Not all atheists are intellectuals, not all intellectuals are atheists.However, all "intellectual atheists" are intellectuals and atheists.
Also, all Objectivist Freethinkers are "Intellectual Atheists" but not all "Intellectual Atheists" are Objectivist Freethinkers. Objectivism means that there are two criteria to be met in order for belief....(1) there is sufficient objective evidence for supporting the claim and (2) there is derivation of rigorous logical proof. Intellectual atheism only requires the latter criteria, which is flimsy because the argument amounts to a logical proof whereby the initial terms can be defined independent of natural processes.
In short, somebody could define a logical proof for the existance or nonexistance of god, assuming that the definitions of the terms are phrased appropriately and thereby the intellectual would be satisfied (variations of Godel's Theorems can be used either way depending on how the term "sets" are defined as per the supernatural and natural sets or by defining God as being "greater than the sum of the net intelligence in the universe" or etc).
However, the objectivist is not satisfied by pure logic, but requires naturalistic evidence to warrant the terms provided.
