I'd prefer to stick to the "deterministic" definition of NP, i.e:
-A language $L\subseteq {0, 1}^*$ is in $NP$ if there exists a polynomial $p : N \rightarrow N$ and a polynomial-time $Turing$ $Machine$ $M$ such that for every $x \in {\{0, 1\}}^*$ (that is, the set of all possible binary strings),
$$x \in L \Leftrightarrow \exists u \in {\{0, 1\}}^{p(|x|)} s.t. M(x, u) = 1,$$
taken from the book by Arora and Barak.
The question is: how can I check that a given $x$ does not belong to $L$ in a finite number of steps?