Consider the following premises. For all x_9, x_9 is a doctor or x_9 will listen to a song. There is at least one x_9 for which if x_9 were a doctor, then x_9 is working. For all x_9, x_9 is a lawyer if and only if x_9 will listen to a song. For all x_9, if x_9 works, then x_9 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is not a lawyer.
 From the fact that for all x_9, x_9 is a lawyer if and only if x_9 will listen to a song we can infer that for all x_9, if x_9 listens to a song, then x_9 is a lawyer via universal biconditional elimination. From the fact that there is at least one x_9 for which if x_9 were a doctor, then x_9 is working, and that for all x_9, if x_9 works, then x_9 is a lawyer we can infer that there is at least one x_9 for which if x_9 were a doctor, then x_9 is a lawyer via existential transitivity. Finally, from the fact that there is at least one x_9 for which if x_9 were a doctor, then x_9 is a lawyer, that for all x_9, if x_9 listens to a song, then x_9 is a lawyer, and that for all x_9, x_9 is a doctor or x_9 will listen to a song we can infer that there is at least one x_9 for which x_9 is a lawyer via existential disjunction elimination, which contradicts that For all x_9, x_9 is not a lawyer. Therefore, the answer is no.