Consider the following premises. For all x_11, if x_11 were a sailor, then x_11 is a janitor. For all x_11, x_11 is a sailor or x_11 is sad. There is at least one x_11 for which if x_11 were sad, then x_11 is a janitor. For all x_11, x_11 is not a janitor or x_11 will write a letter. 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 or x_11 will write a letter.
 From the fact that for all x_11, if x_11 were a sailor, then x_11 is a janitor, that there is at least one x_11 for which if x_11 were sad, then x_11 is a janitor, and that for all x_11, x_11 is a sailor or x_11 is sad we can infer that there is at least one x_11 for which x_11 is a janitor via existential disjunction elimination. From the fact that there is at least one x_11 for which x_11 is a janitor we can infer that there is at least one x_11 for which x_11 is a janitor or x_11 is a politician via existential addition. Finally, from the fact that there is at least one x_11 for which x_11 is a janitor or x_11 is a politician, and that for all x_11, x_11 is not a janitor or x_11 will write a letter we can infer that there is at least one x_11 for which x_11 is a politician or x_11 will write a letter via existential resolution. Therefore, the answer is yes.