Consider the following premises. For all x_5, if x_5 were a poet, then x_5 is poor. For all x_5, x_5 is a server. For all x_5, if x_5 were a server, then x_5 is poor. There is at least one x_5 for which x_5 is an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, either x_5 is an artist or x_5 is poor are not true.
 From the fact that for all x_5, x_5 is a server we can infer that for all x_5, x_5 is a server or x_5 is a poet via universal addition. From the fact that for all x_5, if x_5 were a server, then x_5 is poor, that for all x_5, if x_5 were a poet, then x_5 is poor, and that for all x_5, x_5 is a server or x_5 is a poet we can infer that for all x_5, x_5 is poor via universal disjunction elimination. Finally, from the fact that there is at least one x_5 for which x_5 is an artist, and that for all x_5, x_5 is poor we can infer that there is at least one x_5 for which x_5 is an artist and x_5 is poor via existential conjunction, which contradicts that For all x_5, either x_5 is an artist or x_5 is poor are not true. Therefore, the answer is no.