Negation with not
When a finite clause is negated by the negative adverb not, exactly one auxiliary must occur before the negation. Consider, for example, the following positive-negative pairs, where the verb phrases have been highlighted:
(1a) The solution may seem apparent.
(1b) The solution may not seem apparent.
(2a) The results should be compared to those of our previous experiment.
(2b) The results should not be compared to those of our previous experiment.