Consider the following premises. For all x_1, x_1 is an electrician. For all x_1, x_1 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 will not write a letter.
 From the fact that for all x_1, x_1 is an electrician, and that for all x_1, x_1 will write a letter we can infer that for all x_1, x_1 is an electrician and x_1 will write a letter via universal conjunction. Finally, from the fact that for all x_1, x_1 is an electrician and x_1 will write a letter we can infer that for all x_1, x_1 is an electrician via universal simplification, which contradicts that There is at least one x_1 for which x_1 will not write a letter. Therefore, the answer is no.