\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{l8\_msaterm (TMc6ZKfJtgTBieEvTVtgTGfAYDxRDTDJmy8)}
\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_dtconstr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_dtconstr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\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 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
((r1\_tarski~(k2\_lang1~(k5\_msafree~X0~X1))~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(k1\_tarski~(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_tarski~(k3\_card\_3~(k3\_msafree~\\
(u1\_struct\_0~X0)~X1))~(k1\_lang1~(k5\_msafree~X0~X1))){\unicdcdcdhd}((v2\_relat\_1~\\
X1){\unicdbdjdcd}((k2\_lang1~(k5\_msafree~X0~X1)=k2\_zfmisc\_1~(u4\_struct\_0~X0)~\\
(k1\_tarski~(u1\_struct\_0~X0))){\unicdcdcdhd}(k1\_lang1~(k5\_msafree~X0~X1)=k3\_card\_3~\\
(k3\_msafree~(u1\_struct\_0~X0)~X1)))))))\end{array}
\label{hyp:ehgdpfngdhbgggchfgfg}
\end{equation}
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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_dtconstr~X0){\unicdcdcdhd}(l1\_lang1~X0))){\unicdbdjdcd}\\
(k7\_dtconstr~X0=k2\_lang1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v1\_dtconstr~(k5\_msafree~X0~X1)){\unicdcdcdhd}((v2\_dtconstr~(\\
k5\_msafree~X0~X1)){\unicdcdcdhd}(v3\_dtconstr~(k5\_msafree~X0~X1))))\end{array}
\label{hyp:ggdggdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k5\_msafree~X0~X1)){\unicdcdcdhd}(v1\_lang1~(k5\_msafree~X0~X1)))\end{array}
\label{hyp:ggdgfdpfngdhbgggchfgfg}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_lang1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_dtconstr~X0){\unicdcdcdhd}(l1\_lang1~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k7\_dtconstr~X0)){\unicdcdcdhd}(m1\_subset\_1~(k7\_dtconstr~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflghdpfegehdgpgogdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
(l1\_lang1~(k5\_msafree~X0~X1))\end{array}
\label{hyp:egehpflgfdpfngdhbgggchfgfg}
\end{equation}
\begin{theorem}\label{thm:mgidpfngdhbgehfgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(u1\_struct\_0~(k5\_msafree~\\
X0~X1))~(k7\_dtconstr~(k5\_msafree~X0~X1))){\unicdbdjded}(X2 \in k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(k1\_tarski~(u1\_struct\_0~X0)))))\end{array}$$
\end{theorem}
\end{document}
