Local realism versus quantum theory: Violation of the generalized spin-sBell inequalities for a set of three distinct axes

Some simple inequalities which demonstrate the incompatibility of local realism with quantum theory are derived. They establish, for the first time, necessary conditions for violation of the generalized spin-$s$ Bell inequalities for a set of three distinct noncoplanar axes. For $s=\frac{1}{2}$, however, these inequalities are equivalent to Wigner's results, thus giving necessary and sufficient conditions.