Translate the following inference to logic notation: For all x, if x_6 were happy, then x_6 is taking a plane. For all x, if x_6 listens to a song, then x_6 is happy. There is at least one x for which if x_6 takes a plane, then x_6 is playing a game. For all x, if x_6 plays a game, then x_6 is a sailor. Therefore there is at least one x for which if x_6 listens to a song, then x_6 is a sailor.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> S(x). forall x: S(x) -> T(x). Therefore exists x: R(x) -> T(x).