  In the monograph "Axioms and Hulls" (1992) Donald Knuth studies some
axiomatizations of geometric situations. The structures described by one of the
axiom systems are called CC-systems. Knuth proves that it is NP-complete to
decide, whether a partially defined CC-system can be extended to a complete
CC-system. The aim of this note is to show that Knuth's proof of this result
also implies that it is NP-complete to decide the extendability of partially
defined chirotopes.
