Consider the following premises. For all x_6, if x_6 were a mechanic, then x_6 is working. For all x_6, x_6 will go running or x_6 will not work. For all x_6, if x_6 goes running, then x_6 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which the fact that x_6 works does not imply that x_6 is running.
 From the fact that for all x_6, if x_6 goes running, then x_6 is a mechanic, and that for all x_6, if x_6 were a mechanic, then x_6 is working we can infer that for all x_6, if x_6 goes running, then x_6 is working via universal transitivity. From the fact that for all x_6, x_6 will go running or x_6 will not work we can infer that for all x_6, if x_6 works, then x_6 is running via universal rewriting. From the fact that for all x_6, if x_6 goes running, then x_6 is working, and that for all x_6, if x_6 works, then x_6 is running we can infer that for all x_6, x_6 will go running if and only if x_6 will work via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 will go running if and only if x_6 will work we can infer that for all x_6, if x_6 works, then x_6 is running via universal biconditional elimination, which contradicts that There is at least one x_6 for which the fact that x_6 works does not imply that x_6 is running. Therefore, the answer is no.