On the local closure of clones on countable sets

We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable, then there is a function $f : $\mathbb{N}$ \to $\mathbb{N}$$suchthatthe$n$-arypartof$C$isequaltothe$n$-arypartof$$\mathrm{P}\mathrm{o}\mathrm{l}$,$\mathrm{I}\mathrm{n}\mathrm{v}$^{[f(n)]} C$,where$$\mathrm{I}\mathrm{n}\mathrm{v}$^{[f(n)]} C$denotesthesetof$f(n)$-aryinvariantrelationsof$C$.