\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{l32\_fomodel4 (TMUqY3C9AEVuyfa7j4qFF9GifFuvYicVpJS)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_fomodel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_fomodel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_fomodel4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_fomodel4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_fomodel4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_fomodel4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}\\
((v11\_fomodel1~X1){\unicdcdcdhd}(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k1\_fomodel4~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(k1\_fomodel4~\\
X1))){\unicdbdjdcd}(((r1\_tarski~X4~X5){\unicdcdcdhd}(r1\_tarski~X2~X3)){\unicdbdjdcd}(((\preoh v6\_fomodel4~\\
X3~X1){\unicdcdcdhd}(\preoh v6\_fomodel4~X2~X1)){\unicdcdcdid}(r1\_tarski~(k3\_funct\_2~(k1\_zfmisc\_1~\\
(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k3\_fomodel4~\\
X1~X2~X0)~X4)~(k3\_funct\_2~(k1\_zfmisc\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))~(k3\_fomodel4~X1~X3~X0)~X5)))))))))\end{array}
\label{hyp:mgddbdpfggpgngpgegfgmged}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(m1\_funct\_2~(k9\_funct\_2~\\
X0~X1)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v11\_fomodel1~\\
X0){\unicdcdcdhd}(l1\_fomodel1~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(k9\_funct\_2~\\
(k9\_setfam\_1~(k1\_fomodel4~X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))))){\unicdcdcdhd}\\
(v7\_ordinal1~X2))){\unicdbdjdcd}(m2\_funct\_2~(k3\_fomodel4~X0~X1~X2)~(k9\_setfam\_1~\\
(k1\_fomodel4~X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))~(k9\_funct\_2~\\
(k9\_setfam\_1~(k1\_fomodel4~X0))~(k9\_setfam\_1~(k1\_fomodel4~X0))))\end{array}
\label{hyp:egehpflgddpfggpgngpgegfgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v11\_fomodel1~X0){\unicdcdcdhd}(l1\_fomodel1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_fomodel4~X1~X0){\unicdbdjded}(r1\_tarski~X1~(k1\_fomodel4~\\
X0)))\end{array}
\label{hyp:egddpfggpgngpgegfgmged}
\end{equation}
\begin{theorem}\label{thm:mgddcdpfggpgngpgegfgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}\\
((v11\_fomodel1~X1){\unicdcdcdhd}(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~\\
(k1\_fomodel4~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k9\_funct\_2~(k9\_setfam\_1~(k1\_fomodel4~X1))~(k9\_setfam\_1~(k1\_fomodel4~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v2\_fomodel4~X4~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  (v2\_fomodel4~\\
X5~X1){\unicdbdjdcd}(((r1\_tarski~X4~X5){\unicdcdcdhd}(r1\_tarski~X2~X3)){\unicdbdjdcd}(((\preoh v6\_fomodel4~\\
X3~X1){\unicdcdcdhd}(\preoh v6\_fomodel4~X2~X1)){\unicdcdcdid}(r1\_tarski~(k1\_funct\_1~(k3\_fomodel4~\\
X1~X2~X0)~X4)~(k1\_funct\_1~(k3\_fomodel4~X1~X3~X0)~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
