Consider the following premises. For all x_4, x_4 will make tea. For all x_4, x_4 will play tennis or x_4 is a server. For all x_4, if x_4 plays tennis, then x_4 is an artist. For all x_4, if x_4 were a server, then x_4 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which either x_4 will make tea or x_4 is an artist are not true.
 From the fact that for all x_4, if x_4 plays tennis, then x_4 is an artist, that for all x_4, if x_4 were a server, then x_4 is an artist, and that for all x_4, x_4 will play tennis or x_4 is a server we can infer that for all x_4, x_4 is an artist via universal disjunction elimination. Finally, from the fact that for all x_4, x_4 will make tea, and that for all x_4, x_4 is an artist we can infer that for all x_4, x_4 will make tea and x_4 is an artist via universal conjunction, which contradicts that There is at least one x_4 for which either x_4 will make tea or x_4 is an artist are not true. Therefore, the answer is no.