The Pope is theologically infallible.
If the Pope says that he is not, based on his infallibility, he is correct.
Which means, since he is correct, that he really is fallible.
His statement about being fallible is true, then he may be infallible.
But he said that he is fallible, which in the case of it not being true, he is fallible.
This can go on forever.
Did any Pope ever said anything against Papal Infallibility? What will happen if any will?
The Ultramontanists will employ Jesuitry to explain it away.
The fact remains that trying to identify when he speaks "ex cathedra" resembles trying to nail jello. Before 1870 they explain away all sorts of corners of dogma that the "supeme pontiffs" have, well, cornered themselves in.
Pope Leo III banned the filioque, and nailed the Creed in its Orthodox form on St. Peter's and St. Paul's outside the wall. Pope Leo IX sends his cardinal to force the Orthodox to recite the filioque.
The whole mess of the Cadaver Synod, which, as I've recently pointed out, involved the issue of the Eighth Ecumenical Council.
Looking through Dvornik, I came across this:
At all events, Formosus upheld the legitimacy of Photius' rehabilitation by John VIII and by the Council of 879-80, so that the ordinations made by Photius under his patriarchate were not only valid, but also licit and there was no reason for reconsidering them.p. 254
This has major implications.
Formosus was dug up and deposed by his successor, who was deposed by his successor and Formosus exonerated, but then his successor dug Formosus up again and deposed him etc.
With all the alternating depositions post mortem, a major question was that they considered the deposed's ordinations and other acts void.
Now the problem is that the Vatican now considers Constantinople IV 869 an Ecumenical Council. But Formosus evidently (with John VIII) considered Constantinople IV 879, valid, which voided 869. With Formus' acts voided, 869 would be valid; whenever Formosus was exonerated, 879 was valid. Hence we have a string of pope contradicting themselves ex cathedra on who sat on the cathedra, and hence which was an Ecumenicl Council, and hence a matter of faith and morals which Vatican I claims the pope can never deviate.
Btw, it's been discussed before.
Then there is the whole Pope Honorius, who was a heretic (the Ultramontanists never tire of trying to split hairs over that one, but that great supporter of the Orthodox, the old "Catholic Encyclopedia" says it best:
It is clear that no Catholic has the right to defend Pope Honorius. He was a heretic, not in intention, but in fact; and he is to be considered to have been condemned in the sense in which Origen and Theodore of Mopsuestia, who died in Catholic communion, never having resisted the Church, have been condemned
The condemnation of Pope Honorius was retained in the lessons of the Breviary for 28 June (St. Leo II) until the eighteenth century. Difficulties made themselves felt when, after the Great Western Schism, papal infallibility began to be doubted. Protestantism and Gallicanism made vigorous attacks on the unfortunate pope, and at the time of the Vatican Council Honorius figured in every pamphlet and every speech on ecclesiastical subjects. The question has not only been debated in numerous monographs, but is treated by the historians and the theologians, as well as by the professed controversialists. Only a few typical views need here be mentioned.
Bellarmine and Baronius followed Pighius in denying that Honorius was condemned at all. Baronius argued that the Acts of the Council were falsified by Theodore, a Patriarch of Constantinople, who had been deposed by the emperor, but was restored at a later date; we are to presume that the council condemned him, but that he substituted "Honorius" for "Theodorus" in the Acts. This theory has frequently been shown to be untenable.
Bishop Hefele before 1870 took the view that Honorius's letter was not strictly heretical but was gravely incorrect, and that its condemnation by an ecumenical council was a serious difficulty against the "personal" infallibility of the popes. After his hesitating acceptance of the Vatican decrees he modified his view; he now taught that Honorius's letter was a definition ex cathedra, that it was incorrectly worded, but that the thought of the writer was orthodox (true enough; but, in a definition of faith, surely the words are of primary importance); the council judged Honorius by his words, and condemned him simply as a Monothelite; Leo II accepted and confirmed the condemnation by the council, but, in doing so, he carefully defined in what sense the condemnation was to be understood. These views of Hefele's, which he put forth with edifying modesty and submission as the best explanation he could give of what had previously seemed to him a formidable difficulty, have had a surprisingly wide influence, and have been adopted by many Catholic writers, save only his mistaken notion that a letter like that of Honorius can be supposed to fulfil the conditions laid down by the Vatican Council for an ex cathedra judgment (so Jungmann and many controversialists).
Chapman, J. (1910). Pope Honorius I. In The Catholic Encyclopedia. New York: Robert Appleton Company. Retrieved September 13, 2009 from New Advent: http://www.newadvent.org/cathen/07452b.htm
Ecclesiastical approbation. Nihil Obstat
. June 1, 1910. Remy Lafort, S.T.D., Censor. Imprimatur
. +John Cardinal Farley, Archbishop of New York.
The discovery of the Liber Diurnus Romanorum Pontificum made Honorius rehabilitation impossible for Pastor Aeternas.http://www.newadvent.org/cathen/09215c.htm
Nihil Obstat. October 1, 1910. Remy Lafort, Censor. Imprimatur. +John M. Farley, Archbishop of New York
it can go on and on and on
Not totally on point, but fun nonetheless is Pope Pius II forbidding mass to be said for Pope Alexander VI because "It is blasphemous to pray for the damned." Wrong there too.