Correct, you will have no net capital gain, thus no impact to your taxes owed. I agree it does seem a bit counterintuitive, but that's just how the law is written. For more complicated scenarios reconciling short- and long-term capital gains and losses, I like this article, which goes over the 4 possibilities.
This is just an Answer as to what might be acceptable to enter for Date acquired, when claiming 0 cost-basis (for an "unknown" scenario/strategy)..
This is H & R Block software's help tip for Date acquired field (emphasis on "VAR-L" option for long-term, per @littleadv 'Last Resort' Answer):
Here is a (less-reputable) reference suggesting that "Various"...