  We report physical properties of the brightest ($S_{870\,\mu \rm
m}=12.4$-$19.2\,$mJy) and not strongly lensed 18 870$\,\mu$m selected dusty
star-forming galaxies (DSFGs), also known as submillimeter galaxies (SMGs), in
the COSMOS field. This sample is part of an ALMA band$\,$3 spectroscopic survey
(AS2COSPEC), and spectroscopic redshifts are measured in 17 of them at
$z=2$-$5$. We perform spectral energy distribution analyses and deduce a median
total infrared luminosity of $L_{\rm IR}=(1.3\pm0.1)\times10^{13}\,L_{\odot}$,
infrared-based star-formation rate of ${\rm SFR}_{\rm
IR}=1390\pm150~M_{\odot}\,\rm yr^{-1}$, stellar mass of
$M_\ast=(1.4\pm0.6)\times10^{11}\,M_\odot$, dust mass of $M_{\rm
dust}=(3.7\pm0.5)\times10^9\,M_\odot$, and molecular gas mass of $M_{\rm gas}=
(\alpha_{\rm CO}/0.8)(1.2\pm0.1)\times10^{11}\,M_\odot$, suggesting that they
are one of the most massive, ISM-enriched, and actively star-forming systems at
$z=2$-$5$. In addition, compared to less massive and less active galaxies at
similar epochs, SMGs have comparable gas fractions; however, they have much
shorter depletion time, possibly caused by more active dynamical interactions.
We determine a median dust emissivity index of $\beta=2.1\pm0.1$ for our
sample, and by combining our results with those from other DSFG samples, we
find no correlation of $\beta$ with redshift or infrared luminosity, indicating
similar dust grain compositions across cosmic time for infrared luminous
galaxies. We also find that AS2COSPEC SMGs have one of the highest
dust-to-stellar mass ratios, with a median of $0.02\pm0.01$, significantly
higher than model predictions, possibly due to too strong of a AGN feedback
implemented in the model. Finally, our complete and uniform survey enables us
to put constraints on the most massive end of the dust and molecular gas mass
functions.
