Consider the following premises. For all x_5, x_5 is a carpenter or x_5 will cook. For all x_5, if x_5 were fast, then x_5 is cooking. For all x_5, if x_5 cooks, then x_5 is fast. There is at least one x_5 for which if x_5 were a carpenter, then x_5 is fast. Can we infer the following from them? There is at least one x_5 for which x_5 is fast.
 From the fact that for all x_5, if x_5 cooks, then x_5 is fast, and that for all x_5, if x_5 were fast, then x_5 is cooking we can infer that for all x_5, x_5 will cook if and only if x_5 is fast. From the fact that for all x_5, x_5 will cook if and only if x_5 is fast we can infer that for all x_5, if x_5 cooks, then x_5 is fast. Finally, from the fact that there is at least one x_5 for which if x_5 were a carpenter, then x_5 is fast, that for all x_5, if x_5 cooks, then x_5 is fast, and that for all x_5, x_5 is a carpenter or x_5 will cook we can infer that there is at least one x_5 for which x_5 is fast. Therefore, the answer is yes.