Translate the following inference to logic notation: For all x, if x_11 climbs a mountain, then x_11 is a musician. For all x, if x_11 were a musician, then x_11 is listening to a song. For all x, x_11 is a doctor if and only if x_11 will listen to a song. There is at least one x for which if x_11 drinks water, then x_11 is not listening to a song. For all x, x_11 is a doctor or x_11 will climb a mountain. Therefore there is at least one x for which x_11 will not drink water.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) <-> R(x). exists x: T(x) -> ~R(x). forall x: S(x) or P(x). Therefore exists x: ~T(x).