A b s t r a c t. A set-theoretic property called Property S is introduced as a generalization of the well-known Property B . Property S is named for Schrijver who first used it in a paper \cite{Sch} in connection with the Boolean prime ideal theorem. It was independently introduced by Kolany \cite{Kol} to give a uniform treatment for a variety of satisfiability problems using an abstract resolution method to determine satisfiability. We further investigate Property S and resolution.