\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}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_gate\_1 (TMbUUBH8kjVSbpzxtDrGTraX2yE5kC1X7wr)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_gate\_1 : {{\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 .  (\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~\\
X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}(k13\_gate\_1~X0~X1~X2{\unicdcdgdad}k1\_gate\_1~k1\_xboole\_0)))){\unicdcdcdhd}\\
((\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_xboole\_0~X2))){\unicdbdjdcd}(\\
k13\_gate\_1~X0~X1~X2=k1\_xboole\_0))\end{array}
\label{hyp:egbdddpfhgbgehfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfhgbgehfgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~(k13\_gate\_1~X0~\\
X1~X2)){\unicdbdjded}((v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_xboole\_0~X2)))\end{array}$$
\end{theorem}
\end{document}
