Consider the following premises. For all z_3, z_3 is a scientist or z_3 is not a soldier. There is at least one z_3 for which if z_3 were a soldier, then z_3 is a scientist. For all z_3, z_3 is not a soldier. For all z_3, if z_3 were a scientist, then z_3 is a soldier. Can we infer the following from them? There is at least one z_3 for which z_3 is not a scientist.
 From the fact that for all z_3, z_3 is a scientist or z_3 is not a soldier we can infer that for all z_3, if z_3 were a soldier, then z_3 is a scientist. From the fact that for all z_3, if z_3 were a soldier, then z_3 is a scientist, and that for all z_3, if z_3 were a scientist, then z_3 is a soldier we can infer that for all z_3, z_3 is a soldier if and only if z_3 is a scientist. From the fact that for all z_3, z_3 is a soldier if and only if z_3 is a scientist we can infer that for all z_3, if z_3 were a scientist, then z_3 is a soldier. From the fact that for all z_3, if z_3 were a scientist, then z_3 is a soldier, and that there is at least one z_3 for which if z_3 were a soldier, then z_3 is a scientist we can infer that there is at least one z_3 for which z_3 is a scientist if and only if z_3 is a soldier. Finally, from the fact that there is at least one z_3 for which z_3 is a scientist if and only if z_3 is a soldier, and that for all z_3, z_3 is not a soldier we can infer that there is at least one z_3 for which z_3 is not a scientist. Therefore, the answer is yes.