Inconsistency of Reinhardt cardinals with $\mathsf{Z}\mathsf{F}$

A proof will be presented that the existence of a non-trivial ${\mathrm{\Sigma }}_1$-elementary embedding $j:V_{\lambda +3}\prec V_{\lambda +3}$ is inconsistent with $\mathsf{\text{ZF}}$. Sections 1 and 2 shall review various important contributions from the literature, notably including \cite{Goldberg2020}, \cite{Schlutzenberg2020}, and \cite{Woodin2010}, the latter reference being where the crucial forcing construction is presented. Section 3 shall introduce some new large cardinal properties, of consistency strength intermediate between ${\mathsf{I}}_{\mathsf{3}}$ and ${\mathsf{I}}_{\mathsf{2}}$, and greater than ${\mathsf{I}}_{\mathsf{1}}$, respectively. The proof of the inconsistency with $\mathsf{Z}\mathsf{F}$ of the existence of a non-trivial ${\mathrm{\Sigma }}_1$-elementary embedding $j:V_{\lambda +3}\prec V_{\lambda +3}$ shall be given in Section 4. The claims of Sections 2 and 4 are provable in $\mathsf{\text{ZF}}$; those of Section 3, with the exception of the last two theorems, in $\mathsf{\text{ZFC}}$.