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In this paper, $E_6$ and especially $E_7$ GUT are considered in the F-theorysetting in view of the free fermionic construction of the $4D$ heteroticstring. In particular, the NAHE-Based LRS model of \cite{Cleaver:2000ds,Cleaver:2002ps} is revisited as an illustration where the starting point wastaken to be the $N=4$, $E_7 \times E_7 \times SO(16)$ which through the use ofboundary condition basis vectors is reduced to obtain the flipped $SO(10)$ GUTsymmetry.  We also seek to extend the results of \cite{Faraggi:2002ah} in the case ofthe flipped $SU(5)$ to home in on the flipped $SO(10)$ vacua from theHor\v{a}va-Witten theory where the $E_8$ gauge group on the observable sectordecomposes as $E_{8}\supset E_{6}\times SU(3)$ with $E_{6}$ being the gaugegroup of the effective field theory. We find for the $E_{6}$ GUT symmetry,solutions of type A and solutions of type B where the Hirzebruch surfaces areconsidered for the base contrary to \cite{Faraggi:2002ah} where flipped $SU(5)$vacua were studied and only solutions of type B were found. Moreover, nosolutions are found in the case of the base being the del Pezzo surfaces.Furthermore, this goes hand in hand with the heterotic, low-energystring-derived effective model discussed in\cite{Ashfaque:2016psv,Ashfaque:2016ydg}.

F-Theory $E_7$, Heterotic String-Derived Vacua And Flipped $SO(10)$ In Hor\v{a}va-Witten Theory