Consider the following premises. For all x_13, if x_13 were a lawyer, then x_13 is sleeping. For all x_13, if x_13 were happy, then x_13 is playing a game. For all x_13, x_13 will cook. For all x_13, if x_13 cooks, then x_13 is poor. For all x_13, x_13 is happy or x_13 is a lawyer. For all x_13, x_13 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which either x_13 will sleep or x_13 is poor are not true.
 From the fact that for all x_13, if x_13 were happy, then x_13 is playing a game, and that for all x_13, x_13 will not play a game we can infer that for all x_13, x_13 is not happy via universal modus tollens. From the fact that for all x_13, x_13 is happy or x_13 is a lawyer, and that for all x_13, x_13 is not happy we can infer that for all x_13, x_13 is a lawyer via universal disjunctive syllogism. From the fact that for all x_13, if x_13 cooks, then x_13 is poor, and that for all x_13, x_13 will cook we can infer that for all x_13, x_13 is poor via universal modus ponens. From the fact that for all x_13, if x_13 were a lawyer, then x_13 is sleeping, and that for all x_13, x_13 is a lawyer we can infer that for all x_13, x_13 will sleep via universal modus ponens. Finally, from the fact that for all x_13, x_13 will sleep, and that for all x_13, x_13 is poor we can infer that for all x_13, x_13 will sleep and x_13 is poor via universal conjunction, which contradicts that There is at least one x_13 for which either x_13 will sleep or x_13 is poor are not true. Therefore, the answer is no.