Re: truth/falsity of sentences in first-order logic

If I remember correctly, there is a proof for every valid sentence,
correct?

That's correct.

Is there a corresponding proof for invalid sentences?

I'm not sure what you mean. If a sentence is not valid (i.e.
there is at least one model in which it's false), then the
sentence does not have a proof.

With "invalid" I meant "not valid". So, to restate my question: is it
possible to prove in first-order logic that a sentence is not valid?
Obviously there will not be a proof of the sentence's validity, but can
this non-existence be proved in first-order logic?

ALiX

.