Consider the following premises. For all x_10, if x_10 takes a plane, then x_10 is an artist. For all x_10, if x_10 were an artist, then x_10 is cooking. There is at least one x_10 for which x_10 will take a plane. For all x_10, if x_10 were a doctor, then x_10 is an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not cook.
 From the fact that there is at least one x_10 for which x_10 will take a plane we can infer that there is at least one x_10 for which x_10 will take a plane or x_10 is a doctor via existential addition. From the fact that for all x_10, if x_10 takes a plane, then x_10 is an artist, that for all x_10, if x_10 were a doctor, then x_10 is an artist, and that there is at least one x_10 for which x_10 will take a plane or x_10 is a doctor we can infer that there is at least one x_10 for which x_10 is an artist via existential disjunction elimination. Finally, from the fact that for all x_10, if x_10 were an artist, then x_10 is cooking, and that there is at least one x_10 for which x_10 is an artist we can infer that there is at least one x_10 for which x_10 will cook via existential modus ponens, which contradicts that For all x_10, x_10 will not cook. Therefore, the answer is no.