SOLVED

Let $A\subseteq \mathbb{F}_p$. Let
\[A\hat{+}A = \{ a+b : a\neq b \in A\}.\]
Is it true that
\[\lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)?\]

A question of Erdős and Heilbronn. Solved in the affirmative by da Silva and Hamidoune

[dSHa94].