The phrase "can not" may mean "cannot" or "can't," but it also may mean "able not to," which is much different than "not able to" as it conveys the ability to not do something rather than the inability to do it.
Why is “cannot” spelled as one word whereas other similar constructions such as “do not,” “will not,” “shall not,” “may not” and “must not” are spelled as two words (unless they are contracted as “...
1 There is no correct way to use "cannot help but." There are two traditional and synonymous idioms, "cannot but [do something]" and "cannot help [doing something]." Those who say "cannot help but" are conflating the two (in much the same some people conflate "irrespective" and "regardless" to create the nonsensical "irregardless").
Generally, people use can't in speech and informal writing, and cannot or can not in formal writing or very formal speech. Also (as @Kris points out in a comment), cannot might be used when you need to carefully distinguish it from can't in speech.
differences - When to use "cannot" versus "can't"? - English Language ...
As does Thesaurus.com: The terms cannot and can not are identical in meaning and are typically considered to be alternate forms of one another. However, the form cannot is much more commonly used than can not. Cannot has become the standard form in formal writing (and is typically the form recommended by most grammar resources and style guides).
Why is “cannot” spelled as one word? - English Language & Usage ...
5 OED-cannot definition: the ordinary modern way of writing can not Both cannot and can not are acceptable spellings. There’s no difference in meaning between cannot and can not. but the cannot is much more usual. Some references from ELU - can't vs cannot Why is “cannot” spelled as one word?.. (a few exceptions)