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_12, x_12 is an astronaut or x_12 will not listen to a song. There is at least one x_12 for which x_12 is not a lawyer or x_12 is a doctor. For all x_12, if x_12 were an astronaut, then x_12 is a doctor. For all x_12, x_12 is a lawyer or x_12 will listen to a song. For all x_12, if x_12 were a doctor, then x_12 is an astronaut.
There is at least one x_12 for which x_12 will listen to a song or x_12 is a doctor can be inferred via the existential resolution rule. For all x_12, if x_12 listens to a song, then x_12 is an astronaut can be inferred via the universal rewriting rule. For all x_12, x_12 is an astronaut if and only if x_12 is a doctor can be inferred via the universal biconditional introduction rule. For all x_12, x_12 is a doctor if and only if x_12 is an astronaut can be inferred via the universal biconditional introduction rule.