Consider the following premises. For all x_10, if x_10 were a cashier, then x_10 is not drinking water. There is at least one x_10 for which if x_10 writes a letter, then x_10 is drinking water. For all x_10, if x_10 were excited, then x_10 is drinking water. For all x_10, x_10 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is a cashier.
 From the fact that for all x_10, x_10 will write a letter we can infer that for all x_10, x_10 will write a letter or x_10 is excited via universal addition. From the fact that there is at least one x_10 for which if x_10 writes a letter, then x_10 is drinking water, that for all x_10, if x_10 were excited, then x_10 is drinking water, and that for all x_10, x_10 will write a letter or x_10 is excited we can infer that there is at least one x_10 for which x_10 will drink water via existential disjunction elimination. Finally, from the fact that for all x_10, if x_10 were a cashier, then x_10 is not drinking water, and that there is at least one x_10 for which x_10 will drink water we can infer that there is at least one x_10 for which x_10 is not a cashier via existential modus tollens, which contradicts that For all x_10, x_10 is a cashier. Therefore, the answer is no.