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We present a measurement of the top-quark pair-production cross section in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ using a data sample corresponding to $1.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected with the Collider Detector at Fermilab. We reconstruct $t\overline{t}$ events in the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ channel, consisting of $e\ensuremath{\nu}+\mathrm{\text{jets}}$ and $\ensuremath{\mu}\ensuremath{\nu}+\mathrm{\text{jets}}$ final …