Consider the following premises. For all x_6, x_6 will play squash or x_6 will not listen to a song. For all x_6, x_6 will listen to a song or x_6 is a mechanic. For all x_6, if x_6 plays squash, then x_6 is a taxi driver. For all x_6, if x_6 were a mechanic, then x_6 is playing squash. 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 x_6 is not a taxi driver.
 From the fact that for all x_6, x_6 will play squash or x_6 will not listen to a song we can infer that for all x_6, if x_6 listens to a song, then x_6 is playing squash via universal rewriting. From the fact that for all x_6, if x_6 listens to a song, then x_6 is playing squash, that for all x_6, if x_6 were a mechanic, then x_6 is playing squash, and that for all x_6, x_6 will listen to a song or x_6 is a mechanic we can infer that for all x_6, x_6 will play squash via universal disjunction elimination. Finally, from the fact that for all x_6, if x_6 plays squash, then x_6 is a taxi driver, and that for all x_6, x_6 will play squash we can infer that for all x_6, x_6 is a taxi driver via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 is not a taxi driver. Therefore, the answer is no.