Consider the following premises. There is at least one x_5 for which x_5 is a poet. For all x_5, x_5 is a lawyer or x_5 will go running. For all x_5, if x_5 were a lawyer, then x_5 is happy. For all x_5, x_5 is not happy. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, either x_5 is a poet or x_5 will go running are not true.
 From the fact that for all x_5, if x_5 were a lawyer, then x_5 is happy, and that for all x_5, x_5 is not happy we can infer that for all x_5, x_5 is not a lawyer via universal modus tollens. From the fact that for all x_5, x_5 is a lawyer or x_5 will go running, and that for all x_5, x_5 is not a lawyer we can infer that for all x_5, x_5 will go running via universal disjunctive syllogism. Finally, from the fact that there is at least one x_5 for which x_5 is a poet, and that for all x_5, x_5 will go running we can infer that some poets will go running via existential conjunction, which contradicts that For all x_5, either x_5 is a poet or x_5 will go running are not true. Therefore, the answer is no.