How do you actually execute the test though? A test requires that you be able to produce an artifact which is witness to the results -- what could you produce

How do you actually execute the test though? A test requires that you be able to produce an artifact which is witness to the results -- what could you produce as the result of the test to distinguish between a true, but unprovable theorem and a nearly true theorem with a single (very, very, VERY) large counter-example?