Counterexample
Foundations and logic
A single case satisfying a claim’s hypotheses but failing its conclusion, which is enough to disprove the claim outright.
What is usually left out
The asymmetry is the point: proving a universal statement requires an argument covering every case, while refuting it requires exactly one. This is why a conjecture can accumulate overwhelming numerical support and still be false, and why the smallest known counterexample to a statement is sometimes astronomically large.