  BCK-sequences and n-commutative BCK-algebras were introduced by T. Traczyk,
together with two related problems. The first one, whether BCK-sequences are
always prolongable. The second one, if the class of all n-commutative
BCK-algebras is characterised by one identity. W. A. Dudek proved that the
answer to the former question is positive in some special cases, e.g. when
BCK-algebra is linearly ordered. T. Traczyk showed that the answer to the
latter is affirmative for n = 1, 2. Nonetheless, by providing counterexamples,
we proved that the answers to both those open problems are negative.
