It's standard. Why don't the machines know it?

The teaser reads: Згадайте людей, які віддали життя за нашу з вами країну. Не дозвольте забути. Нікому.
Небесна сотня. Реквієм.

Bing: Remember the people who gave their lives for our country with you. Don't let me forget it. Anyone.
Heavenly hundred. Requiem.
Google: Remember the people who gave their lives for our country with you. Do not be forgotten. None.
Heavenly hundred. Requiem.

What? WHAT? I don't understand this.

Oh, sure, they both have their different problems with the Не дозвольте забути construction - Ukrainian, like Russian, doesn't require the person not being allowed to be specified, and this means "don't let them be forgotten" or, more literally, "don't allow forgetting" - the next, emphatic one-word sentence being "no one" in the dative, that is marked as who must not be allowed to forget, rather than - as both translations suggest - who should not be forgotten. (Actually, Google's possibly means who shouldn't let me forget it.)

But that's not my gripe here.

What is this "gave their lives for our country with you"? They both say that. They're both totally wrong. Ukrainian (again, like Russian) uses this "we with X" construction to specify who the "we" is. "We with you" means "you and I"; "we with my husband" means "my husband and I"; "we with Bob" means, yes, "Bob and I." And that hold true for "our with you", too.

They "gave their lives for our your country and mine". Or possibly "our country" full stop. But certainly not "gave their lives for our country with you", which sounds like "you" are dead, too.

And what's the most annoying is that this construction is utterly standard and typical and something you learn pretty early on. But neither Google nor Bing has the first clue about it.

Remember the people who gave their lives for your country and mine. Do not let them be forgotten. By anyone
The Heavenly Hundred. Requiem.