Consider the following premises. For all x_3, if x_3 were curious, then x_3 is a scientist. For all x_3, x_3 is not a scientist or x_3 is a poet. For all x_3, x_3 is curious. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will write a letter or x_3 is a poet.
 From the fact that for all x_3, if x_3 were curious, then x_3 is a scientist, and that for all x_3, x_3 is curious we can infer that for all x_3, x_3 is a scientist via universal modus ponens. From the fact that for all x_3, x_3 is a scientist we can infer that for all x_3, x_3 is a scientist or x_3 will write a letter via universal addition. Finally, from the fact that for all x_3, x_3 is a scientist or x_3 will write a letter, and that for all x_3, x_3 is not a scientist or x_3 is a poet we can infer that for all x_3, x_3 will write a letter or x_3 is a poet via universal resolution. Therefore, the answer is yes.