\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t37\_gate\_1 (TMa3t9B7YSDi99TphYXxhUKALparKY7Hqph)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k31\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_gate\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k1\_gate\_1}~{X0}})}}}})}}}\label{hyp:ggdgbdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  ((\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_xboole\_0~\\
X5){\unicdcdcdhd}((v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~X7)))))))){\unicdbdjdcd}(k31\_gate\_1~\\
X0~X1~X2~X3~X4~X5~X6~X7=k1\_gate\_1~k1\_xboole\_0)){\unicdcdcdhd}(\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}\\
((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_xboole\_0~\\
X4){\unicdcdcdhd}((v1\_xboole\_0~X5){\unicdcdcdhd}((v1\_xboole\_0~X6){\unicdcdcdhd}((v1\_xboole\_0~X7){\unicdcdcdhd}\\
(k31\_gate\_1~X0~X1~X2~X3~X4~X5~X6~X7{\unicdcdgdad}k1\_xboole\_0)))))))))\end{array}
\label{hyp:egddbdpfhgbgehfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfhgbgehfgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (\preoh (\preoh v1\_xboole\_0~(k31\_gate\_1~X0~X1~X2~X3~X4~\\
X5~X6~X7)){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~\\
X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_xboole\_0~X5){\unicdcdcdhd}\\
((v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~X7))))))))){\unicdcdcdhd}(\preoh (\preoh (v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}\\
((v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_xboole\_0~X5){\unicdcdcdhd}((v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~\\
X7)))))))){\unicdcdcdhd}(v1\_xboole\_0~(k31\_gate\_1~X0~X1~X2~X3~X4~X5~X6~X7)))\end{array}$$
\end{theorem}
\end{document}
