What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all x, if x were sad, then x is an astronaut. For all x, x is an astronaut if and only if x is poor. For all x, if x were an astronaut, then x is sad. For all x, x is not excited or x is sad. For all x, x is excited or x is poor.
For all x, x is poor or x is sad can be inferred via the universal resolution rule. For all x, x is sad if and only if x is an astronaut can be inferred via the universal biconditional introduction rule. For all x, x is an astronaut if and only if x is sad can be inferred via the universal biconditional introduction rule. For all x, if x were an astronaut, then x is poor can be inferred via the universal biconditional elimination rule. For all x, if x were poor, then x is an astronaut can be inferred via the universal biconditional elimination rule.