Consider the following premises. For all x_8, x_8 will play squash or x_8 is a taxi driver. For all x_8, if x_8 were a taxi driver, then x_8 is playing tennis. For all x_8, x_8 is a mechanic and x_8 is fast. For all x_8, if x_8 plays squash, then x_8 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which either x_8 is a mechanic or x_8 will play tennis are not true.
 From the fact that for all x_8, if x_8 plays squash, then x_8 is playing tennis, that for all x_8, if x_8 were a taxi driver, then x_8 is playing tennis, and that for all x_8, x_8 will play squash or x_8 is a taxi driver we can infer that for all x_8, x_8 will play tennis via universal disjunction elimination. From the fact that for all x_8, x_8 is a mechanic and x_8 is fast we can infer that for all x_8, x_8 is a mechanic via universal simplification. Finally, from the fact that for all x_8, x_8 is a mechanic, and that for all x_8, x_8 will play tennis we can infer that for all x_8, x_8 is a mechanic and x_8 will play tennis via universal conjunction, which contradicts that There is at least one x_8 for which either x_8 is a mechanic or x_8 will play tennis are not true. Therefore, the answer is no.