\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t17\_gate\_1 (TMMv2RQBcwMoP8c9MnHPuJMDvEPuUEYbbby)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)){\unicdbdjdcd}(v1\_xboole\_0~(k11\_gate\_1~X2~X0~X1))\end{array}
\label{hyp:ggdgddidpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)){\unicdbdjdcd}(v1\_xboole\_0~(k11\_gate\_1~X0~X2~X1))\end{array}
\label{hyp:ggdgddhdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)){\unicdbdjdcd}(v1\_xboole\_0~(k11\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgddgdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~\\
X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k11\_gate\_1~X2~X0~X1))\end{array}
\label{hyp:ggdgddfdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~\\
X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k11\_gate\_1~X0~X2~X1))\end{array}
\label{hyp:ggdgddedpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~\\
X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k11\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgddddpfhgbgehfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfhgbgehfgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2)){\unicdcdcdhd}(\preoh (\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0))))){\unicdcdcdhd}\\
(\preoh (\preoh (\preoh (\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2)){\unicdcdcdhd}(\preoh (\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)))){\unicdcdcdhd}\\
(v1\_xboole\_0~(k11\_gate\_1~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
