\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdcdhd{\land}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{l131\_quaterni (TMPj4rotX4gdQZqo6tu8DPxgGQDsXptUYbm)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~\\
(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k3\_square\_1~X0)~(k3\_square\_1~\\
X1))~(k3\_square\_1~X2))~(k3\_square\_1~X3))))))\end{array}
\label{hyp:ehhdedpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgfdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k3\_square\_1}~{X0}})}})}}}\label{hyp:ggdgcdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k6\_square\_1}~{X0}})}})}}}\label{hyp:egehpflggdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_xreal\_0~X1){\unicdbdjdcd}((X1=k6\_square\_1~X0){\unicdbdjded}((r1\_xxreal\_0~k6\_numbers~\\
X1){\unicdcdcdhd}(k3\_square\_1~X1=X0)))))\end{array}
\label{hyp:egcdpfdhbhfhbgchfgpfbd}
\end{equation}
\begin{theorem}\label{thm:mgbdddbdpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (v1\_xreal\_0~X6){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (v1\_xreal\_0~X7){\unicdbdjdcd}(k3\_square\_1~(k6\_square\_1~(k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k3\_square\_1~(k2\_xcmplx\_0~X0~X4))~(\\
k3\_square\_1~(k2\_xcmplx\_0~X1~X5)))~(k3\_square\_1~(k2\_xcmplx\_0~X2~\\
X6)))~(k3\_square\_1~(k2\_xcmplx\_0~X3~X7))))=k2\_xcmplx\_0~(k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k3\_square\_1~(k2\_xcmplx\_0~X0~X4))~(k3\_square\_1~(\\
k2\_xcmplx\_0~X1~X5)))~(k3\_square\_1~(k2\_xcmplx\_0~X2~X6)))~(k3\_square\_1~\\
(k2\_xcmplx\_0~X3~X7))))))))))\end{array}$$
\end{theorem}
\end{document}
