Consider the following premises. There is at least one x_7 for which x_7 will play tennis or x_7 is a poet. For all x_7, x_7 is an office clerk if and only if x_7 is a poet. For all x_7, x_7 will not play tennis or x_7 will drive a car. For all x_7, if x_7 drives a car, then x_7 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not an office clerk.
 From the fact that for all x_7, x_7 is an office clerk if and only if x_7 is a poet we can infer that for all x_7, if x_7 were a poet, then x_7 is an office clerk via universal biconditional elimination. From the fact that there is at least one x_7 for which x_7 will play tennis or x_7 is a poet, and that for all x_7, x_7 will not play tennis or x_7 will drive a car we can infer that there is at least one x_7 for which x_7 is a poet or x_7 will drive a car via existential resolution. Finally, from the fact that for all x_7, if x_7 were a poet, then x_7 is an office clerk, that for all x_7, if x_7 drives a car, then x_7 is an office clerk, and that there is at least one x_7 for which x_7 is a poet or x_7 will drive a car we can infer that there is at least one x_7 for which x_7 is an office clerk via existential disjunction elimination, which contradicts that For all x_7, x_7 is not an office clerk. Therefore, the answer is no.