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CK Vul erupted in 1670 and is considered a stellar-merger candidate. Its remnant contains a molecular component of surprisingly rich composition. We present interferometric line surveys with subarcsec resolution with ALMA and SMA. The observations provide interferometric maps of molecular line emission at frequencies between 88 and 243 GHz that allow imaging spectroscopy of more than 180 transitions of 26 species. We present, classify, and analyze the different morphologies of the emission regions displayed by the molecules. We also perform a non-LTE radiative-transfer analysis of emission of most of the observed species, deriving temperatures and column densities in five parts of the nebula. Non-LTE effects are clearly seen in complex species including methanol absorption against the CMB. The temperatures are 17 K in the inner remnant and 14 K in the extended lobes. We find total (hydrogen plus helium) densities in the range of $10^4-10^6$ cm$^{-3}$. The column densities provide relative abundance patterns in the remnant which currently are not understood. Attempts to derive elemental abundances within the assumption of a chemical equilibrium give only loose constraints on the CNO elements. That the formation of many of the observed molecules requires a major involvement of circumstellar shocks remains the preferred possibility. The molecular gas could have formed 350 yr ago or more recently. The molecules are well shielded from the interstellar radiation field by the circumstellar dust. Their presence alone indicates that the unobservable central star cannot be a hot object such as a white dwarf. This excludes some of the proposed scenarios on the nature of CK Vul. The general characteristics of the molecular environment of CK Vul derived in this study resemble quite well those of some pre-planetary nebulae and AGB stars, most notably that of OH231.8.