The class of Fedorchuk compact spaces is anti-multiplicative

A Hausdorff compact space is called a Fedorchuk compactum (or F-compactum) if it admits a decomposition into a special well-ordered inverse system with fully closed neighboring projections. It is known that the product of fully closed mappings is not fully closed, as a rule. We prove the same property for the class of Fedorchuk compacta: the product of F-compacta of spectral height 3 is never an F-compactum of countable spectral height.