Consider a proposition stating something to be true that by the very act of stating denies truth to the speaker.
This is not a fallacy, which is an argument incorrect by virtue of its form. But I am looking for a general term for self-defeating statements of the kind described.
A fallacy is the use of invalid or otherwise faulty reasoning for the construction of an argument.
However, in this case, there is no argument. Alice says something which we know is not true. Then if Alice had used an argument to argue "Bob is smart", that argument would probably have been fallacious. But the simple act of saying something untrue is not fallacious, because there is no reasoning involved.
Self-defeating-in-context sentences are not usually called fallacies, but they do have a name, contextually determined contradictions, or Moor sentences. They are closely related to the knowability paradox anticipated by Church, see Is it provable that epistemically possible (possible for all I know) does not imply possible?. A Moorean sentence if true renders any assertion of it false. Some examples are "I am not here now", "I am asleep" (disregarding talking sleepwalkers), "I am dead" (disregarding talking ghosts, vampires, zombies, and other such beings). The radical skeptical claim "nothing is true" is often interpreted as self-refuting, although what actual skeptics assert is more like a counterfactual "if there was such a thing as truth nothing would be true". Here is a more complicated example that plays a role in disputes between realists and anti-realists: "P is provable but hasn't been proved". To know that P is provable one needs a proof, but any proof of provability of P is convertible into a proof of P, so P has been proved.
Negations of Moorean sentences, contextually determined tautologies, are interesting beasts in their own right. Albeit controversially, they are examples of contingent tautologies, logically true but not necessary. "I am here now" is a tautology, but it could be otherwise, I could be surfing in Hawaii instead. "I am awake", "I am alive" display the same thing. Classically, logical tautologies were considered necessary, but some recent logicians admit contingent ones, see How can a tautology not be necessarily true?
It seems to me "self-undermining" in context is entailed in the very definition of "fallacy."
So the question might be: Is there a fallacy that does not refute or undermine itself? That would be, perhaps, a fallacy translated into a context that justifies it.
"All Cretans are liars," claimed by a Cretan, then repeated by an Ionian may be true or false, but no longer undermines itself.
I agree with @Keelan's answer that the example in your post is not a fallacy.
Consider a proposition stating something to be true that by the very act of stating denies truth to the speaker.
There is the classical example of a Cretan saying: All Cretans are liars.
The characteristics of this type of example is stating a proposition, which refers to itself. As a consequence, such propositions have to be avoided.
"Smart" is a little ambiguous. It can imply intelligence, quick wit, a sharp sensation, neatness or just adequacy to occasion.
If, as a companion example, Alice states, "Bob is 18 years old and ten feet tall" when he is clearly closer to 81 and four feet tall, then she has made a false claim. Note that if Alice sincerely means that "Bob is 18 years of age and ten feet tall" then she is simply incorrect and the truth value can be verified in a variety of ways.
If she instead means something like "Bob has the youthful enthusiasm of an 18 year old" or "Bob is barely as mature as an 18 year old" then she is a poet and truth value is irrelevant - the listener can either agree or disagree with her opinion.
For an examination of how a statement can be "self-refuting" you might enjoy Professor John R. Searle's essay, "The Refutation of Relativism".
Not quite a fallacy, but I suspect that what you are referring to is reminiscent of the liar paradox:
This statement is false.
Cuonzo, Margaret (2014). Paradox. Cambridge, MA MIT Press:
You are referring to what are usually called 'self-refuting' statements.
These can be of different types :
'I am not speaking', said to someone. Practical self-refutation.
'It can be proved that nothing can be proved'. Logical self-refutation (a). If nothing can be proved, then nor can your claim that nothing can be proved.
'There are no truths'. Logical self-refutation (b). You are claiming as a truth that there are no truths.
'It's true but I don't believe it'. Moorean self-refutation (after GE Moore). The situation is possible in which X is true and in which I don't believe that X is true. But it is incoherent for me to say both that X is true and that I don't believe it; belief is the attitude appropriate to truth.
This is a fallacy of peer (or group) pressure. Many other people think something - therefore it must be correct. Either because
