Consider the following premises. For all x_11, x_11 is not poor or x_11 will drink water. There is at least one x_11 for which if x_11 listens to a song, then x_11 is playing squash. For all x_11, if x_11 plays squash, then x_11 is a politician. For all x_11, x_11 is poor or x_11 will listen to a song. For all x_11, x_11 is a politician or x_11 will not drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is a politician.
 From the fact that for all x_11, x_11 is poor or x_11 will listen to a song, and that for all x_11, x_11 is not poor or x_11 will drink water we can infer that for all x_11, x_11 will listen to a song or x_11 will drink water via universal resolution. From the fact that for all x_11, x_11 is a politician or x_11 will not drink water we can infer that for all x_11, if x_11 drinks water, then x_11 is a politician via universal rewriting. From the fact that there is at least one x_11 for which if x_11 listens to a song, then x_11 is playing squash, and that for all x_11, if x_11 plays squash, then x_11 is a politician we can infer that there is at least one x_11 for which if x_11 listens to a song, then x_11 is a politician via existential transitivity. Finally, from the fact that there is at least one x_11 for which if x_11 listens to a song, then x_11 is a politician, that for all x_11, if x_11 drinks water, then x_11 is a politician, and that for all x_11, x_11 will listen to a song or x_11 will drink water we can infer that there is at least one x_11 for which x_11 is a politician via existential disjunction elimination. Therefore, the answer is yes.