  Formulation of the Penrose inequality becomes ambiguous when the past and
future apparent horizons do cross. We test numerically several natural
possibilities of stating the inequality in punctured and boosted single- and
double- black holes, in a Dain-Friedrich class of initial data and in
conformally flat spheroidal data.The Penrose inequality holds true in vacuum
configurations for the outermost element amongst the set of disjoint future and
past apparent horizons (as expected)and (unexpectedly) for each of the
outermost past and future apparent horizons, whenever these two bifurcate from
an outermost minimal surface, regardless of whether they intersect or remain
disjoint. In systems with matter the conjecture breaks down only if matter does
not obey the dominant energy condition.
