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: Elisabeth is a poet or Susan is playing squash. For all x_12, x_12 will play squash if and only if x_12 will sleep. If James were happy, then Susan is sleeping. If Elisabeth were a poet, then James is happy.
If Elisabeth were a poet, then Susan is sleeping can be inferred via the transitivity rule. If Susan were a lawyer, then Elisabeth is a poet can be inferred via the rewriting rule. For all x_12, if x_12 plays squash, then x_12 is sleeping can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 sleeps, then x_12 is playing squash can be inferred via the universal biconditional elimination rule.