In logic the word "imply" is used to mean necessarily leads to the consequent. A ⇒ B means if A is true then B is also true. The arrow in logic means "implies". However in general English "imply" doesn't carry this meaning of necessity. Example:
"His expensive car and clothes imply he's wealthy." (No necessity, only suggestion)
Therefore I'd suggest a stronger word, "entail".
1. To have, impose, or require as a necessary accompaniment or consequence:
The investment entailed a high risk. The proposition
X is a rose entails the proposition X is a flower because all roses
American Heritage Dictionary
"His expensive car and clothes entail he's wealthy." (false premise,
"Killing a person entails you've committed homicide." (Means by
Though it is a rather formal word. Another way of saying it is:
"A doesn't necessarily follow from B."
Also, I would use "necessarily" instead of "automatically". but that's just preference.
Oh, I almost forgot to answer the question. There are some words which mean the negative of another word. For example the negative of "To do" is "To not do", which can be covered by the word "refrain". Or "indulge" - "to not indulge" or "abstain". In this case I can't think of such word for your example, I would just negate it with "not", "it does not entail."