\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t41\_conlat\_1 (TMZ13Zo4ES9ZJrXkF399eyjx1TbEd44SPgb)}
\maketitle
Let $ v1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v9\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}(k1\_binop\_1~(k10\_conlat\_1~X0)~X1~(k6\_conlat\_1~\\
X0)=X1))\end{array}
\label{hyp:ehedadpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_conlat\_1~X2~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~\\
X2~X0){\unicdcdcdhd}((v7\_conlat\_1~X2~X0){\unicdcdcdhd}(l2\_conlat\_1~X2~X0)))){\unicdbdjdcd}(k1\_binop\_1~\\
(k9\_conlat\_1~X0)~X1~(k1\_binop\_1~(k10\_conlat\_1~X0)~X1~X2)=X1)))\end{array}
\label{hyp:ehddhdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_conlat\_1~X2~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~\\
X2~X0){\unicdcdcdhd}((v7\_conlat\_1~X2~X0){\unicdcdcdhd}(l2\_conlat\_1~X2~X0)))){\unicdbdjdcd}(k1\_binop\_1~\\
(k10\_conlat\_1~X0)~X1~X2=k1\_binop\_1~(k10\_conlat\_1~X0)~X2~X1)))\end{array}
\label{hyp:ehddddpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_conlat\_1~X2~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~\\
X2~X0){\unicdcdcdhd}((v7\_conlat\_1~X2~X0){\unicdcdcdhd}(l2\_conlat\_1~X2~X0)))){\unicdbdjdcd}(k1\_binop\_1~\\
(k9\_conlat\_1~X0)~X1~X2=k1\_binop\_1~(k9\_conlat\_1~X0)~X2~X1)))\end{array}
\label{hyp:ehddcdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((v4\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((v7\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((v9\_conlat\_1~(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}(l2\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflggdpfdgpgogmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfdgpgogmgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}(k1\_binop\_1~(k9\_conlat\_1~X0)~X1~(k6\_conlat\_1~\\
X0)=k6\_conlat\_1~X0))\end{array}$$
\end{theorem}
\end{document}
