Answer:

There are four possibilities:

If run {x} produces an instance,
that means x is true under *some* circumstances.
But not necessarily under all circumstances.

If run {x} does not produce an instance,
that means x is false under *every* possible circumstance.

If check {x} produces a counterexample,
that means x is false under *some* circumstance.
But not necessarily under all circumstances.

If check {x} does not produce a counterexample,
that means x is true under *every* possible circumstance.