Predictions: even in a society which has eliminated gender discrimination and doesn't impose any pressure to conform to stereotypical roles, there will be more female teachers and more male engineers, more women than men will quit their jobs to raise children, and males will be overrepresented among criminals, the homeless, and the very top achievers in most fields.
Granted that will be hard to demonstrate, because the very fact of any disparity in outcomes can also "prove" that discrimination still exists.