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_15, if x_15 were a taxi driver, then x_15 is playing squash. For all x_15, if x_15 cooks, then x_15 is a taxi driver. For all x_15, if x_15 writes a letter, then x_15 is cooking. For all x_15, x_15 will write a letter or x_15 is a carpenter. For all x_15, x_15 will play squash if and only if x_15 is an astronaut. For all x_15, if x_15 were a carpenter, then x_15 is a taxi driver.
For all x_15, if x_15 cooks, then x_15 is playing squash can be inferred via the universal transitivity rule. For all x_15, if x_15 writes a letter, then x_15 is a taxi driver can be inferred via the universal transitivity rule. For all x_15, if x_15 were a carpenter, then x_15 is playing squash can be inferred via the universal transitivity rule. For all x_15, if x_15 plays squash, then x_15 is an astronaut can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 were an astronaut, then x_15 is playing squash can be inferred via the universal biconditional elimination rule.