No clear case known
- Some statement X was made, intended to be infallible
- Later, 1) evidence has shown X to be false or 2) X was retracted/reformulated/revised by a subsequent statement, illustrating that the previous statement was obviously not infallible
It is not possible to find a simple contraction like this, because the statement is mostly not marked as "infallible" when made, its infallibility is only derived from context. There are only two statements made by a pope which are not disputed regarding their "ex cathedra" status, and those are two recent dogmas of the Immaculate Conception (1854) and the Assumption (1950). See Instances of papal infallibility in Wikipedia.
With any other statement which you may think that it was made ex-cathedra in its time and can be shown as not held any more, or not true, the proponents of the papal infallibility faith will claim it was not made "ex cathedra" at all.
I will try to search for some particular case which could could be used to demonstrate this, but as it is time consuming, I have no idea now when I will be able to do it.
What is ex-cathedra
The currently used definition comes from First Vatican Council (1869-1870):
"When the Roman Pontiff speaks ex cathedra...as the pastor and teacher of all Christians [and] defines a doctrine of faith and morals that must be held by the Universal Church, he is empowered, through the divine assistance promised him in blessed Peter, with the infallibility with which the Divine Redeemer willed to endow his Church."(24)
A trouble is there is not a clear consensus between catholics regarding how to recognize when a statement is made Ex cathedra, therefore it may easily happen a statement which might had been considered as ex cathedra at the time it was issued is classified as an ordinary statement later. See e.g. Encyclical entry in the New Advent Catholic Encyclopedia:
it is generally admitted that the mere fact that the pope should have given to any of his utterances the form of an encyclical does not necessarily constitute it an ex-cathedra pronouncement and invest it with infallible authority. The degree in which the infallible magisterium of the Holy See is committed must be judged from the circumstances, and from the language used in the particular case.
The guide how you can distinguish an "infallible statement" nowadays, as accepted by the Catholic Church is as follows:
- "the Roman Pontiff"
- "speaks ex cathedra" ("that is, when in the discharge of his office as shepherd and teacher of all Christians, and by virtue of his supreme apostolic authority….")
- "he defines"
- "that a doctrine concerning faith or morals"
- "must be held by the whole Church" (Pastor Aeternus, chap. 4)
And there are similiar rules for "infallible council teaching":
- a verbal formula indicating that this teaching is definitive (such as "We declare, decree and define..."), or
- an accompanying anathema stating that anyone who deliberately dissents is outside the Catholic Church.
However, there is a caveat: there is no guarantee the guide will not change in the future, as it has never been rigorously formulated by an "infallible" authority.