Consider the following premises. For all x_6, x_6 will not cook. For all x_6, x_6 is a sailor or x_6 will cook. For all x_6, x_6 will play squash. For all x_6, x_6 is not a sailor or x_6 will make tea. 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 either x_6 will make tea or x_6 will play squash are not true.
 From the fact that for all x_6, x_6 is a sailor or x_6 will cook, and that for all x_6, x_6 is not a sailor or x_6 will make tea we can infer that for all x_6, x_6 will cook or x_6 will make tea via universal resolution. From the fact that for all x_6, x_6 will cook or x_6 will make tea, and that for all x_6, x_6 will not cook we can infer that for all x_6, x_6 will make tea via universal disjunctive syllogism. Finally, from the fact that for all x_6, x_6 will make tea, and that for all x_6, x_6 will play squash we can infer that for all x_6, x_6 will make tea and x_6 will play squash via universal conjunction, which contradicts that There is at least one x_6 for which either x_6 will make tea or x_6 will play squash are not true. Therefore, the answer is no.