Consider the following premises. For all z_1, z_1 is not sad. For all z_1, z_1 is an astronaut if and only if z_1 is a server. For all z_1, if z_1 were sad, then z_1 is an astronaut. For all z_1, if z_1 were a server, then z_1 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_1 for which z_1 is a server.
 From the fact that for all z_1, z_1 is an astronaut if and only if z_1 is a server we can infer that for all z_1, if z_1 were an astronaut, then z_1 is a server via universal biconditional elimination. From the fact that for all z_1, if z_1 were sad, then z_1 is an astronaut, and that for all z_1, if z_1 were an astronaut, then z_1 is a server we can infer that for all z_1, if z_1 were sad, then z_1 is a server via universal transitivity. From the fact that for all z_1, if z_1 were a server, then z_1 is sad, and that for all z_1, if z_1 were sad, then z_1 is a server we can infer that for all z_1, z_1 is a server if and only if z_1 is sad via universal biconditional introduction. Finally, from the fact that for all z_1, z_1 is a server if and only if z_1 is sad, and that for all z_1, z_1 is not sad we can infer that for all z_1, z_1 is not a server via universal biconditional elimination, which contradicts that There is at least one z_1 for which z_1 is a server. Therefore, the answer is no.