\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\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t76\_complex2 (TMWEaKrLKHTFxXt9oEMffX6kaf9rz3azU7k)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k4\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k3\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(\preoh (k3\_complex1~\\
(k1\_complex2~X0~X1)=k6\_numbers){\unicdbdjded}((k4\_complex2~X0~k6\_numbers~\\
X1=k13\_complex1~k32\_sin\_cos~np\_\_2){\unicdcdcdid}(k4\_complex2~X0~k6\_numbers~\\
X1=k4\_real\_1~(k13\_complex1~np\_\_3~np\_\_2)~k32\_sin\_cos))))))\end{array}
\label{hyp:ehhdfdpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}((k3\_complex1~(k1\_complex2~X0~X1)=k6\_numbers){\unicdbdjded}\\
((k4\_complex1~(k1\_complex2~X0~X1)=k8\_real\_1~(k17\_complex1~X0)~\\
(k17\_complex1~X1)){\unicdcdcdid}(k4\_complex1~(k1\_complex2~X0~X1)=k1\_real\_1~\\
(k8\_real\_1~(k17\_complex1~X0)~(k17\_complex1~X1))))))\end{array}
\label{hyp:ehfdadpfdgpgngahmgfgihcd}
\end{equation}
\begin{theorem}\label{thm:ehhdgdpfdgpgngahmgfgihcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(\preoh (\preoh ((\\
k4\_complex1~(k1\_complex2~X0~X1)=k8\_real\_1~(k17\_complex1~X0)~(\\
k17\_complex1~X1)){\unicdcdcdid}(k4\_complex1~(k1\_complex2~X0~X1)=k1\_real\_1~\\
(k8\_real\_1~(k17\_complex1~X0)~(k17\_complex1~X1)))){\unicdcdcdhd}((k4\_complex2~\\
X0~k6\_numbers~X1{\unicdcdgdad}k13\_complex1~k32\_sin\_cos~np\_\_2){\unicdcdcdhd}(k4\_complex2~\\
X0~k6\_numbers~X1{\unicdcdgdad}k4\_real\_1~(k13\_complex1~np\_\_3~np\_\_2)~k32\_sin\_cos))){\unicdcdcdhd}\\
(\preoh ((k4\_complex2~X0~k6\_numbers~X1=k13\_complex1~k32\_sin\_cos~np\_\_2){\unicdcdcdid}\\
(k4\_complex2~X0~k6\_numbers~X1=k4\_real\_1~(k13\_complex1~np\_\_3~np\_\_2)~\\
k32\_sin\_cos)){\unicdcdcdhd}((k4\_complex1~(k1\_complex2~X0~X1){\unicdcdgdad}k8\_real\_1~(\\
k17\_complex1~X0)~(k17\_complex1~X1)){\unicdcdcdhd}(k4\_complex1~(k1\_complex2~\\
X0~X1){\unicdcdgdad}k1\_real\_1~(k8\_real\_1~(k17\_complex1~X0)~(k17\_complex1~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
