counterexample

As a noun counterexample

is (logic) an exception to a proposed general rule; a specific instance of the falsity of a universally quantified statement.

As an adjective undefined is

lacking a definition or value.

As nouns the difference between instance and counterexample

is that instance is (obsolete) urgency of manner or words; an urgent request; insistence while counterexample is (logic) an exception to a proposed general rule; a specific instance of the falsity of a universally quantified statement.

As a verb instance

is to mention as a case or example; to refer to; to cite; as, to instance a fact.

As nouns the difference between example and counterexample

is that example is something that is representative of all such things in a group while counterexample is an exception to a proposed general rule; a specific instance of the falsity of a universally quantified statement.

As a verb example

is to be illustrated or exemplified (by).