Consider the following premises. For all x_11, x_11 is an office clerk and x_11 will drive a car. For all x_11, x_11 is a mechanic or x_11 is not an office clerk. There is at least one x_11 for which if x_11 were a mechanic, then x_11 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is not a musician.
 From the fact that for all x_11, x_11 is a mechanic or x_11 is not an office clerk we can infer that for all x_11, if x_11 were an office clerk, then x_11 is a mechanic via universal rewriting. From the fact that for all x_11, if x_11 were an office clerk, then x_11 is a mechanic, and that there is at least one x_11 for which if x_11 were a mechanic, then x_11 is a musician we can infer that there is at least one x_11 for which if x_11 were an office clerk, then x_11 is a musician via existential transitivity. From the fact that for all x_11, x_11 is an office clerk and x_11 will drive a car we can infer that for all x_11, x_11 is an office clerk via universal simplification. Finally, from the fact that there is at least one x_11 for which if x_11 were an office clerk, then x_11 is a musician, and that for all x_11, x_11 is an office clerk we can infer that there is at least one x_11 for which x_11 is a musician via existential modus ponens, which contradicts that For all x_11, x_11 is not a musician. Therefore, the answer is no.