On a generalization of property B

A set-theoretic property called Property S is introduced as a generalization of the well-known Property B. Property S is named for A.Schrijver who first used it to formulate an equivalent of the boolean prime ideal theorem. It was independently introduced by A. Kolany to give a uniform treatment for a variety of satisfiability problems who then used a generalized resolution method to determine satisfiability. Here we further investigate Property S and the resolution method.