  We exhibit a knot $P$ in the solid torus, representing a generator of first
homology, such that for any knot $K$ in the 3-sphere, the satellite knot with
pattern $P$ and companion $K$ is not smoothly slice in any homology 4-ball. As
a consequence, we obtain a knot in a homology 3-sphere that does not bound a
piecewise-linear disk in any homology 4-ball.
