The verb 'to do' does exist, but the auxiliary 'do' does not exist (and I just used the auxiliary twice).
In English grammar, the negation of a verb uses a form of the auxiliary 'do'. We also use it when we ask questions and when we affirm, or make emphasis.
I know. (no emphasis)
I do know. (emphasis, or affirmation)
I don't know. (negation)
Lo sé. (no emphasis)
(Yo) sí lo sé. (emphasis, or affirmation)
No lo sé. (negation)
You know the answer. ((affirmed) statement)
You don't know the answer. (negated statement)
Do you know the answer? (question)
Don't you know the answer? ((negated) question)
Sabes la respuesta. ((affirmed) statement)
No sabes la respuesta. (negated statement)
¿Sabes la respuesta? (question)
¿No sabes la respuesta? ((negated) question)
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