Consider the following premises. For all x_7, x_7 will write a letter or x_7 is an office clerk. For all x_7, x_7 is not a server. For all x_7, x_7 is a server if and only if x_7 is a soldier. For all x_7, if x_7 writes a letter, then x_7 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not an office clerk.
 From the fact that for all x_7, x_7 is a server if and only if x_7 is a soldier, and that for all x_7, x_7 is not a server we can infer that for all x_7, x_7 is not a soldier via universal biconditional elimination. From the fact that for all x_7, if x_7 writes a letter, then x_7 is a soldier, and that for all x_7, x_7 is not a soldier we can infer that for all x_7, x_7 will not write a letter via universal modus tollens. Finally, from the fact that for all x_7, x_7 will write a letter or x_7 is an office clerk, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 is an office clerk via universal disjunctive syllogism, which contradicts that There is at least one x_7 for which x_7 is not an office clerk. Therefore, the answer is no.