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Context. IRAS 19312+1950 is an isolated infrared source that exhibits a characteristic quasi-point-symmetric morphology in the near- and mid-infrared images and is also very bright in molecular radio lines. Because of its unique observational characteristics, various observational studies have been conducted and several hypotheses have been proposed regarding its origin, which is still unclear. So far, it has been suggested that it could be a peculiar evolved star, a young stellar object, or even a red nova remnant. Regardless of which type of object it is ultimately classified as, IRAS 19312+1950 is exceptionally bright in the infrared and molecular radio lines and therefore will undoubtedly be crucial as a prototype of this kind of object having a peculiar nature or unusual evolutionary phase. Aims. This study aims to reveal the molecular composition of the central part of IRAS 19312+1950 by performing an unbiased molecular radio line survey and discussing the origin of the object from a molecular chemical point of view. Methods. We carried out a spectral line survey with the IRAM 30 m telescope towards the center of IRAS 19312+1950 in the 3 and 1.3 mm windows. Results. In total, 28 transition lines of 22 molecular species and those isotopologues are detected towards IRAS 19312+1950, some of which exhibit a broad and a narrow components. Seventeen thermal lines and 1 maser line are newly detected. The molecular species of C$^{17}$O, $^{30}$SiO, HN$^{13}$C, HC$^{18}$O$^{+}$, H$_{2}$CO, and $c$-C$_{3}$H$_{2}$ are detected for the first time in this object. Conclusions. Our results, in combination with previous studies, favor the hypothesis that IRAS 19312+1950 might be a red nova remnant, in which the progenitors that merged to become a red nova may have contained at least two evolved stars with oxygen-rich and carbon-rich chemistry, respectively.