Consider the following premises. There is at least one x_11 for which x_11 is fast or x_11 will not play tennis. For all x_11, x_11 is not fast. For all x_11, x_11 will play tennis if and only if x_11 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is a sailor.
 From the fact that there is at least one x_11 for which x_11 is fast or x_11 will not play tennis we can infer that there is at least one x_11 for which if x_11 plays tennis, then x_11 is fast via existential rewriting. From the fact that there is at least one x_11 for which if x_11 plays tennis, then x_11 is fast, and that for all x_11, x_11 is not fast we can infer that there is at least one x_11 for which x_11 will not play tennis via existential modus tollens. Finally, from the fact that for all x_11, x_11 will play tennis if and only if x_11 is a sailor, and that there is at least one x_11 for which x_11 will not play tennis we can infer that there is at least one x_11 for which x_11 is not a sailor via existential biconditional elimination, which contradicts that For all x_11, x_11 is a sailor. Therefore, the answer is no.