Are women superior to men?

Men are need to maintain society, imagine if this only happened in America and everywhere else remained the same. I'd give the country a generous month before it was invaded by everyone and their dog. Would women fight back? Maybe. Would women's like of proficiency in combat relative to men result in them losing? Do I need to ask$1  
Although, this might be a good basis for a sociological experiment. You and everyone else who believes that women can exist without men should petition the UN for your own country; or at least form your own independent community. The only rule being that you must build and maintain everything from scratch without outside help, especially that of men. The only manmade instrument you'd be allowed is the means to produce artificial semen. If women are truly superior in every way described on this page, then you should have no problems creating a thriving community in a matter of months.