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_5, if x_5 were curious, then x_5 is working. For all x_5, x_5 will not write a letter. For all x_5, x_5 is curious if and only if x_5 will write a letter. For all x_5, if x_5 works, then x_5 is curious.
For all x_5, x_5 is curious if and only if x_5 will work can be inferred via the universal biconditional introduction rule. For all x_5, x_5 will work if and only if x_5 is curious can be inferred via the universal biconditional introduction rule. For all x_5, if x_5 were curious, then x_5 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 writes a letter, then x_5 is curious can be inferred via the universal biconditional elimination rule. For all x_5, x_5 is not curious can be inferred via the universal biconditional elimination rule.