To be and auxiliary verbs like have (have eaten etc.) are negated by adding "not" after the verb, whereas most verbs are negated by prefixing a negated auxiliary to do:
The sheep are wolves in disguise / The sheep are not (aren't) wolves in disguise
The sheep have exploded / The sheep have not (haven't) exploded
The sheep can juggle flaming torches / The sheep cannot juggle flaming torches
The sheep will pay the tab / The sheep will not pay the tab
Those sheep should behave like mature adults / Those sheep should not behave like mature adults
The sheep discuss quantum mechanics / The sheep do not (don't) discuss quantum mechanics
The sheep danced the Lindy Hop / The sheep did not (didn't) dance the Lindy Hop
Notice that to do takes the tense: "did not danced" is wrong.
That's the basics. Hope it helps! Search "negative verbs in English grammar" for more.