Consider the following premises. For all x_10, if x_10 were a taxi driver, then x_10 is a carpenter. For all x_10, x_10 is a taxi driver. There is at least one x_10 for which if x_10 were a scientist, then x_10 is a carpenter. For all x_10, x_10 will go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will go running and x_10 is a carpenter.
 From the fact that for all x_10, x_10 is a taxi driver we can infer that for all x_10, x_10 is a taxi driver or x_10 is a scientist via universal addition. From the fact that for all x_10, if x_10 were a taxi driver, then x_10 is a carpenter, that there is at least one x_10 for which if x_10 were a scientist, then x_10 is a carpenter, and that for all x_10, x_10 is a taxi driver or x_10 is a scientist we can infer that there is at least one x_10 for which x_10 is a carpenter via existential disjunction elimination. Finally, from the fact that for all x_10, x_10 will go running, and that there is at least one x_10 for which x_10 is a carpenter we can infer that there is at least one x_10 for which x_10 will go running and x_10 is a carpenter via existential conjunction. Therefore, the answer is yes.