I looked at the snail pictures. The snail appears to be genus Oxychilus.
They are definitely not Haplotrema, which are native California omnivorous
snails (that will eat plants as well as other snails). Combining information
from the photos and from the size measurements (about 16 mm diam) you gave,
I concur with Phil Liff-Grieff who said they are probably Oxychilus
draparnaudi. They have been introduced from Europe, and are indeed
carnivorous, eating other snails, as well as other soil invertebrates. I
raised some related O. cellarius (up to about 9 mm diam) for a few months
and never got them to eat plant material - they would readily eat other
snails, though. I never checked whether they would eat Helix aspersa,
though.
   Best wishes,   -Tim-

Timothy A. Pearce, Ph.D., Curator of Mollusks
Carnegie Museum of Natural History
4400 Forbes Ave, Pittsburgh, PA 15213-4080
phone: 412-622-1916; fax: 412-622-8837
email: [log in to unmask]