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Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
counterexample is a noun meaning "refutation by example". It carries one recorded sense.
refutation by example
Forms marked · are formed by the regular rule rather than recorded in the source data. English keeps a few hundred irregulars and the rest follow the pattern, so the rule is right far more often than not — but it is a rule, and the mark says so.
Definitions, synonyms and semantic relations for counterexample come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.