\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{t1\_msualg\_4 (TMdLFE52UtwqhTRcNmHfyjHkfLRymBpHjxv)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}\\
(v1\_partfun1~X1~X0)))){\unicdcdcdhd}(((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdcdcdhd}((m1\_msualg\_4~X3~X0~X1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X4~X0))))){\unicdbdjdcd}(k1\_msualg\_4~X0~X1~X2~X3~X4=k1\_funct\_1~\\
X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l2\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}(l2\_msualg\_1~X1~X0))\end{array}
\label{hyp:egehpfmgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}\\
(v1\_partfun1~X1~X0)))){\unicdcdcdhd}(((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdcdcdhd}((m1\_msualg\_4~X3~X0~X1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X4~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_msualg\_4~X0~X1~X2~\\
X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~X1~X4)~(k1\_funct\_1~\\
X2~X4))))\end{array}
\label{hyp:egehpflgbdpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_msualg\_4~X2~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}((v2\_msualg\_4~X2~X0~\\
X1){\unicdbdjded}(v1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)))))\end{array}
\label{hyp:egddpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_msualg\_4~\\
X2~X0~X1~X1){\unicdbdjdcd}((v1\_msualg\_4~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~X1~X3)~(k1\_funct\_1~X1~\\
X3)))){\unicdbdjdcd}(((X3 \in X0){\unicdcdcdhd}(k1\_funct\_1~X2~X3=X4)){\unicdbdjdcd}((v3\_relat\_2~X4){\unicdcdcdhd}(\\
(v8\_relat\_2~X4){\unicdcdcdhd}((v1\_partfun1~X4~(k1\_funct\_1~X1~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~X1~X3)~(k1\_funct\_1~X1~\\
X3)))))))))))\end{array}
\label{hyp:egcdpfngdhfhbgmghgpfed}
\end{equation}
\begin{theorem}\label{thm:ehbdpfngdhfhbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v2\_msualg\_4~X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}(\\
(v3\_relat\_2~(k1\_msualg\_4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X1)~X3~X2)){\unicdcdcdhd}((v8\_relat\_2~(k1\_msualg\_4~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)~X3~X2)){\unicdcdcdhd}((v1\_partfun1~\\
(k1\_msualg\_4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)~X3~X2)~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X2)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_msualg\_4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)~X3~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~(u3\_msualg\_1~\\
X0~X1)~X2)~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X2))))))))))\end{array}$$
\end{theorem}
\end{document}
