  We prove that many pretzel knots of the form $P(2n,m,-2n\pm1,-m)$ are not
topologically slice, even though their positive mutants $P(2n, -2n\pm1, m, -m)$
are ribbon. We use the sliceness obstruction of Kirk and Livingston related to
the twisted Alexander polynomials associated to prime power cyclic covers of
knots.
