According to wiki we know that $$\mathsf{ACC^0\subseteq TC^0\subseteq NC^1\subseteq L\subseteq P\subseteq NP\subsetneq NEXPTIME}$$ the last inequality from Time hierarchy theorem (http://en.wikipedia.org/wiki/NEXPTIME). 

So does it mean, we already know $\mathsf{ACC^0\subsetneq NEXPTIME}$ even before Ryan Williams' breakthrough?