Post-asymptotic giant branch ( post-AGB ) stars are known to be chemically diverse .
In this paper we present the first observational evidence of a star that has failed the third dredge-up ( TDU ) .
J005252.87-722842.9 is a A-type ( T _ { eff } = 8250 \pm 250K ) luminous ( 8200 \pm 700 L _ { \odot } ) , metal-poor ( [ Fe/H ] = -1.18 \pm 0.10 ) , low-mass ( M _ { initial } \approx 1.5 - 2.0 M _ { \odot } ) post-AGB star in the Small Magellanic Cloud .
Through a systematic abundance study , using high-resolution optical spectra from UVES , we found that this likely post-AGB object shows an intriguing photospheric composition with no confirmed carbon-enhancement ( upper limit of [ C/Fe ] < 0.50 ) nor enrichment of s -process elements .
We derived an oxygen abundance of [ O/Fe ] = 0.29 \pm 0.1 .
For Fe and O , we took into account the effects of non-local thermodynamic equilibrium ( NLTE ) .
We could not derive an upper limit for the nitrogen abundance as there are no useful nitrogen lines within our spectral coverage .
The chemical pattern displayed by this object has not been observed in single or binary post-AGBs .
Based on its derived stellar parameters and inferred evolutionary state , single star nucleosynthesis models predict that this star should have undergone TDU episodes while on the AGB and be carbon-enriched .
However , our observations are in contrast with these predictions .
We identify two possible Galactic analogues which are likely to be post-AGB stars , but the lack of accurate distances ( hence luminosities ) to these objects does not allow us to confirm their post-AGB status .
If they have low luminosities then they are likely to be dusty post-RGB stars .
The discovery of J005252.87-722842.9 reveals a new stellar evolutionary channel whereby a star evolves without any third dredge-up episodes .