Consider the following premises. For all x_16, if x_16 works, then x_16 is drinking water. For all x_16, if x_16 drinks water, then x_16 is a soldier. For all x_16, x_16 will not write a letter. For all x_16, x_16 will make tea if and only if x_16 will write a letter. There is at least one x_16 for which if x_16 were a soldier, then x_16 is making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_16 for which x_16 will not work.
 From the fact that for all x_16, x_16 will make tea if and only if x_16 will write a letter, and that for all x_16, x_16 will not write a letter we can infer that for all x_16, x_16 will not make tea via universal biconditional elimination. From the fact that there is at least one x_16 for which if x_16 were a soldier, then x_16 is making tea, and that for all x_16, x_16 will not make tea we can infer that there is at least one x_16 for which x_16 is not a soldier via existential modus tollens. From the fact that for all x_16, if x_16 works, then x_16 is drinking water, and that for all x_16, if x_16 drinks water, then x_16 is a soldier we can infer that for all x_16, if x_16 works, then x_16 is a soldier via universal transitivity. Finally, from the fact that for all x_16, if x_16 works, then x_16 is a soldier, and that there is at least one x_16 for which x_16 is not a soldier we can infer that there is at least one x_16 for which x_16 will not work via existential modus tollens. Therefore, the answer is yes.