Consider the following premises. There is at least one x_2 for which if x_2 were a scientist, then x_2 is running. For all x_2, x_2 will go running or x_2 is not a poet. For all x_2, x_2 is a poet or x_2 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will not go running.
 From the fact that for all x_2, x_2 will go running or x_2 is not a poet we can infer that for all x_2, if x_2 were a poet, then x_2 is running via universal rewriting. Finally, from the fact that for all x_2, if x_2 were a poet, then x_2 is running, that there is at least one x_2 for which if x_2 were a scientist, then x_2 is running, and that for all x_2, x_2 is a poet or x_2 is a scientist we can infer that there is at least one x_2 for which x_2 will go running via existential disjunction elimination, which contradicts that For all x_2, x_2 will not go running. Therefore, the answer is no.