Consider the following premises. For all x_3, if x_3 were a lawyer, then x_3 is an office clerk. There is at least one x_3 for which if x_3 listens to a song, then x_3 is a musician. For all x_3, x_3 will go running or x_3 will listen to a song. For all x_3, x_3 will not go running or x_3 is a lawyer. For all x_3, if x_3 were a musician, then x_3 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 is not an office clerk.
 From the fact that there is at least one x_3 for which if x_3 listens to a song, then x_3 is a musician, and that for all x_3, if x_3 were a musician, then x_3 is an office clerk we can infer that there is at least one x_3 for which if x_3 listens to a song, then x_3 is an office clerk via existential transitivity. From the fact that for all x_3, x_3 will go running or x_3 will listen to a song, and that for all x_3, x_3 will not go running or x_3 is a lawyer we can infer that for all x_3, x_3 will listen to a song or x_3 is a lawyer via universal resolution. Finally, from the fact that there is at least one x_3 for which if x_3 listens to a song, then x_3 is an office clerk, that for all x_3, if x_3 were a lawyer, then x_3 is an office clerk, and that for all x_3, x_3 will listen to a song or x_3 is a lawyer we can infer that there is at least one x_3 for which x_3 is an office clerk via existential disjunction elimination, which contradicts that For all x_3, x_3 is not an office clerk. Therefore, the answer is no.