Consider the following premises. There is at least one x_13 for which if x_13 sleeps, then x_13 is an artist. For all x_13, if x_13 were an astronaut, then x_13 is a sailor. For all x_13, x_13 is an astronaut or x_13 is poor. For all x_13, x_13 will sleep. For all x_13, if x_13 were poor, then x_13 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, either x_13 is a sailor or x_13 is an artist are not true.
 From the fact that for all x_13, if x_13 were an astronaut, then x_13 is a sailor, that for all x_13, if x_13 were poor, then x_13 is a sailor, and that for all x_13, x_13 is an astronaut or x_13 is poor we can infer that for all x_13, x_13 is a sailor via universal disjunction elimination. From the fact that there is at least one x_13 for which if x_13 sleeps, then x_13 is an artist, and that for all x_13, x_13 will sleep we can infer that there is at least one x_13 for which x_13 is an artist via existential modus ponens. Finally, from the fact that for all x_13, x_13 is a sailor, and that there is at least one x_13 for which x_13 is an artist we can infer that there is at least one x_13 for which x_13 is a sailor and x_13 is an artist via existential conjunction, which contradicts that For all x_13, either x_13 is a sailor or x_13 is an artist are not true. Therefore, the answer is no.