\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{t12\_int\_4 (TMZZ1Uv6VSbkKPTTnDea6PxNsUVHCcru6t5)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}(((k6\_int\_1~X1~X0=k6\_int\_1~X2~X0){\unicdbdjdcd}((X0=k6\_numbers){\unicdcdcdid}\\
(r2\_int\_1~X1~X2~X0))){\unicdcdcdhd}((r2\_int\_1~X1~X2~X0){\unicdbdjdcd}(k6\_int\_1~X1~X0=k6\_int\_1~\\
X2~X0)))))\end{array}
\label{hyp:ehgdedpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{{k6\_int\_1}~{X0}}~{X0}}={k6\_numbers}})}}}\label{hyp:ehfdadpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}((r2\_int\_1~X0~k6\_numbers~X0){\unicdcdcdhd}(r2\_int\_1~\\
k6\_numbers~X0~X0))\end{array}
\label{hyp:ehbdcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v1\_int\_1}~{X0}}}\label{hyp:chdgcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k6\_int\_1~X0~X1))\end{array}
\label{hyp:egehpflggdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfjgogehpfed}
${{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{k6\_numbers}={{{k6\_int\_1}~{k6\_numbers}}~{X0}}})}}}$.
\end{theorem}
\end{document}
