Intuit

From dictionary.reference.com:

The use of intuit as a verb is well established in reputable writing, but some critics have objected to it. Only 34 percent of the Usage Panel accepts it in the sentence Claude often intuits my feelings about things long before I am really aware of them myself. This lack of acceptance is often attributed to the verb's status as a back-formation from intuition, but in fact the verb has existed as long as other back-formations, such as diagnose and donate, that are now wholly acceptable. The source of the objections most likely lies in the fact that the verb is often used in reference to more trivial sorts of insight than would be permitted by a full appreciation of the traditional meaning of intuition. In this connection, a greater percentage of the Panel, 46 percent, accepts intuit in the sentence Mathematicians sometimes intuit the truth of a theorem long before they are able to prove it. See Usage Note at enthuse.