Should i greet someone who treats me with scorn?

Hello Pals, i need ur oppinion on this:

Should i greet someone, (good morning), who treats me with scorn?

We see everyday bcos we work in the same place. We have no special interest except our place of work.
Ordinarily, she will most times not initiate a greeting (eg Good morning) and when i do, i look so artificial and so uncomfortable
with lip greetings. General oppinion branded her as very difficult. My relationship with her is strictly official on job related issues.
as one of my decisions to avoid quarrels bcos she can do so publicly.
I'm sure am older. Am higher in rank and more knowledgeable in the job but i dont give her instructions and do assist her
with some of her job related difficulties even when she is reluctant. Her disrespectful act is really painful sometimes.

Also, am a human being, am not perfect...........But

I want to stop greeting her but not certainly enmity. Am convinced about that. Thanks.

Because you keep greeting her, she probably thinks you are interested in her. So she is trying to keep her 'pride' by not greeting you. If truly you are not interested in her, stop greeting her and keep all contacts with her official. Some ladies think too highly of themselves and they should be ignored. Simple.