(complement x) ==#'(lambda (&rest arguments) (not (apply x arguments)))
In Common Lisp, functions with names like "xxx-if-not"
are related to functions with names like "xxx-if" 
in that
(xxx-if-not f . arguments) ==(xxx-if (complement f) . arguments)
For example,
 (find-if-not #'zerop '(0 0 3)) ==
 (find-if (complement #'zerop) '(0 0 3))  3
 3
Note that since the "xxx-if-not" functions
and the :test-not arguments have been deprecated,
uses of "xxx-if" functions or 
:test arguments with complement are preferred.