whether our Orthodox Church attended or even agreed upon their conclusions or decisions is considered unnecessary! And you cannot claim we were invited then didn't come to the council so you had to proceed!!
Ecumenical means all the inhabited world, in other words ALL the Christians, ALL CHURCHES. Since the Disciples, these councils were held for major replies against heresies, for consolidation of faith where ALL meet. It is not a one party or a one man show.
And for instance, when you say Ecumenical Patriachate do you mean ALL Churches united or just All members of your own Church?