Consider the following premises. For all x_8, if x_8 were fast, then x_8 is a poet. For all x_8, if x_8 were a poet, then x_8 is running. There is at least one x_8 for which x_8 is fast. For all x_8, x_8 will go running or x_8 is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not go running.
 From the fact that for all x_8, if x_8 were fast, then x_8 is a poet, and that for all x_8, if x_8 were a poet, then x_8 is running we can infer that for all x_8, if x_8 were fast, then x_8 is running via universal transitivity. From the fact that there is at least one x_8 for which x_8 is fast we can infer that there is at least one x_8 for which x_8 is fast or x_8 is a mechanic via existential addition. From the fact that for all x_8, x_8 will go running or x_8 is not a mechanic we can infer that for all x_8, if x_8 were a mechanic, then x_8 is running via universal rewriting. Finally, from the fact that for all x_8, if x_8 were fast, then x_8 is running, that for all x_8, if x_8 were a mechanic, then x_8 is running, and that there is at least one x_8 for which x_8 is fast or x_8 is a mechanic we can infer that there is at least one x_8 for which x_8 will go running via existential disjunction elimination, which contradicts that For all x_8, x_8 will not go running. Therefore, the answer is no.