Is it going to be proof that I am precognitive if after reading this thread I dream of precognitive penguins, and I will have written this post beforehand? Sorry, just a thought I had. And I really hope that I will actually dream of precognitive penguins, and that my mind will recognize this, and allow me to become lucid.

Precognition is just such a hard thing to prove. It would be cool if it were real. But alas coincidence is often a viable explanation or there are other viable explanations, and if there is a possible explanation that does not require a supernatural occurrence, then while it does not prove that nothing supernatural could have happened, but it does prove that the supernatural did not necessarily happen, and thus there is no proof for the supernatural there.