Formal:
* Is not
* Has not
* Lacks
* Fails to
* Is devoid of
* Is absent of
* Is without
Informal:
* Doesn't
* Ain't (informal, can be considered slang)
* Hasn't got
* Is no
* Don't (if the verb is "do")
More specific:
* Is contrary to
* Is incompatible with
* Is inconsistent with
* Is the opposite of
Figurative:
* Is far from
* Is a long way from
* Is nowhere near
Example:
* "The cat does not like the dog." could be rewritten as:
* "The cat is not fond of the dog."
* "The cat lacks affection for the dog."
* "The cat hasn't got a liking for the dog."
The best alternative depends on the specific situation and the desired tone of your writing or speech.