Why didn't the Jewish Pharisees PROVE Jesus Didn't Rise From the Dead?

You know, if Jesus really did not rise from the dead, the Jewish Pharisees who had Jesus crucified could have saved us all a lot of time and put a quick, easy end to the whole Christian movement by just saying "Jesus didn't die. We'll prove it. Here's his body!" Why didn't they do that? And in fact, why did one of the Pharisees, Paul (who doubtless was in a position to know if the body was gone or not) give up a life of luxury as a respected Pharisee to preach that He's seen Jesus alive...even though it cost him a lot of persecution and eventually death?