Bell-Kochen-Specker theorem: A proof with 18 vectors

We present a ''state-independent'' proof of the Bell-Kochen-Specker theorem using only 18 four-dimensional vectors, which is a record for this kind of proof. This set of vectors contains subsets which allow us to develop a ''state-specific'' proof with ten vectors (also a record) and a ''probabilistic'' proof with seven vectors which reflects the algebraic structure of Hardy's nonlocality theorem.