Consider the following premises. For all x_11, if x_11 were a writer, then x_11 is playing tennis. For all x_11, x_11 is a writer. For all x_11, x_11 is poor if and only if x_11 is a doctor. For all x_11, x_11 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which either x_11 will play tennis or x_11 is a doctor are not true.
 From the fact that for all x_11, x_11 is poor if and only if x_11 is a doctor we can infer that for all x_11, if x_11 were poor, then x_11 is a doctor via universal biconditional elimination. From the fact that for all x_11, if x_11 were a writer, then x_11 is playing tennis, and that for all x_11, x_11 is a writer we can infer that for all x_11, x_11 will play tennis via universal modus ponens. From the fact that for all x_11, if x_11 were poor, then x_11 is a doctor, and that for all x_11, x_11 is poor we can infer that for all x_11, x_11 is a doctor via universal modus ponens. Finally, from the fact that for all x_11, x_11 will play tennis, and that for all x_11, x_11 is a doctor we can infer that for all x_11, x_11 will play tennis and x_11 is a doctor via universal conjunction, which contradicts that There is at least one x_11 for which either x_11 will play tennis or x_11 is a doctor are not true. Therefore, the answer is no.