Consider the following premises. For all x_6, x_6 is a politician or x_6 is a doctor. For all x_6, x_6 will drink water or x_6 is not a politician. For all x_6, if x_6 drinks water, then x_6 is playing squash. For all x_6, if x_6 were a doctor, then x_6 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not play squash.
 From the fact that for all x_6, x_6 will drink water or x_6 is not a politician we can infer that for all x_6, if x_6 were a politician, then x_6 is drinking water via universal rewriting. From the fact that for all x_6, if x_6 were a politician, then x_6 is drinking water, that for all x_6, if x_6 were a doctor, then x_6 is drinking water, and that for all x_6, x_6 is a politician or x_6 is a doctor we can infer that for all x_6, x_6 will drink water via universal disjunction elimination. Finally, from the fact that for all x_6, if x_6 drinks water, then x_6 is playing squash, and that for all x_6, x_6 will drink water we can infer that for all x_6, x_6 will play squash via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 will not play squash. Therefore, the answer is no.