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_8, x_8 is happy. For all x_8, if x_8 were an astronaut, then x_8 is not happy. For all x_8, if x_8 were an astronaut, then x_8 is running. For all x_8, if x_8 were an astronaut, then x_8 is running. For all x_8, if x_8 goes running, then x_8 is an astronaut.
For all x_8, x_8 is not an astronaut can be inferred via the universal modus tollens rule. For all x_8, x_8 is an astronaut if and only if x_8 will go running can be inferred via the universal biconditional introduction rule. For all x_8, x_8 is an astronaut if and only if x_8 will go running can be inferred via the universal biconditional introduction rule. For all x_8, x_8 will go running if and only if x_8 is an astronaut can be inferred via the universal biconditional introduction rule. For all x_8, x_8 will go running if and only if x_8 is an astronaut can be inferred via the universal biconditional introduction rule.