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I think you might be arguing that if a pope says something false, and says that that is infallible, it is still false. I know it would be false, but MattofTexas saidSuch a thing has never happened and is not likely to happen, but given the circumstances of your hypothetical, the answer is this: the statement, oral or written, would simply be false. The pope, though claiming to be speaking infallibly, would obviously not be, because he would be contradicting a doctrine. The Church would immediately know that the Pope, though claiming to be speaking infallibly, would not be.
You say it is unlikely that it would occur, so do you mean that the Holy Spirit does not constrain the popes’ free will to claim they are speaking infallibly when they are not? Obviously popes do not have the freedom to decide what doctrine is true or false, but MattofTexas said that the Holy Spirit would prevent the situation from ever occurring where a pope uses the infallible-style language to claim a falsehood is true or vice versa. It sounds like you’re saying that this is not necessarily true: that the Holy Spirit does not constrain the free will of the popes to claim they are speaking infallibly when they aren’t, but only constrains their free will to actually make the claim a different truth value by saying they said so infallibly, which is clear.the Holy Spirit would prevent such a situation from ever occurring.