Consider the following premises. For all x_6, x_6 is fast or x_6 will play squash. For all x_6, x_6 will not work. For all x_6, x_6 will work or x_6 will read a book. For all x_6, if x_6 plays squash, then x_6 is sleeping. For all x_6, if x_6 were fast, then x_6 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which either x_6 will sleep or x_6 will read a book are not true.
 From the fact that for all x_6, x_6 will work or x_6 will read a book, and that for all x_6, x_6 will not work we can infer that for all x_6, x_6 will read a book via universal disjunctive syllogism. From the fact that for all x_6, if x_6 were fast, then x_6 is sleeping, that for all x_6, if x_6 plays squash, then x_6 is sleeping, and that for all x_6, x_6 is fast or x_6 will play squash we can infer that for all x_6, x_6 will sleep via universal disjunction elimination. Finally, from the fact that for all x_6, x_6 will sleep, and that for all x_6, x_6 will read a book we can infer that for all x_6, x_6 will sleep and x_6 will read a book via universal conjunction, which contradicts that There is at least one x_6 for which either x_6 will sleep or x_6 will read a book are not true. Therefore, the answer is no.