Is it appropriate to omit "will not be"?

ellipsis modal-verbs future will-be-going present-tense

Solution 1:

Your two quotes don't actually have the same meaning. "I'm not living there!" is close to "I refuse to live there", while "I'm not going to be living there" is a prediction. Technically, the first is "I will not live there", while the second is "I shall not live there", but I doubt whether many people these days appreciate the difference, particularly with exclamation marks and apostrophes involved.

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