Consider the following premises. For all x, x is a politician or x will not drink water. There is at least one x for which if x drinks water, then x is a politician. For all x, x will not drink water. For all x, if x were a politician, then x is drinking water. Can we infer the following from them? There is at least one x for which x is not a politician.
 From the fact that for all x, x is a politician or x will not drink water we can infer that for all x, if x drinks water, then x is a politician. From the fact that for all x, if x drinks water, then x is a politician, and that for all x, if x were a politician, then x is drinking water we can infer that for all x, x will drink water if and only if x is a politician. From the fact that for all x, x will drink water if and only if x is a politician we can infer that for all x, if x were a politician, then x is drinking water. From the fact that for all x, if x were a politician, then x is drinking water, and that there is at least one x for which if x drinks water, then x is a politician we can infer that there is at least one x for which x is a politician if and only if x will drink water. Finally, from the fact that there is at least one x for which x is a politician if and only if x will drink water, and that for all x, x will not drink water we can infer that there is at least one x for which x is not a politician. Therefore, the answer is yes.