Batman clearly didn't die in Batman R.I.P., because Final Crisis takes place immediately after it. Technically, Bruce Wayne died for a short time (I think it was like 4 minutes?) after being shot in the Black Glove story arc that lead up to R.I.P. But he never actually died in R.I.P., despite coming very close. After Final Crisis Bruce Wayne is assumed to be dead, but really he's just sent through time by Darkseid.
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