Consider the following premises. If Joseph sleeps, then Patricia is playing tennis. Elisabeth is playing squash if and only if Patricia is playing tennis. For all x_13, x_13 will sleep or x_13 is an astronaut. Elisabeth is not playing squash. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not an astronaut.
 From the fact that for all x_13, x_13 will sleep or x_13 is an astronaut we can infer that Joseph is sleeping or Joseph is an astronaut via universal instantiation. From the fact that Elisabeth is playing squash if and only if Patricia is playing tennis, and that Elisabeth is not playing squash we can infer that Patricia is not playing tennis via biconditional elimination. From the fact that if Joseph sleeps, then Patricia is playing tennis, and that Patricia is not playing tennis we can infer that Joseph is not sleeping via modus tollens. Finally, from the fact that Joseph is sleeping or Joseph is an astronaut, and that Joseph is not sleeping we can infer that Joseph is an astronaut via disjunctive syllogism, which contradicts that Joseph is not an astronaut. Therefore, the answer is no.