Consider the following premises. For all x_8, if x_8 were curious, then x_8 is poor. For all x_8, x_8 is a musician or x_8 is curious. There is at least one x_8 for which x_8 will play squash. For all x_8, x_8 is poor or x_8 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is poor.
 From the fact that for all x_8, x_8 is poor or x_8 is not a musician we can infer that for all x_8, if x_8 were a musician, then x_8 is poor via universal rewriting. From the fact that for all x_8, if x_8 were a musician, then x_8 is poor, that for all x_8, if x_8 were curious, then x_8 is poor, and that for all x_8, x_8 is a musician or x_8 is curious we can infer that for all x_8, x_8 is poor via universal disjunction elimination. From the fact that for all x_8, x_8 is poor, and that there is at least one x_8 for which x_8 will play squash we can infer that there is at least one x_8 for which x_8 is poor and x_8 will play squash via existential conjunction. Finally, from the fact that there is at least one x_8 for which x_8 is poor and x_8 will play squash we can infer that there is at least one x_8 for which x_8 is poor via existential simplification. Therefore, the answer is yes.