Consider the following premises. For all x_6, x_6 will play tennis or x_6 is not a musician. For all x_6, x_6 is a musician or x_6 will take a plane. For all x_6, x_6 will play tennis if and only if x_6 will take a plane. 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 x_6 will not play tennis.
 From the fact that for all x_6, x_6 will play tennis or x_6 is not a musician we can infer that for all x_6, if x_6 were a musician, then x_6 is playing tennis via universal rewriting. From the fact that for all x_6, x_6 will play tennis if and only if x_6 will take a plane we can infer that for all x_6, if x_6 takes a plane, then x_6 is playing tennis via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 were a musician, then x_6 is playing tennis, that for all x_6, if x_6 takes a plane, then x_6 is playing tennis, and that for all x_6, x_6 is a musician or x_6 will take a plane we can infer that for all x_6, x_6 will play tennis via universal disjunction elimination, which contradicts that There is at least one x_6 for which x_6 will not play tennis. Therefore, the answer is no.