"not without doubt" is correct and usable in written English.
You can use it when you want to state that something might be true, but it is not certain. Example sentence: His sincerity is not without doubt, as he has not always been honest in the past.
He is not without doubt as to the success of such a venture.
Their historical premises are not without doubt and, at the very least, are overstated.
When his boots fell apart he took some, not without doubt and deliberation, from a nameless corpse; they served him well.
Commitment is healthiest when it is not without doubt but in spite of doubt".
Today's fans can feel some of the same thrill, but not without doubts and cynicism creeping in, and nothing can really undo that change.
"No wonder you are finding Sarah!" After the show, Ms. Ferguson was exhilarated, but not without doubts about the audience's reaction.
"Although the dealers are predominantly U.K.-based, the art is not, and without doubt it reflects the diversity of London, which, after all, is the most cosmopolitan city.
These results report students' attitudes toward the various medical conditions, but the findings do not confirm without doubt why students reported such a level of regard.
Know what is beyond your target and never fire uphill when you do not know without doubt what lies beyond the horizon line within range.
"Without ambiguity, we don't accept to do business with countries that don't accept, without doubt, international controls," she said.
So rather than list out all of the things Heins needs to do to save the company (which, we can all agree, would take a really long time), I'm going to tell you guys the five things that Mr. Heins absolutely must not, without a doubt, under no circumstances… do.
