Consider the following premises. For all x_5, x_5 will not go running. For all x_5, x_5 will go running and x_5 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a doctor.
 From the fact that for all x_5, x_5 will go running and x_5 is a mechanic we can infer that for all x_5, x_5 will go running via universal simplification. From the fact that for all x_5, x_5 will go running we can infer that for all x_5, x_5 will go running or x_5 is a doctor via universal addition. Finally, from the fact that for all x_5, x_5 will go running or x_5 is a doctor, and that for all x_5, x_5 will not go running we can infer that for all x_5, x_5 is a doctor via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.