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Questions about decision problems that can be solved on nondeterministic Turing machines in time polynomial in the length of the input.

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Is $NP$ "minimal", i.e. does $\Pi\notin NP$ imply $\Pi$ is $NP$-hard?

Does $\Pi\not \in NP$ imply $\Pi$ is $NP$-Hard? Edit: if we assume there exists $\Pi\in coNP\setminus NP$ then we are done. Can we refute the claim without any unknown assumptions? …
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