  Any class of languages $\mathbf{L}$ accepted in time $\mathbf{T}$ has a
counterpart $\mathbf{NL}$ accepted in nondeterministic time $\mathbf{NT}$. It
follows from the definition of nondeterministic languages that $\mathbf{L}
\subseteq \mathbf{NL}$. This work shows that every sufficiently powerful
language in $\mathbf{L}$ contains a string corresponding to G\"{o}del's
undecidable proposition, but this string is not contained in its
nondeterministic counterpart. This inconsistency in the definition of
nondeterministic languages shows that certain questions regarding
nondeterministic time complexity equivalences are irrevocably ill-posed.
