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WordNet records no synonym and no antonym for beneficially. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
WordNet records no synonym, antonym, broader or narrower term for any of the 1 sense of beneficially. That is a fact about the database, not a gap we intend to fill by guessing: a great deal of technical, taxonomic and proper-noun vocabulary sits alone in its synset because English has no other word for it. The full entry still carries every definition, example and pronunciation.
Synonyms, antonyms and the broader and narrower relations for beneficially come from Princeton University’s WordNet. Full sources and licences.