Consider the following premises. For all x_6, x_6 is an astronaut or x_6 is not happy. For all x_6, if x_6 were an astronaut, then x_6 is not fast. For all x_6, x_6 is fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is happy.
 From the fact that for all x_6, x_6 is an astronaut or x_6 is not happy we can infer that for all x_6, if x_6 were happy, then x_6 is an astronaut via universal rewriting. From the fact that for all x_6, if x_6 were an astronaut, then x_6 is not fast, and that for all x_6, x_6 is fast we can infer that for all x_6, x_6 is not an astronaut via universal modus tollens. Finally, from the fact that for all x_6, if x_6 were happy, then x_6 is an astronaut, and that for all x_6, x_6 is not an astronaut we can infer that for all x_6, x_6 is not happy via universal modus tollens, which contradicts that There is at least one x_6 for which x_6 is happy. Therefore, the answer is no.