I have heard that the catholic church moved christs' birthday to dec.25th to overshadow a "pagan" holiday?

when rome fell they had public baths,plumbing and many other advances the church didn't want people to have there is proof that a past pope sold thousands of pardons to absolve people of the earthly sins all signed by the sitting pope. past history of the church to me gives credence that this is true, if so what is the true date of christ's birth and what pagan holiday do they do away with?