\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l6\_hilbert1 (TMHJVKtWqiJm26cCANSd2HsL2HWtLUHrQCz)}
\maketitle
Let $ v5\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v5\_hilbert1~X0){\unicdbdjded}((r1\_tarski~X0~(k13\_finseq\_1~k5\_numbers)){\unicdcdcdhd}\\
((v1\_hilbert1~X0){\unicdcdcdhd}((v2\_hilbert1~X0){\unicdcdcdhd}((v3\_hilbert1~X0){\unicdcdcdhd}(v4\_hilbert1~\\
X0)))))\end{array}
\label{hyp:egfdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_hilbert1}~{X0}})}{\unicdbdjded}{({{{{k12\_finseq\_1}~{k5\_numbers}}~{k6\_numbers}} \in {X0}})}}}\label{hyp:egbdpfigjgmgcgfgchehbd}
\end{equation}
\begin{theorem}\label{thm:mggdpfigjgmgcgfgchehbd}
${{\unicdcdadad} X0 .  {{\preoh{{({{v5\_hilbert1}~{X0}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X0}})}}}$.
\end{theorem}
\end{document}
