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, x is an astronaut or x is an artist. There is at least one x for which if x were an astronaut, then x is happy. For all x, x is not happy. For all x, if x were happy, then x is an astronaut.
There is at least one x for which x is not an astronaut can be inferred via the existential modus tollens rule. There is at least one x for which x is an astronaut if and only if x is happy can be inferred via the existential biconditional introduction rule. There is at least one x for which x is happy if and only if x is an astronaut can be inferred via the existential biconditional introduction rule.