Consider the following premises. For all x, if x goes running, then x is playing squash. For all x, if x were an artist, then x is running. For all x, x is a mechanic or x will not play squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which the fact that x were an artist does not imply that x is a mechanic.
 From the fact that for all x, x is a mechanic or x will not play squash we can infer that for all x, if x plays squash, then x is a mechanic via universal rewriting. From the fact that for all x, if x were an artist, then x is running, and that for all x, if x goes running, then x is playing squash we can infer that for all x, if x were an artist, then x is playing squash via universal transitivity. Finally, from the fact that for all x, if x were an artist, then x is playing squash, and that for all x, if x plays squash, then x is a mechanic we can infer that for all x, if x were an artist, then x is a mechanic via universal transitivity, which contradicts that There is at least one x for which the fact that x were an artist does not imply that x is a mechanic. Therefore, the answer is no.