Consider the following premises. For all x_11, x_11 is a server if and only if x_11 is a scientist. There is at least one x_11 for which if x_11 were a carpenter, then x_11 is a scientist. For all x_11, x_11 is not a carpenter. For all x_11, if x_11 were a server, then x_11 is a carpenter. Can we infer the following from them? There is at least one x_11 for which x_11 is not a server.
 From the fact that for all x_11, x_11 is a server if and only if x_11 is a scientist we can infer that for all x_11, if x_11 were a scientist, then x_11 is a server. From the fact that there is at least one x_11 for which if x_11 were a carpenter, then x_11 is a scientist, and that for all x_11, if x_11 were a scientist, then x_11 is a server we can infer that there is at least one x_11 for which if x_11 were a carpenter, then x_11 is a server. From the fact that for all x_11, if x_11 were a server, then x_11 is a carpenter, and that there is at least one x_11 for which if x_11 were a carpenter, then x_11 is a server we can infer that there is at least one x_11 for which x_11 is a server if and only if x_11 is a carpenter. Finally, from the fact that there is at least one x_11 for which x_11 is a server if and only if x_11 is a carpenter, and that for all x_11, x_11 is not a carpenter we can infer that there is at least one x_11 for which x_11 is not a server. Therefore, the answer is yes.