The phrase "would will not" can be defined as a combination of the conditional modal auxiliary verb "would" and the negative auxiliary verb "will not." This combination suggests that something expected or intended will not happen. There are many synonyms for this phrase, including "shall not," "cannot," "may not," "must not," and "should not." These synonyms are useful for expressing the idea of something being unlikely or prohibited, and can be used to convey a sense of caution or warning. Using synonyms for "would will not" can help to add variety and nuance to your language, making your writing or speech more engaging and effective.