  Fix an arbitrary prime $p$. Let $F$ be a field, containing a primitive $p$-th
root of unity, with absolute Galois group $G_F$. The triple Massey product (in
the mod-$p$ Galois cohomology) is a partially defined, multi-valued function
$\langle \cdot,\cdot,\cdot \rangle: H^1(G_F)^3\rightarrow H^2(G_F).$ In this
work we prove a conjecture made in [11] stating that any defined triple Massey
product contains zero. As a result the pro-$p$ groups appearing in [11] are
excluded from being absolute Galois groups of fields $F$ as above.
