  A search for the standard model production of four top quarks (pp $\to$
$\mathrm{t\bar{t}t\bar{t}}$) is reported using single-lepton plus jets and
opposite-sign dilepton plus jets signatures. Proton-proton collisions are
recorded with the CMS detector at the LHC at a center-of-mass energy of 13 TeV
in a sample corresponding to an integrated luminosity of 35.8 fb$^{-1}$. A
multivariate analysis exploiting global event and jet properties is used to
discriminate $\mathrm{t\bar{t}t\bar{t}}$ from $\mathrm{t\bar{t}}$ production.
No significant deviation is observed from the predicted background. An upper
limit is set on the cross section for $\mathrm{t\bar{t}t\bar{t}}$ production in
the standard model of 48 fb at 95% confidence level. When combined with a
previous measurement by the CMS experiment from an analysis of other final
states, the observed signal significance is 1.4 standard deviations, and the
combined cross section measurement is 13 $^{+11}_{-9}$ fb. The result is also
interpreted in the framework of effective field theory.
