Consider the following premises. For all x_5, x_5 will make tea or x_5 will not write a letter. For all x_5, if x_5 were a soldier, then x_5 is making tea. For all x_5, if x_5 were excited, then x_5 is a soldier. There is at least one x_5 for which x_5 is excited or x_5 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not make tea.
 From the fact that for all x_5, if x_5 were excited, then x_5 is a soldier, and that for all x_5, if x_5 were a soldier, then x_5 is making tea we can infer that for all x_5, if x_5 were excited, then x_5 is making tea via universal transitivity. From the fact that for all x_5, x_5 will make tea or x_5 will not write a letter we can infer that for all x_5, if x_5 writes a letter, then x_5 is making tea via universal rewriting. Finally, from the fact that for all x_5, if x_5 were excited, then x_5 is making tea, that for all x_5, if x_5 writes a letter, then x_5 is making tea, and that there is at least one x_5 for which x_5 is excited or x_5 will write a letter we can infer that there is at least one x_5 for which x_5 will make tea via existential disjunction elimination, which contradicts that For all x_5, x_5 will not make tea. Therefore, the answer is no.