Consider the following premises. For all x_14, x_14 is a taxi driver. For all x_14, x_14 is not a taxi driver. David is cooking. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will play squash and x_14 will cook.
 From the fact that for all x_14, x_14 is a taxi driver we can infer that for all x_14, x_14 is a taxi driver or x_14 will play squash via universal addition. From the fact that for all x_14, x_14 is a taxi driver or x_14 will play squash, and that for all x_14, x_14 is not a taxi driver we can infer that for all x_14, x_14 will play squash via universal disjunctive syllogism. From the fact that David is cooking we can infer that there is at least one x_14 for which x_14 will cook via existential generalization. Finally, from the fact that for all x_14, x_14 will play squash, and that there is at least one x_14 for which x_14 will cook we can infer that there is at least one x_14 for which x_14 will play squash and x_14 will cook via existential conjunction. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.