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 \({f : \mathbb{N} \rightarrow \mathbb{N}}\) such that the n-ary part of C is equal to the n-ary part of Pol \({{\rm Inv}^{f(n)]} C}\), where \({{\rm Inv}^{f(n)]} C}\) denotes the set of f(n)-ary invariant relations of C.