Translate the following inference to logic notation: For all x, if x_13 writes a letter, then x_13 is listening to a song. For all x, x_13 will not listen to a song. For all x, if x_13 makes tea, then x_13 is writing a letter. There is at least one x for which if x_13 plays a game, then x_13 is making tea. For all x, if x_13 listens to a song, then x_13 is playing a game. Therefore there is at least one x for which x_13 will not make tea.
forall x: P(x) -> Q(x). forall x: ~Q(x). forall x: R(x) -> P(x). exists x: S(x) -> R(x). forall x: Q(x) -> S(x). Therefore exists x: ~R(x).