Translate the following inference to logic notation: There is at least one x for which x_12 is a doctor. For all x, x_12 will play squash. For all x, if x_12 plays squash, then x_12 is running. Therefore there is at least one x for which x_12 is a doctor or x_12 will listen to a song.
exists x: P(x). forall x: Q(x). forall x: Q(x) -> R(x). Therefore exists x: P(x) or S(x).