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We present the first results of a high-spectral-resolution survey of the carbon-rich evolved star IRC+10216 that was carried out with the HIFI spectrometer onboard Herschel. This survey covers all HIFI bands, with a spectral range from 488 to 1901GHz. In this letter we focus on the band-1b spectrum, in a spectral range 554.5-636.5GHz, where we identified 130 spectral features with intensities above 0.03 K and a signal-to-noise ratio >5. Detected lines arise from HCN, SiO, SiS, CS, CO, metal-bearing species and, surprisingly, silicon dicarbide (SiC2). We identified 55 SiC2 transitions involving energy levels between 300 and 900 K. By analysing these rotational lines, we conclude that SiC2 is produced in the inner dust formation zone, with an abundance of ~2x10^-7 relative to molecular hydrogen. These SiC2 lines have been observed for the first time in space and have been used to derive an SiC2 rotational temperature of ~204 K and a source-averaged column density of ~6.4x10^15 cm^-2. Furthermore, the high quality of the HIFI data set was used to improve the spectroscopic rotational constants of SiC2.