Consider the following premises. For all x_11, x_11 will play squash. For all x_11, x_11 is not a writer or x_11 is a bartender. There is at least one x_11 for which x_11 is a writer or x_11 will play a game. For all x_11, x_11 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, either x_11 is a bartender or x_11 will play squash are not true.
 From the fact that there is at least one x_11 for which x_11 is a writer or x_11 will play a game, and that for all x_11, x_11 is not a writer or x_11 is a bartender we can infer that there is at least one x_11 for which x_11 will play a game or x_11 is a bartender via existential resolution. From the fact that there is at least one x_11 for which x_11 will play a game or x_11 is a bartender, and that for all x_11, x_11 will not play a game we can infer that there is at least one x_11 for which x_11 is a bartender via existential disjunctive syllogism. Finally, from the fact that there is at least one x_11 for which x_11 is a bartender, and that for all x_11, x_11 will play squash we can infer that some bartenders will play squash via existential conjunction, which contradicts that For all x_11, either x_11 is a bartender or x_11 will play squash are not true. Therefore, the answer is no.