Consider the following premises. For all x_14, x_14 will not climb a mountain. For all x_14, if x_14 works, then x_14 is a nurse. For all x_14, x_14 will climb a mountain if and only if x_14 will work. For all x_14, if x_14 were a nurse, then x_14 is working. There is at least one x_14 for which x_14 is a nurse or x_14 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will not play tennis.
 From the fact that for all x_14, if x_14 were a nurse, then x_14 is working, and that for all x_14, if x_14 works, then x_14 is a nurse we can infer that for all x_14, x_14 is a nurse if and only if x_14 will work via universal biconditional introduction. From the fact that for all x_14, x_14 will climb a mountain if and only if x_14 will work, and that for all x_14, x_14 will not climb a mountain we can infer that for all x_14, x_14 will not work via universal biconditional elimination. From the fact that for all x_14, x_14 is a nurse if and only if x_14 will work, and that for all x_14, x_14 will not work we can infer that for all x_14, x_14 is not a nurse via universal biconditional elimination. From the fact that there is at least one x_14 for which x_14 is a nurse or x_14 will not play tennis we can infer that there is at least one x_14 for which if x_14 plays tennis, then x_14 is a nurse via existential rewriting. Finally, from the fact that there is at least one x_14 for which if x_14 plays tennis, then x_14 is a nurse, and that for all x_14, x_14 is not a nurse we can infer that there is at least one x_14 for which x_14 will not play tennis via existential modus tollens. Therefore, the answer is yes.