\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{t10\_int\_2 (TMT7syAQs2AgrCBsJfP3H2ci8uEHtqYNXR2)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\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}(((r1\_int\_1~X0~X1){\unicdcdcdhd}(r1\_int\_1~X1~X2)){\unicdbdjdcd}(r1\_int\_1~\\
X0~X2))))\end{array}
\label{hyp:mgfdpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}((r1\_int\_1~X0~(k4\_xcmplx\_0~X0)){\unicdcdcdhd}(r1\_int\_1~\\
(k4\_xcmplx\_0~X0)~X0))\end{array}
\label{hyp:mgedpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}((v1\_xcmplx\_0~(k4\_xcmplx\_0~X0)){\unicdcdcdhd}(v1\_int\_1~\\
(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdgddpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfjgogehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(((r1\_int\_1~\\
X0~X1){\unicdbdjdcd}(r1\_int\_1~X0~(k4\_xcmplx\_0~X1))){\unicdcdcdhd}(((r1\_int\_1~X0~(k4\_xcmplx\_0~\\
X1)){\unicdbdjdcd}(r1\_int\_1~X0~X1)){\unicdcdcdhd}(((r1\_int\_1~X0~X1){\unicdbdjdcd}(r1\_int\_1~(k4\_xcmplx\_0~\\
X0)~X1)){\unicdcdcdhd}(((r1\_int\_1~(k4\_xcmplx\_0~X0)~X1){\unicdbdjdcd}(r1\_int\_1~X0~X1)){\unicdcdcdhd}(\\
((r1\_int\_1~X0~X1){\unicdbdjdcd}(r1\_int\_1~(k4\_xcmplx\_0~X0)~(k4\_xcmplx\_0~X1))){\unicdcdcdhd}\\
(((r1\_int\_1~(k4\_xcmplx\_0~X0)~(k4\_xcmplx\_0~X1)){\unicdbdjdcd}(r1\_int\_1~X0~X1)){\unicdcdcdhd}\\
(((r1\_int\_1~X0~(k4\_xcmplx\_0~X1)){\unicdbdjdcd}(r1\_int\_1~(k4\_xcmplx\_0~X0)~X1)){\unicdcdcdhd}\\
((r1\_int\_1~(k4\_xcmplx\_0~X0)~X1){\unicdbdjdcd}(r1\_int\_1~X0~(k4\_xcmplx\_0~X1)))))))))))\end{array}$$
\end{theorem}
\end{document}
