I think that if you argue so, you must also admit that mathematical prowess isn't related to intelligence (and such, that your mathematician adversary being faster than you at symbolic logic didn't prove him or her smarter) or you would be on contradiction.

Another discussion is IQ correlation with chess prowess or mathematics ability. I would argue that chess and mathematics are two separated skills which are applications of intelligence; so there's definitely a correlation between both, but entirely determined by experience.