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_11, x_11 is a carpenter if and only if x_11 will cook. For all x_11, x_11 is poor and x_11 is a cashier. For all x_11, if x_11 were a carpenter, then x_11 is not poor. There is at least one x_11 for which x_11 will cook if and only if x_11 is happy.
For all x_11, x_11 is poor can be inferred via the universal simplification rule. For all x_11, x_11 is a cashier can be inferred via the universal simplification rule. For all x_11, if x_11 were a carpenter, then x_11 is cooking can be inferred via the universal biconditional elimination rule. There is at least one x_11 for which if x_11 cooks, then x_11 is happy can be inferred via the existential biconditional elimination rule. For all x_11, if x_11 cooks, then x_11 is a carpenter can be inferred via the universal biconditional elimination rule. There is at least one x_11 for which if x_11 were happy, then x_11 is cooking can be inferred via the existential biconditional elimination rule.