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Ok, after doing some extra research, I've put together that there was a movie titles "The Aristocrats" (which was all based around that popular joke), and Trey and Matt make an appearance in it. The crew of the movie asked them to make this short film with Cartman and his friends. But I do not yet know if it ever appeared on TV or what it was used for. I recommend going to the South Park FAQ page and hope they will give you some useful information: