Consider the following premises. For all x_14, if x_14 climbs a mountain, then x_14 is driving a car. For all x_14, x_14 will drink water if and only if x_14 will climb a mountain. There is at least one x_14 for which if x_14 drives a car, then x_14 is climbing a mountain. For all x_14, if x_14 drives a car, then x_14 is drinking water. Can we infer the following from them? For all x_14, if is not true that x_14 will climb a mountain if and only if x_14 will drive a car.
That contradicts the premises. Therefore the answer is no.