\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{t13\_msualg\_3 (TMbDGXfuBTUmPZ8VA9HDqTsABPaybytuQ4i)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r3\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r1\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(v1\_msualg\_3~X3))))))\end{array}
\label{hyp:egjdpfngdhfhbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r2\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r1\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(v2\_msualg\_3~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X2)))))))\end{array}
\label{hyp:egidpfngdhfhbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r4\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r2\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(r3\_msualg\_3~X0~X1~X2~X3))))))\end{array}
\label{hyp:egbdadpfngdhfhbgmghgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfngdhfhbgmghgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r4\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r1\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}((v2\_msualg\_3~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X2)){\unicdcdcdhd}(v1\_msualg\_3~X3)))))))\end{array}$$
\end{theorem}
\end{document}
