Consider the following premises. For all x_2, if x_2 were an office clerk, then x_2 is a sailor. For all x_2, if x_2 were a sailor, then x_2 is working. For all x_2, x_2 is not an office clerk. For all x_2, if x_2 works, then x_2 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 is a sailor.
 From the fact that for all x_2, if x_2 were a sailor, then x_2 is working, and that for all x_2, if x_2 works, then x_2 is an office clerk we can infer that for all x_2, if x_2 were a sailor, then x_2 is an office clerk via universal transitivity. From the fact that for all x_2, if x_2 were an office clerk, then x_2 is a sailor, and that for all x_2, if x_2 were a sailor, then x_2 is an office clerk we can infer that for all x_2, x_2 is an office clerk if and only if x_2 is a sailor via universal biconditional introduction. Finally, from the fact that for all x_2, x_2 is an office clerk if and only if x_2 is a sailor, and that for all x_2, x_2 is not an office clerk we can infer that for all x_2, x_2 is not a sailor via universal biconditional elimination, which contradicts that There is at least one x_2 for which x_2 is a sailor. Therefore, the answer is no.