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.