  Bell's theorem guarantees that no model based on local variables can
reproduce quantum correlations. Also some models based on non-local variables,
if subject to apparently "reasonable" constraints, may fail to reproduce
quantum physics. In this paper, we introduce a family of inequalities, which
allow testing Leggett's non-local model versus quantum physics, and which can
be tested in an experiment without additional assumptions. Our experimental
data falsify Leggett's model and are in agreement with quantum predictions.
