Santa Exists
Of course there are loads of interesting ways of generating a contradiction and using it to prove something humorously false, but I thought this one was worth copying.
Let S be the sentence, "If S is true, Santa exists".
1. Assume S is true.
Then, substituting for S, and by assumption:
2. "If S is true, Santa exists" is true.
So, by our assumption:
3. Santa exists
From only the assumption 1, we have reached 3, so we may conclude (without assumption):
4. If S is true, Santa exists.
So we have shown 4 is true, thus
5. "If S is true, Santa exists" is true.
Hence
6. S is true.
Using 4 and 6, we reach:
7. Santa exists.