I batch sparge, but am not sure what you're asking.
Are you asking how much sparge water to add, and in how many additions?
If so, you should work backwards: 5.5 gallons + deadspace in your cooler + boil off + trub + grain absorption = total volume necessary.
From there, subtract off 1.25 x 12.5 qts, and that leaves you with how much sparge water you'll need to add. Most things I've read indicate that splitting this amount into two equal halves increases efficiency a bit, likely due to the add'l stirring that happens when the second part is added.