Alumino-silicate refractories contain both alumina:
\[
Al_2O_3
\]
and silica:
\[
SiO_2.
\]
Common alumino-silicate minerals include:
\[
\text{Andalusite},
\]
\[
\text{Sillimanite},
\]
and
\[
\text{Kyanite}.
\]
These minerals have the same general chemical composition:
\[
Al_2SiO_5.
\]
Thus, they contain both alumina and silica.
Corundum, however, is crystalline alumina.
Its formula is:
\[
Al_2O_3.
\]
It does not contain silica as part of its chemical formula.
Therefore, corundum is not an alumino-silicate refractory.
Hence, the correct answer is:
\[
\text{Corundum}.
\]