Finding an NP Problem

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This project is to ether find a problem that is \mathbb{N}\mathbb{P}, but neither \mathbb{N}\mathbb{P}-Complete or \mathbb{P}. It could be proved that there does not exists a problem that is \mathbb{N}\mathbb{P}, but neither \mathbb{N}\mathbb{P}-Complete or \mathbb{P}. If this was true then there would be three separate problem classes \mathbb{P}, \mathbb{N}\mathbb{P}-Complete, and \mathbb{N}\mathbb{P}-Hard.

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