The South Pole Telescope ( SPT ) has systematically identified 81 high-redshift , strongly gravitationally lensed , dusty star-forming galaxies ( DSFGs ) in a 2500 square degree cosmological mm-wave survey .
We present the final spectroscopic redshift survey of this flux-limited ( S _ { 870 \mathrm { \mu m } } > 25 \mathrm { mJy } ) sample .
The redshift survey was conducted with the Atacama Large Millimeter/submillimeter Array across the 3 \mathrm { mm } spectral window , targeting carbon monoxide line emission .
The SPT sample is now spectroscopically complete , with redshifts spanning the range 1.9 < z < 6.9 , with a median of z = 3.9 \pm 0.2 .
We present the mm through far-infrared photometry and spectral energy density fits for all sources , along with their inferred intrinsic properties .

Comparing the properties of the SPT sources to the unlensed DSFG population , we demonstrate that the SPT-selected DSFGs represent the most extreme infrared-luminous galaxies , even after accounting for strong gravitational lensing .
The SPT sources have a median star formation rate of 2.3 ( 2 ) \times 10 ^ { 3 } \mathrm { M _ { \odot } yr ^ { -1 } } and a median dust mass of 1.4 ( 1 ) \times 10 ^ { 9 } \mathrm { M _ { \odot } } .
However , the inferred gas depletion timescales of the SPT sources are comparable to those of unlensed DSFGs , once redshift is taken into account .
This SPT sample contains roughly half of the known spectroscopically confirmed DSFGs at z > 5 , making this the largest sample of high-redshift DSFGs to-date , and enables us to measure the “ high-redshift tail ” of the distribution of luminous DSFGs .
Though galaxy formation models struggle to account for the SPT redshift distribution , the larger sample statistics from this complete and well-defined survey will help inform future theoretical efforts .