\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{t1\_gate\_5 (TMPQTCuYVBX7U1JwEPzvCVhj1b4A2WiBYMV)}
\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 $ k1\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_gate\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_gate\_5 : {{\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 $ k35\_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 v1\_xboole\_0~(k2\_gate\_1~X0~X1)){\unicdbdjded}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1))\end{array}
\label{hyp:ehedpfhgbgehfgpfbd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh (\preoh v1\_xboole\_0~(k10\_gate\_1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdcdcdid}((v1\_xboole\_0~\\
X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1))){\unicdcdcdhd}(v1\_xboole\_0~X2)){\unicdcdcdhd}(\preoh (\preoh (\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdcdcdhd}((\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdcdcdhd}\\
(\preoh v1\_xboole\_0~X2))))){\unicdcdcdhd}(\preoh (((((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)){\unicdcdcdid}((v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1))){\unicdcdcdhd}(v1\_xboole\_0~X2)){\unicdcdcdid}\\
((\preoh (\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdcdcdhd}((\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}\\
(\preoh v1\_xboole\_0~X1)){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2)))){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~\\
X0~X1~X2)))\end{array}
\label{hyp:ehbdgdpfhgbgehfgpfbd}
\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){\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 .  ((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}(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}
{{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 .  {\unicdcdadad} X3 .  k4\_gate\_5~X0~X1~X2~\\
X3=k36\_gate\_1~(k2\_gate\_1~X1~X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0~(\\
k2\_gate\_1~X1~X3)~k1\_xboole\_0\end{array}
\label{hyp:egedpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k3\_gate\_5~X0~X1~X2~\\
X3=k35\_gate\_1~(k2\_gate\_1~X1~X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0~(\\
k2\_gate\_1~X1~X3)~k1\_xboole\_0\end{array}
\label{hyp:egddpfhgbgehfgpffd}
\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 .  k2\_gate\_5~X0~X1~X2~\\
X3=k10\_gate\_1~(k2\_gate\_1~X1~X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0\end{array}
\label{hyp:egcdpfhgbgehfgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k1\_gate\_5~X0~X1~X2~\\
X3=k2\_gate\_1~X0~X2\end{array}
\label{hyp:egbdpfhgbgehfgpffd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfhgbgehfgpffd}
$$\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 .  \preoh (\preoh (\preoh v1\_xboole\_0~X8){\unicdcdcdhd}(v1\_xboole\_0~(k2\_gate\_1~X0~\\
X2))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k2\_gate\_1~X0~X2)){\unicdcdcdhd}(v1\_xboole\_0~X8)){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~X9){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~(k2\_gate\_1~X1~\\
X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k10\_gate\_1~\\
(k2\_gate\_1~X1~X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X9)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X10){\unicdcdcdhd}(v1\_xboole\_0~(k11\_gate\_1~(k2\_gate\_1~\\
X1~X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~\\
(k2\_gate\_1~X1~X2)~(k2\_gate\_1~X0~X3)~k1\_xboole\_0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X10)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X11){\unicdcdcdhd}(v1\_xboole\_0~(k10\_gate\_1~(k2\_gate\_1~\\
X1~X3)~k1\_xboole\_0~X10))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k10\_gate\_1~(k2\_gate\_1~\\
X1~X3)~k1\_xboole\_0~X10)){\unicdcdcdhd}(v1\_xboole\_0~X11)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~\\
X12){\unicdcdcdhd}(v1\_xboole\_0~(k11\_gate\_1~(k2\_gate\_1~X1~X3)~k1\_xboole\_0~X10))){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~(k11\_gate\_1~(k2\_gate\_1~X1~X3)~k1\_xboole\_0~X10)){\unicdcdcdhd}\\
(v1\_xboole\_0~X12)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(v1\_xboole\_0~X8)){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~X8){\unicdcdcdhd}(v1\_xboole\_0~X4)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X5){\unicdcdcdhd}\\
(v1\_xboole\_0~X9)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X9){\unicdcdcdhd}(v1\_xboole\_0~X5)){\unicdcdcdhd}(\\
(\preoh (\preoh v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~X11)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X11){\unicdcdcdhd}\\
(v1\_xboole\_0~X6)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X7){\unicdcdcdhd}(v1\_xboole\_0~X12)){\unicdcdcdhd}\\
((\preoh (\preoh v1\_xboole\_0~X12){\unicdcdcdhd}(v1\_xboole\_0~X7)){\unicdcdcdhd}(\preoh (\preoh (\preoh v1\_xboole\_0~\\
X4){\unicdcdcdhd}(v1\_xboole\_0~(k1\_gate\_5~X0~X1~X2~X3))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(\\
k1\_gate\_5~X0~X1~X2~X3)){\unicdcdcdhd}(v1\_xboole\_0~X4)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X5){\unicdcdcdhd}\\
(v1\_xboole\_0~(k2\_gate\_5~X0~X1~X2~X3))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k2\_gate\_5~\\
X0~X1~X2~X3)){\unicdcdcdhd}(v1\_xboole\_0~X5)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X6){\unicdcdcdhd}(v1\_xboole\_0~\\
(k3\_gate\_5~X0~X1~X2~X3))){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~(k3\_gate\_5~X0~X1~X2~X3)){\unicdcdcdhd}\\
(v1\_xboole\_0~X6)){\unicdcdcdhd}((\preoh (\preoh v1\_xboole\_0~X7){\unicdcdcdhd}(v1\_xboole\_0~(k4\_gate\_5~\\
X0~X1~X2~X3))){\unicdcdcdhd}(\preoh (\preoh v1\_xboole\_0~(k4\_gate\_5~X0~X1~X2~X3)){\unicdcdcdhd}(v1\_xboole\_0~\\
X7))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
