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_18, x_18 will play tennis if and only if x_18 will sleep. For all x_18, x_18 will not sleep. Barbara is poor or Thomas is a carpenter. For all x_18, x_18 will play tennis if and only if x_18 will write a letter. Barbara is poor if and only if Michael is writing a letter.
If Barbara were poor, then Michael is writing a letter can be inferred via the biconditional elimination rule. If Michael writes a letter, then Barbara is poor can be inferred via the biconditional elimination rule. For all x_18, if x_18 plays tennis, then x_18 is sleeping can be inferred via the universal biconditional elimination rule. For all x_18, if x_18 plays tennis, then x_18 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_18, if x_18 sleeps, then x_18 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_18, if x_18 writes a letter, then x_18 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_18, x_18 will not play tennis can be inferred via the universal biconditional elimination rule.