Translate the following inference to logic notation: There is at least one x for which x_6 is a doctor. For all x, x_6 will play a game. For all x, x_6 will go running or x_6 will not play a game. Therefore there is at least one x for which x_6 is a doctor and x_6 will go running.
exists x: P(x). forall x: Q(x). forall x: R(x) or ~Q(x). Therefore exists x: P(x) and R(x).