Consider the following premises. For all z_1, z_1 is a carpenter if and only if z_1 is excited. There is at least one z_1 for which z_1 is poor. For all z_1, z_1 is a carpenter. For all z_1, if z_1 were poor, then z_1 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all z_1, either z_1 is excited or z_1 is a musician are not true.
 From the fact that for all z_1, z_1 is a carpenter if and only if z_1 is excited we can infer that for all z_1, if z_1 were a carpenter, then z_1 is excited via universal biconditional elimination. From the fact that for all z_1, if z_1 were a carpenter, then z_1 is excited, and that for all z_1, z_1 is a carpenter we can infer that for all z_1, z_1 is excited via universal modus ponens. From the fact that for all z_1, if z_1 were poor, then z_1 is a musician, and that there is at least one z_1 for which z_1 is poor we can infer that there is at least one z_1 for which z_1 is a musician via existential modus ponens. Finally, from the fact that for all z_1, z_1 is excited, and that there is at least one z_1 for which z_1 is a musician we can infer that there is at least one z_1 for which z_1 is excited and z_1 is a musician via existential conjunction, which contradicts that For all z_1, either z_1 is excited or z_1 is a musician are not true. Therefore, the answer is no.