Single word meaning a statement which is proving itself wrong

Incongruous, inconsistent, or paradoxical is sufficient.

It is said to be self-contradictory.

I like self-refuting.

• self-contradictory and self-refuting imply an logical contradiction
• oxymoron implies only a surface contradiction, like the living dead or jumbo shrimp
• paradoxical implies a genuine question about its truth value

Responding to a couple points here...

Oxymoron(ic) can only be used in reference to a phrase - I think only a noun phrase - but not to a statement. And officially, I think, it should be used when the apparent contradiction is resolved when you understand what the phrase is referring to. (Like, the first time you hear "living dead" you're like, "WTF? Ohhhhhh... it's zombies!" And then it makes sense.") If it's really not resolvable, but is just an error, like "free-market communist", then it would be a contradiction in terms. (Though in common usage, I think you can use oxymoron for both.)

For a complete statement, you could use simply use self-contradictory, self-negating... I actually stumbled here looking for the same thing. I'm sure there's a cool latin phrase somewhere...