What's the word — an ironic situation
Solution 1:
The word is self-refuting (or self-defeating).
In his Introduction to Logic, Harry Gensler defines a self-refuting statement as “[A] statement that makes negative claims so sweeping that it ends up denying itself.”
For instance, Truth does not exist (Is that a true statement?); Nothing is absolute (Is that absolutely true?); "I cannot speak a word of English”
There is a difference between self-contradiction and self-refutation.
Are you asleep? yes (self-refutation).
I am sleeping and not sleeping. (self contradiction)