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I'm guessing that your statement is sarcastic but there's more truth in it than you probably realize. Most of the encylical linked is background, the infallible statement comes towards the end: "We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful.

(Declaramus, pronuntiamus et definimus doctrinam quae tenet beatissimam Virginem Mariam in primo instanti suae conceptionis fuisse singulari Omnipotentis Dei gratia et privilegio, intuitu meritorum Christi Jesu Salvatoris humani generis, ab omni originalis culpae labe praeservatam immunem, esse a Deo revelatam, atque idcirco ab omnibus fidelibus firmiter constanterque credendam.)

This is a very rare thing, the exercise of papal infallibility, John Paul II has used it only a few times, the most famous being:

“Therefore, by the authority which Christ conferred upon Peter and his Successors, in communion with the bishops—who are various occasions have condemned abortion and who in the aforementioned consultation, albeit dispersed throughout the world, have shown unanimous agreement concerning this doctrine declare that direct abortion, that is, abortion willed as an end or as a means, always constitutes a grave moral disorder, since it is the deliberate killing of an innocent human being. This doctrine is based upon the natural law and upon the written Word of God, is transmitted by the Church’s Tradition and taught by the ordinary and universal Magisterium.”

(Evangelium vitae, #62) "

This is a great statement to use as an example since it pretty much spells out the requirements for an ex cathedra statement