Translate the following inference to logic notation: For all x, if x_6 climbs a mountain, then x_6 is a taxi driver. There is at least one x for which if x_6 were a taxi driver, then x_6 is playing tennis. For all x, if x_6 were a doctor, then x_6 is happy. For all x, x_6 is a doctor or x_6 will climb a mountain. For all x, if x_6 plays tennis, then x_6 is happy. Therefore there is at least one x for which x_6 is happy.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: S(x) -> T(x). forall x: S(x) or P(x). forall x: R(x) -> T(x). Therefore exists x: T(x).