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You can see some examples here, here and here.
The official notice from YouTube under the video says the following:
"This video contains an audio track that has not been authorised by all copyright holders. The audio has been disabled."
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If YouTube starts being thorough about this, you can expect to see a significant percentage of all YouTube videos muted. The implications are a bit different than with removing copyrighted professionally produced content, like an official music video; we're talking about tens of thousands of fan made videos, funny spoofs, remixes and the like being pretty much destroyed, and I'm guessing users will be less than thrilled about it.