Somehow I assumed that you'll need to resolve them in order
Resolved in order, not broke in order.
Rules page 18 wrote:
When the Runner encounters a piece of ice, he has the
opportunity to break any subroutines on that piece of ice.After
the Runner finishes breaking any subroutines that he wishes
to break, each unbroken subroutine on that ice triggers in the
order as listed on the card. If a subroutine ends the run, then
the run ends immediately and no further subroutines on that
piece of ice trigger.