counterexample vs falsification

counterexample and falsification both are nouns.

Word	Noun	Adjective	Verb	Adverb
counterexample	Yes	No	No	No
falsification	Yes	No	No	No

As nouns, falsification is a hypernym of counterexample; that is, falsification is a word with a broader meaning than counterexample:

counterexample: refutation by example
falsification: any evidence that helps to establish the falsity of something

Other hypernyms of counterexample include disproof, refutation.

counterexample (noun)	falsification (noun)
refutation by example	the act of rendering something false as by fraudulent changes (of documents or measures etc.) or counterfeiting
	the act of determining that something is false
	a willful perversion of facts
	any evidence that helps to establish the falsity of something