Translate the following inference to logic notation: There is at least one x for which x_6 will go running if and only if x_6 will listen to a song. For all x, if x_6 listens to a song, then x_6 is not a nurse. For all x, x_6 is excited or x_6 is a nurse. For all x, x_6 is not excited. Therefore there is at least one x for which x_6 will not go running.
exists x: P(x) <-> Q(x). forall x: Q(x) -> ~R(x). forall x: S(x) or R(x). forall x: ~S(x). Therefore exists x: ~P(x).