Consider the following premises. For all x_3, x_3 is an office clerk. For all x_3, if x_3 drinks water, then x_3 is a writer. There is at least one x_3 for which x_3 will drink water. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, either x_3 is an office clerk or x_3 is a writer are not true.
 From the fact that for all x_3, if x_3 drinks water, then x_3 is a writer, and that there is at least one x_3 for which x_3 will drink water we can infer that there is at least one x_3 for which x_3 is a writer via existential modus ponens. Finally, from the fact that for all x_3, x_3 is an office clerk, and that there is at least one x_3 for which x_3 is a writer we can infer that there is at least one x_3 for which x_3 is an office clerk and x_3 is a writer via existential conjunction, which contradicts that For all x_3, either x_3 is an office clerk or x_3 is a writer are not true. Therefore, the answer is no.