[erikerikson]

A contradiction (A ^ ~A) is the point at which reductio ad absurdum is achieved. It proves that a false assumption was made.

A counter example to a universal proposition is but one means of finding a contradiction since the universal allows you to assert the positive. A proof that no examples exist would contradict the statement that some do, just as effectively achieving reductio ad absurdum.

[whimsicalism]

What you're saying is not incongruous with what I'm saying.

statement leads to contradiction -> "general-statement is actually false in at least one case", so if reductio ad absurdum is defined as achieving a contradiction, then the original statement is false in at least one case.