Consider the following premises. For all x_17, x_17 will cook if and only if x_17 is an astronaut. For all x_17, if x_17 plays tennis, then x_17 is an astronaut. David is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, neither x_17 is an astronaut nor x_17 will take a plane.
 From the fact that David is cooking we can infer that there is at least one x_17 for which x_17 will cook via existential generalization. From the fact that there is at least one x_17 for which x_17 will cook we can infer that there is at least one x_17 for which x_17 will cook or x_17 will play tennis via existential addition. From the fact that for all x_17, x_17 will cook if and only if x_17 is an astronaut we can infer that for all x_17, if x_17 cooks, then x_17 is an astronaut via universal biconditional elimination. From the fact that for all x_17, if x_17 cooks, then x_17 is an astronaut, that for all x_17, if x_17 plays tennis, then x_17 is an astronaut, and that there is at least one x_17 for which x_17 will cook or x_17 will play tennis we can infer that there is at least one x_17 for which x_17 is an astronaut via existential disjunction elimination. Finally, from the fact that there is at least one x_17 for which x_17 is an astronaut we can infer that there is at least one x_17 for which x_17 is an astronaut or x_17 will take a plane via existential addition, which contradicts that For all x_17, neither x_17 is an astronaut nor x_17 will take a plane. Therefore, the answer is no.