Consider the following premises. For all x_11, x_11 is a musician. There is at least one x_11 for which if x_11 were fast, then x_11 is not a musician. For all x_11, if x_11 were a doctor, then x_11 is fast. For all x_11, if x_11 were a carpenter, then x_11 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is not a carpenter.
 From the fact that there is at least one x_11 for which if x_11 were fast, then x_11 is not a musician, and that for all x_11, x_11 is a musician we can infer that there is at least one x_11 for which x_11 is not fast via existential modus tollens. From the fact that for all x_11, if x_11 were a doctor, then x_11 is fast, and that there is at least one x_11 for which x_11 is not fast we can infer that there is at least one x_11 for which x_11 is not a doctor via existential modus tollens. Finally, from the fact that for all x_11, if x_11 were a carpenter, then x_11 is a doctor, and that there is at least one x_11 for which x_11 is not a doctor we can infer that there is at least one x_11 for which x_11 is not a carpenter via existential modus tollens. Therefore, the answer is yes.