Consider the following premises. For all x_8, if x_8 listens to a song, then x_8 is playing tennis. There is at least one x_8 for which x_8 will play tennis if and only if x_8 is a carpenter. For all x_8, x_8 will cook or x_8 will listen to a song. For all x_8, if x_8 cooks, then x_8 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not a carpenter.
 From the fact that there is at least one x_8 for which x_8 will play tennis if and only if x_8 is a carpenter we can infer that there is at least one x_8 for which if x_8 plays tennis, then x_8 is a carpenter via existential biconditional elimination. From the fact that for all x_8, if x_8 cooks, then x_8 is playing tennis, that for all x_8, if x_8 listens to a song, then x_8 is playing tennis, and that for all x_8, x_8 will cook or x_8 will listen to a song we can infer that for all x_8, x_8 will play tennis via universal disjunction elimination. Finally, from the fact that there is at least one x_8 for which if x_8 plays tennis, then x_8 is a carpenter, and that for all x_8, x_8 will play tennis we can infer that there is at least one x_8 for which x_8 is a carpenter via existential modus ponens, which contradicts that For all x_8, x_8 is not a carpenter. Therefore, the answer is no.