Consider the following premises. For all x_11, if x_11 were a doctor, then x_11 is making tea. For all x_11, if x_11 drives a car, then x_11 is cooking. For all x_11, x_11 is a doctor or x_11 will drive a car. For all x_11, if x_11 makes tea, then x_11 is playing tennis. For all x_11, if x_11 plays tennis, then x_11 is a doctor. There is at least one x_11 for which if x_11 cooks, then x_11 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 will not make tea.
 From the fact that for all x_11, if x_11 makes tea, then x_11 is playing tennis, and that for all x_11, if x_11 plays tennis, then x_11 is a doctor we can infer that for all x_11, if x_11 makes tea, then x_11 is a doctor via universal transitivity. From the fact that for all x_11, if x_11 makes tea, then x_11 is a doctor, and that for all x_11, if x_11 were a doctor, then x_11 is making tea we can infer that for all x_11, x_11 will make tea if and only if x_11 is a doctor via universal biconditional introduction. From the fact that for all x_11, x_11 will make tea if and only if x_11 is a doctor we can infer that for all x_11, if x_11 were a doctor, then x_11 is making tea via universal biconditional elimination. From the fact that for all x_11, if x_11 drives a car, then x_11 is cooking, and that there is at least one x_11 for which if x_11 cooks, then x_11 is making tea we can infer that there is at least one x_11 for which if x_11 drives a car, then x_11 is making tea via existential transitivity. Finally, from the fact that for all x_11, if x_11 were a doctor, then x_11 is making tea, that there is at least one x_11 for which if x_11 drives a car, then x_11 is making tea, and that for all x_11, x_11 is a doctor or x_11 will drive a car we can infer that there is at least one x_11 for which x_11 will make tea via existential disjunction elimination, which contradicts that For all x_11, x_11 will not make tea. Therefore, the answer is no.