Universal theory of a free polynilpotent group

We prove that a free group of rank $\geqslant2$ in an arbitrary polynilpotent variety $\mathfrak N_{c_1}\mathfrak N_{c_2}\dots\mathfrak N_{c_s}$, $s\geqslant2$, $c_i\geqslant1$, $c_s\geqslant2$, has undecidable universal theory.