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High-redshift dusty star-forming galaxies with very high star formation rates(500 -- 3000 M$_{\odot}$ yr$^{-1}$) are key to understanding the formation ofthe most extreme galaxies in the early Universe. Characterising the gasreservoir of these systems can reveal the driving factor behind the high starformation. Using molecular gas tracers like high-J CO lines, neutral carbonlines and the dust continuum, we can estimate the gas density and radiationfield intensity in their interstellar media. In this paper, we present highresolution ($\sim$0.4$^{\prime\prime}$) observations of CO(7-6), [CI](2-1) anddust continuum of 3 lensed galaxies from the SPT-SMG sample at $z\sim$ 3 withthe Atacama Large Millimeter/submillimeter Array. Our sources have highintrinsic star-formation rates ($>$850 M$_{\odot}$yr$^{-1}$) and rather shortdepletion timescales ($<$100 Myr). Based on the L$_{[\rm CI](2-1)}$/L$_{\rmCO(7-6)}$ and L$_{[\rm CI](2-1)}$/L$_{\rm IR}$ ratios, our galaxy sample hassimilar radiation field intensities and gas densities compared to othersubmillimetre galaxies. We perform visibility-based lens modelling on theseobjects to reconstruct the kinematics in the source plane. We find that thecold gas masses of the sources are compatible with simple dynamical massestimates using ULIRG-like values of the CO-H$_2$ conversion factor$\alpha_{\rm CO}$ but not Milky Way-like values. We find diverse sourcekinematics in our sample: SPT0103-45 and SPT2147-50 are likely rotating diskswhile SPT2357-51 is possibly a major merger. The analysis presented in thepaper could be extended to a larger sample to determine better statistics ofmorphologies and interstellar medium properties of high-$z$ dusty star-forminggalaxies.

High resolution spectral imaging of CO(7-6), [CI](2-1) and continuum of three high-z lensed dusty star-forming galaxies using ALMA