Is the shape category of Hausdorff compact spaces complete with respect to the inverse limit operation?

WARNING: the shape theory of Hausdorff compact spaces is continuous with respect to inverse limit; this (by itself) doesn't mean that the shape theory of Hausdorff compact spaces is complete--as long as I know, it is as open question as it was since the time when the shape theory of Hausdorff compact spaces was defined.

REMARK: the inverse limit of a shape inverse sequence of Hausdorff compact spaces always exists; the countable case is fine.