\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{t11\_hilbert3 (TMVxCfAyUEyHwwzcur85e6NM5FvXr89GFxR)}
\maketitle
Let $ k4\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X0{\unicdcdgdad}X1){\unicdbdjdcd}(k4\_card\_3~\\
(k4\_funct\_4~X0~X1~(k1\_tarski~X2)~(k1\_tarski~X3))=k1\_tarski~(k4\_funct\_4~\\
X0~X1~X2~X3))\end{array}
\label{hyp:ehedhdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~X2~X3)){\unicdbdjdcd}(r1\_tarski~(k4\_card\_3~(\\
k4\_funct\_4~X4~X5~X0~X2))~(k4\_card\_3~(k4\_funct\_4~X4~X5~X1~X3)))\end{array}
\label{hyp:ehcdbdpfehpgahchfgbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{X1}})}{\unicdbdjded}{({{X0} \in {X1}})}}}}\label{hyp:mgbdpfkhggngjgdhdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfigjgmgcgfgchehdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((X2 \in X4){\unicdcdcdhd}(X3 \in X5)){\unicdbdjdcd}((X0=X1){\unicdcdcdid}(k4\_funct\_4~X0~X1~X2~X3 \in k4\_card\_3~\\
(k4\_funct\_4~X0~X1~X4~X5)))\end{array}$$
\end{theorem}
\end{document}
