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We have carried out the first spatially resolved investigation of the multiphase interstellar medium (ISM) at high redshift, using the z = 4.24 strongly lensed submillimetre galaxy H-ATLASJ142413.9+022303 (ID141). We present high-resolution (down to ∼350 pc) ALMA observations in dust continuum emission and in the CO(7–6), $\rm H_2O (2_{1,1} - 2_{0,2})$, [C i] (1–0), and [C i] (2–1) lines, the latter two allowing us to spatially resolve the cool phase of the ISM for the first time. Our modelling of the kinematics reveals that the system appears to be dominated by a rotationally-supported gas disc with evidence of a nearby perturber. We find that the [C i] (1–0) line has a very different distribution to the other lines, showing the existence of a reservoir of cool gas that might have been missed in studies of other galaxies. We have estimated the mass of the ISM using four different tracers, always obtaining an estimate in the range of $\rm 3.2{\!-\!}3.8 \times 10^{11}\ M_{\odot }$, significantly higher than our dynamical mass estimate of $\rm 0.8{\!-\!}1.3 \times 10^{11}\ M_{\odot }$. We suggest that this conflict and other similar conflicts reported in the literature is because the gas-to-tracer ratios are ≃4 times lower than the Galactic values used to calibrate the ISM in high-redshift galaxies. We demonstrate that this could result from a top-heavy initial mass function and strong chemical evolution. Using a variety of quantitative indicators, we show that, extreme though it is at z = 4.24, ID141 will likely join the population of quiescent galaxies that appears in the Universe at z ∼ 3.