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, x_5 will not play squash. For all x_5, if x_5 cooks, then x_5 is writing a letter. For all x_5, x_5 will play squash if and only if x_5 will cook. There is at least one x_5 for which if x_5 writes a letter, then x_5 is cooking.
There is at least one x_5 for which x_5 will write a letter if and only if x_5 will cook can be inferred via the existential biconditional introduction rule. There is at least one x_5 for which x_5 will cook if and only if x_5 will write a letter can be inferred via the existential biconditional introduction rule. For all x_5, if x_5 plays squash, then x_5 is cooking can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 cooks, then x_5 is playing squash can be inferred via the universal biconditional elimination rule. For all x_5, x_5 will not cook can be inferred via the universal biconditional elimination rule.