There are different ways TRP might argue that men are smarter than women, but the most common seems to be that women don't need intelligence because their gender gives them a free ride through life, and that their intelligence atrophies as a result.

A previously sidebarred post argues that intelligence is inversely proportional with attractiveness (and is met pretty evenly with upvotes and downvotes). Esthar Vilar's "The Manipulated Man" makes the same argument (I've posted some of her comments below the break), and is highly regarded within /r/TheRedPill (may also have been sidebarred at one time).

Another argument states that women find smarter men attractive, so it is to their evolutionary advantage to be stupid.

Yet another suggests that women know virtually nothing beyond their own personal experiences, and recommends you "Never Listen To A Woman."

Women do not use their mental capacity: they deliberately let it disintegrate. After a few years of sporadic training, they revert to a state of irreversible mental torpor.

This is an active decision, apparently made around age 5:

By the age of five, any girl will have been persuaded that she wants to get married and have a home and children; and when girls are ten, fifteen, or twenty, they still want the same things. So if a woman decides, even as a child, to live at man's expense, what good will intelligence and reasoning be to her?

A short selection of Vilar's comments on the stupidity of women, just to demonstrate this is a careful argument of hers and not something taken out of context here:

One of man's worst mistakes, and one he makes over and over again, is to assume that woman is his equal, that is, a human being of equal mental and emotional capacity.

To someone from outer space surely men would appear infinitely more worthy of admiration than women, for man has intelligence as well as beauty.

There is no female gourmet; women are good for almost nothing.

Once a human being is free, if it happens to be rather stupid (and women are stupid) it will be quite happy with its freedom and try to retain it.

The situation of the intelligent person, i.e., a man, is very different.

A critical man might well say that women have no self-respect. If they had, they would never admit the incredible extent of their ignorance as happily as they do.

it would never occur to [psychologists] for a minute that woman's so-called psyche is unfathomable merely because of the absence of intelligence; that feminine work appears unattractive to the male only because he is incapable of imagining the required degree of stupidity necessary to be able to enjoy it.

Women's stupidity is so overwhelming that anyone who comes into contact with it will become, in a way, infected by it.