  The Halpern-Shoham logic is a modal logic of time intervals. Some effort has
been put in last ten years to classify fragments of this beautiful logic with
respect to decidability of its satisfiability problem. We contribute to this
effort by showing - what we believe is quite an unexpected result - that the
logic of subintervals, the fragment of the Halpern-Shoham where only the
operator "during", or D, is allowed, is undecidable over discrete structures.
This is surprising as this logic is decidable over dense orders and its
reflexive variant is known to be decidable over discrete structures.
