Consider the following premises. For all x_10, x_10 is poor. For all x_10, if x_10 goes running, then x_10 is sad. There is at least one x_10 for which x_10 is an electrician. For all x_10, if x_10 were an electrician, then x_10 is running. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, either x_10 is poor or x_10 is sad are not true.
 From the fact that for all x_10, if x_10 were an electrician, then x_10 is running, and that for all x_10, if x_10 goes running, then x_10 is sad we can infer that for all x_10, if x_10 were an electrician, then x_10 is sad via universal transitivity. From the fact that for all x_10, if x_10 were an electrician, then x_10 is sad, and that there is at least one x_10 for which x_10 is an electrician we can infer that there is at least one x_10 for which x_10 is sad via existential modus ponens. Finally, from the fact that for all x_10, x_10 is poor, and that there is at least one x_10 for which x_10 is sad we can infer that there is at least one x_10 for which x_10 is poor and x_10 is sad via existential conjunction, which contradicts that For all x_10, either x_10 is poor or x_10 is sad are not true. Therefore, the answer is no.