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a good example of irony is the song: Ironic by Alanis Morissette

whose lyrics aren't ironic (they're examples of unfortunate situations), thus having a song about irony - that isn't actually ironic (in its lyrics)

thus making it the best ironic song ever

With the possible exception of the lyrics "rain on your wedding day," which in some ways seems like a bad thing, but is supposedly good luck.

Aside from that, the entire song is filled with non-ironic scenarios, yep. Agreed: the most unintentionally ironic song ever.