There are various synonyms for the phrase "refuse to acknowledge" which have very similar meanings. Some of the most common alternatives include "ignore," "deny," "reject," "disclaim," "disavow," "repudiate," "turn a blind eye," "deny knowledge," "refute," "rebut," and "contest." All of these synonyms imply a lack of acceptance or recognition of a certain fact or situation. They also imply a certain level of defiance or resistance to the truth. These words can be used in different contexts such as in personal interactions, legal proceedings, and even in news reporting. Overall, these synonyms are useful tools for expressing a refusal to accept something as true.