A set $\Sigma$ of group identities is called bounded if there is $n\geq 1$ such that for any $(w\approx 1)\in \Sigma$, we have $w\in F(x_1, \ldots, x_n)$. A variety $\mathbf{V}$ is called bounded defined if $\mathbf{V}=Mod(\Sigma)$ for some bounded set $\Sigma$.

Question: Is there an example of a bounded defined non-finitely based variety of groups?

P.S. $F(x_1, \ldots, x_n)$ is the free group of rank $n$.