Consider the following premises. For all x_6, x_6 is rich or x_6 is curious. For all x_6, x_6 will make tea or x_6 is not curious. For all x_6, x_6 will make tea or x_6 is not rich. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not make tea.
 From the fact that for all x_6, x_6 will make tea or x_6 is not curious we can infer that for all x_6, if x_6 were curious, then x_6 is making tea via universal rewriting. From the fact that for all x_6, x_6 will make tea or x_6 is not rich we can infer that for all x_6, if x_6 were rich, then x_6 is making tea via universal rewriting. Finally, from the fact that for all x_6, if x_6 were rich, then x_6 is making tea, that for all x_6, if x_6 were curious, then x_6 is making tea, and that for all x_6, x_6 is rich or x_6 is curious we can infer that for all x_6, x_6 will make tea via universal disjunction elimination, which contradicts that There is at least one x_6 for which x_6 will not make tea. Therefore, the answer is no.