A standard trick reveals that knowing whether a problem has a solution is almost as helpful as knowing the solution. Here is a (very inefficient) way to use this ability

I figure the AI will be smart enough to recognize the strategy you are using. In that case, it can choose to not cooperate and output a malicious solution. If the different AIs you are running are similar enough, it's not improbable for all of them to come to the same conclusion. In fact, I feel like there is a sort of convergence for the most "unfriendly" output they can give. If that's the case, all UFAIs will give the same output.