  We present the Spitzer 10-37um IRS high resolution (R~600) spectroscopic
survey of the Seyfert galaxies of the 12 micron Galaxy Sample. The new spectra
of 61 galaxies, with those already published, gives us a total of 91 12micron
Seyfert galaxies observed, out of 112. We use an improved AGN classification
for Seyfert galaxies: instead of the type 1 and 2 classes, we use the
spectropolarimetric data to divide them into "AGN 1" and "AGN 2", where AGN 1's
include all broad-line objects, including the Seyfert 2's showing hidden broad
lines in polarized light, while AGN 2's contains only Seyferts with no
detectable broad lines at all. We present various mid-IR observables and we
find that these properties characterize the AGN 1's objects as a single family,
with strongly AGN-dominated spectra. In contrast, the AGN 2's can be divided in
two groups, the first one with properties similar to the AGN 1's and the second
similar to the non-Seyfert galaxies, such as LINERs or starburst galaxies. We
computed a semianalytical model to estimate the AGN and the starburst
contributions to the mid-IR galaxy emission at 19um. We find that AGN 1 have an
AGN contribution >73% and AGN 2 >45% of their total emission at 19um. The
detection of [NeV] lines is an almost perfect signature of energy production by
an AGN. We present mean spectra of the various AGN categories. We derive the
first local luminosity functions for the mid-infrared lines and the PAH
feature. No statistical difference is found in the space densities for Seyfert
1's and 2's, nor for the new classes of AGN 1's and 2's. The global output of
accretion-powered galactic nuclei in the local universe is derived from the
correlation between [NeV] line and the nonstellar IR continuum luminosity.
