Consider the following premises. For all x_10, x_10 is an astronaut. For all x_10, if x_10 were an astronaut, then x_10 is happy. For all x_10, if x_10 were excited, then x_10 is a sailor. There is at least one x_10 for which if x_10 were happy, then x_10 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is not a sailor.
 From the fact that for all x_10, if x_10 were an astronaut, then x_10 is happy, and that for all x_10, x_10 is an astronaut we can infer that for all x_10, x_10 is happy via universal modus ponens. From the fact that there is at least one x_10 for which if x_10 were happy, then x_10 is excited, and that for all x_10, x_10 is happy we can infer that there is at least one x_10 for which x_10 is excited via existential modus ponens. Finally, from the fact that for all x_10, if x_10 were excited, then x_10 is a sailor, and that there is at least one x_10 for which x_10 is excited we can infer that there is at least one x_10 for which x_10 is a sailor via existential modus ponens, which contradicts that For all x_10, x_10 is not a sailor. Therefore, the answer is no.