Does sperm make a pregnant woman's cervix dilate faster?

I am no Expert, or Pro on this subject but my girlfriend is currently pregnant and i have asked many question and read a lot on subjects like these. according to our doctor and a couple books there is a hormone in sperm which reacts with a hormone in the cervix which some say can cause it to dilate...... on the other hand this is not a fact. it has not been prooven 100% in my opinion my wife is nine months and 2 days past due we have had sex for the last week before her due date and ive injected my sperm in her each time and she has not dialated anymore then before she is now 2 days past due and she is still only 2cm.