Consider the following premises. For all x_11, if x_11 drives a car, then x_11 is cooking. There is at least one x_11 for which if x_11 plays tennis, then x_11 is a scientist. For all x_11, x_11 will make tea or x_11 will play tennis. For all x_11, x_11 will cook or x_11 is not a scientist. For all x_11, x_11 will not make tea or x_11 will drive a car. 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 will cook.
 From the fact that for all x_11, x_11 will make tea or x_11 will play tennis, and that for all x_11, x_11 will not make tea or x_11 will drive a car we can infer that for all x_11, x_11 will play tennis or x_11 will drive a car via universal resolution. From the fact that for all x_11, x_11 will cook or x_11 is not a scientist we can infer that for all x_11, if x_11 were a scientist, then x_11 is cooking via universal rewriting. From the fact that there is at least one x_11 for which if x_11 plays tennis, then x_11 is a scientist, and that for all x_11, if x_11 were a scientist, then x_11 is cooking we can infer that there is at least one x_11 for which if x_11 plays tennis, then x_11 is cooking via existential transitivity. Finally, from the fact that there is at least one x_11 for which if x_11 plays tennis, then x_11 is cooking, that for all x_11, if x_11 drives a car, then x_11 is cooking, and that for all x_11, x_11 will play tennis or x_11 will drive a car we can infer that there is at least one x_11 for which x_11 will cook via existential disjunction elimination. Therefore, the answer is yes.