  Chru\'sciel, Isenberg, and Pollack constructed a class of vacuum cosmological
spacetimes that do not admit Cauchy surfaces with constant mean curvature. We
prove that, for sufficiently large values of the gluing parameter, these
examples are both future and past null geodesically incomplete.
  The authors are honored to dedicate this paper to Robert Bartnik on the
occasion of his 60th birthday.
