it would be impossible to measure this and prove it because of all of the different factors that you cannot control for. Even if gender does make a difference, it can't possibly out-weigh all of the other factors that play into intelligence.
The only way to argue this is by having an exact definition of what intelligence is. Is it a one-dimensional value? Are there different kinds of intelligence? How do we measure it? As-is, the word "intelligence" has no clear definition so we cannot prove the claim. High risk of Equivocation fallacy
This is untestable. Even if we had a way to measure overall intelligence effectively, you certainly couldn't isolate gender alone as a variable. Even then, it's unclear whether gender here means biological gender, or gender roles, or both.
There is a difference in IQ distribution between the genders. There are more males with very high or low IQ, whereas females tend to have an IQ that is closer to average with less deviation from the middle.