Translate the following inference to logic notation: For all x, x_16 will go running if and only if x_16 will write a letter. For all x, if x_16 goes running, then x_16 is happy. For all x, x_16 will read a book if and only if x_16 is happy. For all x, x_16 will not read a book. For all x, if x_16 listens to a song, then x_16 is writing a letter. Therefore for all x, x_16 will not listen to a song.
forall x: P(x) <-> Q(x). forall x: P(x) -> R(x). forall x: S(x) <-> R(x). forall x: ~S(x). forall x: T(x) -> Q(x). Therefore forall x: ~T(x).