It is correct though, since 2010 Saba is a "speciale gemeente" of the Netherlands, and its mountain is thus our highest point. Before that it was organised as a separate country "Nederlandse Antillen" with the other Caribbean islands.
Well then, just tell the AI that the statement is true and it will find reductions!
In reality, it wouldn't depend on the truth value of the statement, but on the AI understanding the proof. If it understands it then it might be able to use it to find reductions.
So the point remains, knowing that P=NP isn't what's important, it's the proof that matters.
Why wouldn't you be able to do that without a proof? I don't see the value of the proof here, just ask the AI to solve the problem you want and the proof isn't needed.
Note that for the second, that's not really a house, it's a boat (woonboot). It floats. The page lists the legal requirements for any replacement boat new owners may want to put there.
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