\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\preoh[1]{\lnot #1}
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\begin{document}
\title{t30\_functor3 (TMU1gfJ1z9KzYHFjDcA9tcamRLosQcPuBu4)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k7\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\\
v2\_altcat\_1~X2){\unicdcdcdhd}((v11\_altcat\_1~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}(l2\_altcat\_1~\\
X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~\\
X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_functor0~X4~X0~X1){\unicdcdcdhd}(m2\_functor0~X4~X0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v15\_functor0~X5~X1~X2){\unicdcdcdhd}(m2\_functor0~X5~X1~X2)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((v15\_functor0~X6~X1~X2){\unicdcdcdhd}(m2\_functor0~X6~X1~X2)){\unicdbdjdcd}(\\
{\unicdcdadad} X7 .  (m2\_functor2~X7~X1~X2~X5~X6){\unicdbdjdcd}({\unicdcdadad} X8 .  (m2\_functor2~\\
X8~X0~X1~X3~X4){\unicdbdjdcd}(((r2\_functor2~X0~X1~X3~X4){\unicdcdcdhd}(r2\_functor2~X1~X2~X5~X6)){\unicdbdjdcd}\\
((r2\_functor2~X0~X2~(k1\_functor3~X0~X1~X2~X3~X5)~(k1\_functor3~X0~X1~\\
X2~X4~X6)){\unicdcdcdhd}(m2\_functor2~(k7\_functor3~X0~X1~X2~X3~X4~X5~X6~X8~X7)~X0~X2~\\
(k1\_functor3~X0~X1~X2~X3~X5)~(k1\_functor3~X0~X1~X2~X4~X6))))))))))))\end{array}
\label{hyp:mgddcdpfggfhogdgehpgchdd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfggfhogdgehpgchdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\\
v2\_altcat\_1~X2){\unicdcdcdhd}((v11\_altcat\_1~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}(l2\_altcat\_1~\\
X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~\\
X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_functor0~X4~X0~X1){\unicdcdcdhd}(m2\_functor0~X4~X0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v15\_functor0~X5~X1~X2){\unicdcdcdhd}(m2\_functor0~X5~X1~X2)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((v15\_functor0~X6~X1~X2){\unicdcdcdhd}(m2\_functor0~X6~X1~X2)){\unicdbdjdcd}(\\
{\unicdcdadad} X7 .  (m2\_functor2~X7~X0~X1~X3~X4){\unicdbdjdcd}({\unicdcdadad} X8 .  (m2\_functor2~\\
X8~X1~X2~X5~X6){\unicdbdjdcd}(((r2\_functor2~X0~X1~X3~X4){\unicdcdcdhd}(r2\_functor2~X1~X2~X5~X6)){\unicdbdjdcd}\\
((r2\_functor2~X0~X2~(k1\_functor3~X0~X1~X2~X3~X5)~(k1\_functor3~X0~X1~\\
X2~X4~X6)){\unicdcdcdhd}(m2\_functor2~(k7\_functor3~X0~X1~X2~X3~X4~X5~X6~X7~X8)~X0~X2~\\
(k1\_functor3~X0~X1~X2~X3~X5)~(k1\_functor3~X0~X1~X2~X4~X6))))))))))))\end{array}$$
\end{theorem}
\end{document}
