Consider the following premises. For all x_6, x_6 will work. For all x_6, if x_6 reads a book, then x_6 is playing tennis. For all x_6, x_6 will read a book. For all x_6, x_6 is a poet. 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 either x_6 will play tennis or x_6 is a poet are not true.
 From the fact that for all x_6, if x_6 reads a book, then x_6 is playing tennis, and that for all x_6, x_6 will read a book we can infer that for all x_6, x_6 will play tennis via universal modus ponens. From the fact that for all x_6, x_6 will play tennis, and that for all x_6, x_6 will work we can infer that for all x_6, x_6 will play tennis and x_6 will work via universal conjunction. From the fact that for all x_6, x_6 will play tennis and x_6 will work we can infer that for all x_6, x_6 will play tennis via universal simplification. Finally, from the fact that for all x_6, x_6 will play tennis, and that for all x_6, x_6 is a poet we can infer that for all x_6, x_6 will play tennis and x_6 is a poet via universal conjunction, which contradicts that There is at least one x_6 for which either x_6 will play tennis or x_6 is a poet are not true. Therefore, the answer is no.