KöMaL 2011 B4350

In a tetrahedron $A_1 A_2 A_3 A_4$, for every interior point $P$ and for any order $i$, $j$, $k$, $l$ of the numbers 1, 2, 3, 4, the following inequality is true: $PA_i$+$PA_j$+$PA_k$<$A_l A_i$+$A_l A_j$+$A_l A_k$. Does it follow that the tetrahedron is regular?