Consider the following premises. For all x_2, x_2 will not work. For all x_2, x_2 will work or x_2 will make tea. For all x_2, x_2 will sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which either x_2 will make tea or x_2 will sleep are not true.
 From the fact that for all x_2, x_2 will work or x_2 will make tea, and that for all x_2, x_2 will not work we can infer that for all x_2, x_2 will make tea via universal disjunctive syllogism. Finally, from the fact that for all x_2, x_2 will make tea, and that for all x_2, x_2 will sleep we can infer that for all x_2, x_2 will make tea and x_2 will sleep via universal conjunction, which contradicts that There is at least one x_2 for which either x_2 will make tea or x_2 will sleep are not true. Therefore, the answer is no.