Translate the following inference to logic notation: For all x, if x_13 sleeps, then x_13 is writing a letter. For all x, if x_13 goes running, then x_13 is listening to a song. For all x, x_13 is bored if and only if x_13 will write a letter. For all x, x_13 will go running. For all x, if x_13 listens to a song, then x_13 is sleeping. Therefore for all x, x_13 will write a letter.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: T(x) <-> Q(x). forall x: R(x). forall x: S(x) -> P(x). Therefore forall x: Q(x).