Complex sentence: In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule, i.e., a specific instance of the falsity of a universal quantification (a "for all" statement).
Split into simpler sentences: In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. More precisely, a counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement).