\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{t40\_gate\_1 (TMHvresMTPdoaNZMqv18gb2tojiphA5cwsF)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh v1\_xboole\_0~(k3\_gate\_1~X0~X1)){\unicdcdcdhd}((v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v1\_xboole\_0~X1))){\unicdcdcdhd}(\preoh (\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdcdcdhd}\\
(v1\_xboole\_0~(k3\_gate\_1~X0~X1)))\end{array}
\label{hyp:ehfdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~\\
(k18\_gate\_1~X0~X1~X2~X3~X4)){\unicdbdjded}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(\preoh v1\_xboole\_0~X4)))))\end{array}
\label{hyp:ehcdedpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:ehbdhdpfhgbgehfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfhgbgehfgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  {\unicdcdadad} X10 .  {\unicdcdadad} X11 .  \\
{\unicdcdadad} X12 .  {\unicdcdadad} X13 .  {\unicdcdadad} X14 .  {\unicdcdadad} X15 .  {\unicdcdadad} X16 .  \\
{\unicdcdadad} X17 .  {\unicdcdadad} X18 .  \preoh (\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~X1~X5~X0)){\unicdcdcdhd}\\
(v1\_xboole\_0~X9)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~X2~X6~X9)){\unicdcdcdhd}(v1\_xboole\_0~\\
X10)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~X3~X7~X10)){\unicdcdcdhd}(v1\_xboole\_0~\\
X11)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~X4~X8~X11)){\unicdcdcdhd}(v1\_xboole\_0~\\
X12)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X13){\unicdcdcdhd}(v1\_xboole\_0~(k3\_gate\_1~X1~X5))){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~X14){\unicdcdcdhd}(v1\_xboole\_0~(k3\_gate\_1~X2~X6))){\unicdcdcdhd}((\preoh (\\
\preoh v1\_xboole\_0~X15){\unicdcdcdhd}(v1\_xboole\_0~(k3\_gate\_1~X3~X7))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
X16){\unicdcdcdhd}(v1\_xboole\_0~(k3\_gate\_1~X4~X8))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X17){\unicdcdcdhd}\\
(v1\_xboole\_0~(k18\_gate\_1~X0~X13~X14~X15~X16))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
X18){\unicdcdcdhd}(v1\_xboole\_0~(k3\_gate\_1~X12~X17))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k3\_gate\_1~\\
X12~X17)){\unicdcdcdhd}(v1\_xboole\_0~X18)){\unicdcdcdhd}(\preoh (\preoh (\preoh v1\_xboole\_0~X12){\unicdcdcdhd}(v1\_xboole\_0~\\
X18)){\unicdcdcdhd}(\preoh (\preoh v1\_xboole\_0~X18){\unicdcdcdhd}(v1\_xboole\_0~X12)))))))))))))\end{array}$$
\end{theorem}
\end{document}
