Consider the following premises. For all x_7, x_7 is an artist. For all x_7, x_7 is not an artist or x_7 will play a game. For all x_7, x_7 is not a scientist. There is at least one x_7 for which x_7 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, either x_7 is a bartender or x_7 will play a game are not true.
 From the fact that for all x_7, x_7 is an artist we can infer that for all x_7, x_7 is an artist or x_7 is a scientist via universal addition. From the fact that for all x_7, x_7 is an artist or x_7 is a scientist, and that for all x_7, x_7 is not an artist or x_7 will play a game we can infer that for all x_7, x_7 is a scientist or x_7 will play a game via universal resolution. From the fact that for all x_7, x_7 is a scientist or x_7 will play a game, and that for all x_7, x_7 is not a scientist we can infer that for all x_7, x_7 will play a game via universal disjunctive syllogism. Finally, from the fact that there is at least one x_7 for which x_7 is a bartender, and that for all x_7, x_7 will play a game we can infer that some bartenders will play a game via existential conjunction, which contradicts that For all x_7, either x_7 is a bartender or x_7 will play a game are not true. Therefore, the answer is no.