Translate the following inference to logic notation: For all x, x_14 will go running. For all x, x_14 will work if and only if x_14 is bored. There is at least one x for which x_14 is bored. Therefore there is at least one x for which x_14 will work.
forall x: P(x). forall x: Q(x) <-> R(x). exists x: R(x). Therefore exists x: Q(x).