\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{t4\_gate\_5 (TMVpxAxKaM6XLCYBqS9rVjA7AiX5fkPRRhf)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k11\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k16\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k17\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k5\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k6\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k10\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k11\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k12\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k13\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k38\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k8\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k37\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k7\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k35\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k36\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k15\_gate\_5 : {{\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 .  ((v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdbdjdcd}(\\
v1\_xboole\_0~(k3\_gate\_1~X0~X1))\end{array}
\label{hyp:ggdggdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k3\_gate\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgfdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}(v1\_xboole\_0~(k2\_gate\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgedpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k2\_gate\_1~X0~X1))\end{array}
\label{hyp:ggdgddpfhgbgehfgpfbd}
\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~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}
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){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k10\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgddcdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(v1\_xboole\_0~X2))){\unicdbdjdcd}(v1\_xboole\_0~(k10\_gate\_1~X2~X0~X1))\end{array}
\label{hyp:ggdgddbdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(v1\_xboole\_0~X2))){\unicdbdjdcd}(v1\_xboole\_0~(k10\_gate\_1~X0~X2~X1))\end{array}
\label{hyp:ggdgddadpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(v1\_xboole\_0~X2))){\unicdbdjdcd}(v1\_xboole\_0~(k10\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgcdjdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k10\_gate\_1~X2~X0~X1))\end{array}
\label{hyp:ggdgcdidpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k10\_gate\_1~X0~X2~X1))\end{array}
\label{hyp:ggdgcdhdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k10\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgcdgdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(v1\_xboole\_0~X2))){\unicdbdjdcd}(v1\_xboole\_0~(k10\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgcdfdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_gate\_1~X1~X0~X2))\end{array}
\label{hyp:ggdgcdddpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgcdcdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(v1\_xboole\_0~X2))){\unicdbdjdcd}(v1\_xboole\_0~(k9\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgcdbdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_xboole\_0~X0){\unicdbdjdcd}(v1\_xboole\_0~\\
(k8\_gate\_1~X1~X2~X0))\end{array}
\label{hyp:ggdgcdadpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_xboole\_0~X0){\unicdbdjdcd}(v1\_xboole\_0~\\
(k8\_gate\_1~X1~X0~X2))\end{array}
\label{hyp:ggdgbdjdpfhgbgehfgpfbd}
\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){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k8\_gate\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgbdhdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k9\_gate\_5~\\
X0~X1~X2~X3~X4=k38\_gate\_1~(k2\_gate\_1~X1~X3)~(k2\_gate\_1~X0~X4)~(k2\_gate\_1~\\
X2~X3)~(k2\_gate\_1~X1~X4)~k1\_xboole\_0~(k2\_gate\_1~X2~X4)~k1\_xboole\_0\end{array}
\label{hyp:egjdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k8\_gate\_5~\\
X0~X1~X2~X3~X4=k37\_gate\_1~(k2\_gate\_1~X1~X3)~(k2\_gate\_1~X0~X4)~(k2\_gate\_1~\\
X2~X3)~(k2\_gate\_1~X1~X4)~k1\_xboole\_0~(k2\_gate\_1~X2~X4)~k1\_xboole\_0\end{array}
\label{hyp:egidpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k7\_gate\_5~\\
X0~X1~X2~X3~X4=k35\_gate\_1~(k2\_gate\_1~X1~X3)~(k2\_gate\_1~X0~X4)~(k2\_gate\_1~\\
X2~X3)~(k2\_gate\_1~X1~X4)~k1\_xboole\_0\end{array}
\label{hyp:eghdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k6\_gate\_5~\\
X0~X1~X2~X3~X4=k10\_gate\_1~(k2\_gate\_1~X1~X3)~(k2\_gate\_1~X0~X4)~k1\_xboole\_0\end{array}
\label{hyp:eggdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k5\_gate\_5~\\
X0~X1~X2~X3~X4=k2\_gate\_1~X0~X3\end{array}
\label{hyp:egfdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  k38\_gate\_1~X0~X1~X2~X3~X4~X5~X6=k11\_gate\_1~X4~X5~(k36\_gate\_1~\\
X0~X1~X2~X3~X6)\end{array}
\label{hyp:egddidpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  k37\_gate\_1~X0~X1~X2~X3~X4~X5~X6=k10\_gate\_1~X4~X5~(k36\_gate\_1~\\
X0~X1~X2~X3~X6)\end{array}
\label{hyp:egddhdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k36\_gate\_1~\\
X0~X1~X2~X3~X4=k11\_gate\_1~X2~X3~(k11\_gate\_1~X0~X1~X4)\end{array}
\label{hyp:egddgdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k35\_gate\_1~\\
X0~X1~X2~X3~X4=k10\_gate\_1~X2~X3~(k11\_gate\_1~X0~X1~X4)\end{array}
\label{hyp:egddfdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  k17\_gate\_5~X0~X1~X2~X3~X4~X5~X6=k9\_gate\_1~(k2\_gate\_1~X4~\\
X5)~(k2\_gate\_1~(k3\_gate\_1~X4~X5)~(k2\_gate\_1~X2~X3))~(k8\_gate\_1~(\\
k3\_gate\_1~X4~X5)~(k3\_gate\_1~X2~X3)~(k11\_gate\_1~X0~X1~X6))\end{array}
\label{hyp:egbdhdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  k16\_gate\_5~X0~X1~X2~X3~X4~X5~X6=k10\_gate\_1~X4~X5~(k15\_gate\_5~\\
X0~X1~X2~X3~X6)\end{array}
\label{hyp:egbdgdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k15\_gate\_5~\\
X0~X1~X2~X3~X4=k3\_gate\_1~(k2\_gate\_1~X2~X3)~(k2\_gate\_1~(k3\_gate\_1~\\
X2~X3)~(k11\_gate\_1~X0~X1~X4))\end{array}
\label{hyp:egbdfdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k14\_gate\_5~\\
X0~X1~X2~X3~X4=k10\_gate\_1~X2~X3~(k11\_gate\_1~X0~X1~X4)\end{array}
\label{hyp:egbdedpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
k13\_gate\_5~X0~X1~X2~X3~X4~X5=k38\_gate\_1~(k7\_gate\_5~X0~X1~X2~X3~X4)~(\\
k2\_gate\_1~X0~X5)~(k8\_gate\_5~X0~X1~X2~X3~X4)~(k2\_gate\_1~X1~X5)~(k9\_gate\_5~\\
X0~X1~X2~X3~X4)~(k2\_gate\_1~X2~X5)~k1\_xboole\_0\end{array}
\label{hyp:egbdddpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
k12\_gate\_5~X0~X1~X2~X3~X4~X5=k37\_gate\_1~(k7\_gate\_5~X0~X1~X2~X3~X4)~(\\
k2\_gate\_1~X0~X5)~(k8\_gate\_5~X0~X1~X2~X3~X4)~(k2\_gate\_1~X1~X5)~(k9\_gate\_5~\\
X0~X1~X2~X3~X4)~(k2\_gate\_1~X2~X5)~k1\_xboole\_0\end{array}
\label{hyp:egbdcdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
k11\_gate\_5~X0~X1~X2~X3~X4~X5=k35\_gate\_1~(k7\_gate\_5~X0~X1~X2~X3~X4)~(\\
k2\_gate\_1~X0~X5)~(k8\_gate\_5~X0~X1~X2~X3~X4)~(k2\_gate\_1~X1~X5)~k1\_xboole\_0\end{array}
\label{hyp:egbdbdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
k10\_gate\_5~X0~X1~X2~X3~X4~X5=k10\_gate\_1~(k7\_gate\_5~X0~X1~X2~X3~X4)~(\\
k2\_gate\_1~X0~X5)~k1\_xboole\_0\end{array}
\label{hyp:egbdadpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_gate\_1}~{X0}}~{X1}}={{{k3\_gate\_1}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_gate\_1}~{X0}}~{X1}}={{{k2\_gate\_1}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfhgbgehfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfhgbgehfgpffd}
$$\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~X12){\unicdcdcdhd}(v1\_xboole\_0~\\
(k2\_gate\_1~X0~X3))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k2\_gate\_1~X0~X3)){\unicdcdcdhd}(v1\_xboole\_0~\\
X12)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X13){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~(k2\_gate\_1~\\
X1~X3)~(k2\_gate\_1~X0~X4)~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k10\_gate\_1~\\
(k2\_gate\_1~X1~X3)~(k2\_gate\_1~X0~X4)~k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X13)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X16){\unicdcdcdhd}(v1\_xboole\_0~(k11\_gate\_1~(k2\_gate\_1~\\
X1~X3)~(k2\_gate\_1~X0~X4)~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~\\
(k2\_gate\_1~X1~X3)~(k2\_gate\_1~X0~X4)~k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X16)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X14){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~(k2\_gate\_1~\\
X2~X3)~(k2\_gate\_1~X1~X4)~(k2\_gate\_1~X0~X5)))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
(k10\_gate\_1~(k2\_gate\_1~X2~X3)~(k2\_gate\_1~X1~X4)~(k2\_gate\_1~X0~X5))){\unicdcdcdhd}\\
(v1\_xboole\_0~X14)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X17){\unicdcdcdhd}(v1\_xboole\_0~(k11\_gate\_1~\\
(k2\_gate\_1~X2~X3)~(k2\_gate\_1~X1~X4)~(k2\_gate\_1~X0~X5)))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
(k11\_gate\_1~(k2\_gate\_1~X2~X3)~(k2\_gate\_1~X1~X4)~(k2\_gate\_1~X0~X5))){\unicdcdcdhd}\\
(v1\_xboole\_0~X17)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X15){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~\\
(k2\_gate\_1~X2~X4)~(k2\_gate\_1~X1~X5)~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
(k10\_gate\_1~(k2\_gate\_1~X2~X4)~(k2\_gate\_1~X1~X5)~k1\_xboole\_0)){\unicdcdcdhd}\\
(v1\_xboole\_0~X15)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X18){\unicdcdcdhd}(v1\_xboole\_0~(k11\_gate\_1~\\
(k2\_gate\_1~X2~X4)~(k2\_gate\_1~X1~X5)~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
(k11\_gate\_1~(k2\_gate\_1~X2~X4)~(k2\_gate\_1~X1~X5)~k1\_xboole\_0)){\unicdcdcdhd}\\
(v1\_xboole\_0~X18)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~X12)){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~X12){\unicdcdcdhd}(v1\_xboole\_0~X6)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X7){\unicdcdcdhd}\\
(v1\_xboole\_0~X13)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X13){\unicdcdcdhd}(v1\_xboole\_0~X7)){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~X8){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~X14~X16~k1\_xboole\_0))){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~(k10\_gate\_1~X14~X16~k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X8)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X9){\unicdcdcdhd}(v1\_xboole\_0~(k14\_gate\_5~X14~X16~X15~\\
X17~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k14\_gate\_5~X14~X16~X15~X17~\\
k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~X9)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X10){\unicdcdcdhd}(v1\_xboole\_0~\\
(k16\_gate\_5~X14~X16~X15~X17~(k2\_gate\_1~X2~X5)~X18~k1\_xboole\_0))){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~(k16\_gate\_5~X14~X16~X15~X17~(k2\_gate\_1~X2~X5)~X18~\\
k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~X10)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X11){\unicdcdcdhd}(v1\_xboole\_0~\\
(k17\_gate\_5~X14~X16~X15~X17~(k2\_gate\_1~X2~X5)~X18~k1\_xboole\_0))){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~(k17\_gate\_5~X14~X16~X15~X17~(k2\_gate\_1~X2~X5)~X18~\\
k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~X11)){\unicdcdcdhd}(\preoh (\preoh (\preoh v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~\\
(k5\_gate\_5~X0~X1~X2~X3~X4))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k5\_gate\_5~X0~X1~X2~\\
X3~X4)){\unicdcdcdhd}(v1\_xboole\_0~X6)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X7){\unicdcdcdhd}(v1\_xboole\_0~\\
(k6\_gate\_5~X0~X1~X2~X3~X4))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k6\_gate\_5~X0~X1~X2~\\
X3~X4)){\unicdcdcdhd}(v1\_xboole\_0~X7)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X8){\unicdcdcdhd}(v1\_xboole\_0~\\
(k10\_gate\_5~X0~X1~X2~X3~X4~X5))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k10\_gate\_5~X0~\\
X1~X2~X3~X4~X5)){\unicdcdcdhd}(v1\_xboole\_0~X8)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X9){\unicdcdcdhd}(v1\_xboole\_0~\\
(k11\_gate\_5~X0~X1~X2~X3~X4~X5))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_5~X0~\\
X1~X2~X3~X4~X5)){\unicdcdcdhd}(v1\_xboole\_0~X9)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X10){\unicdcdcdhd}(v1\_xboole\_0~\\
(k12\_gate\_5~X0~X1~X2~X3~X4~X5))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k12\_gate\_5~X0~\\
X1~X2~X3~X4~X5)){\unicdcdcdhd}(v1\_xboole\_0~X10)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X11){\unicdcdcdhd}(v1\_xboole\_0~\\
(k13\_gate\_5~X0~X1~X2~X3~X4~X5))){\unicdcdcdhd}(\preoh (\preoh v1\_xboole\_0~(k13\_gate\_5~X0~\\
X1~X2~X3~X4~X5)){\unicdcdcdhd}(v1\_xboole\_0~X11))))))))))))))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
