Consider the following premises. For all x_12, x_12 will listen to a song if and only if x_12 will take a plane. For all x_12, x_12 is an office clerk or x_12 will not go running. For all x_12, if x_12 listens to a song, then x_12 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which the fact that x_12 takes a plane does not imply that x_12 is an office clerk.
 From the fact that for all x_12, x_12 will listen to a song if and only if x_12 will take a plane we can infer that for all x_12, if x_12 takes a plane, then x_12 is listening to a song via universal biconditional elimination. From the fact that for all x_12, x_12 is an office clerk or x_12 will not go running we can infer that for all x_12, if x_12 goes running, then x_12 is an office clerk via universal rewriting. From the fact that for all x_12, if x_12 listens to a song, then x_12 is running, and that for all x_12, if x_12 goes running, then x_12 is an office clerk we can infer that for all x_12, if x_12 listens to a song, then x_12 is an office clerk via universal transitivity. Finally, from the fact that for all x_12, if x_12 takes a plane, then x_12 is listening to a song, and that for all x_12, if x_12 listens to a song, then x_12 is an office clerk we can infer that for all x_12, if x_12 takes a plane, then x_12 is an office clerk via universal transitivity, which contradicts that There is at least one x_12 for which the fact that x_12 takes a plane does not imply that x_12 is an office clerk. Therefore, the answer is no.