According to wiki we know that $$\mathsf{ACC^0\subseteq TC^0\subseteq NC^1\subseteq L\subseteq P\subseteq NP\subsetneq NEXPTIME}.$

Class $\mathsf{ACC^0}$ is included in $\mathsf{TC^0}$ is in http://en.wikipedia.org/wiki/ACC0#Computational_power.

Class $\mathsf{TC^0}$ is included in $\mathsf{NC^1}$ is in https://en.wikipedia.org/wiki/TC0.

Class $\mathsf{NC^1}$ is included in $\mathsf{L}$ which is included in $\mathsf{P}$ is in 
https://en.wikipedia.org/wiki/NC_(complexity)#The_NC_hierarchy.

Class $\mathsf{P}$ is included in $\mathsf{NP}$ is in https://en.wikipedia.org/wiki/P_(complexity)#Relationships_to_other_classes.

Class $\mathsf{NP\subsetneq NEXPTIME}$ is in http://en.wikipedia.org/wiki/NEXPTIME from time hierarchy theorem.

So does it mean, we already know $\mathsf{ACC^0\subsetneq NEXPTIME}$ even before Ryan Williams' breakthrough(http://en.wikipedia.org/wiki/ACC0#Computational_power)?