\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t35\_gate\_1 (TMTioZSScbUbrykGJ3fVd6K3AsVWXXMRsvd)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k29\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k21\_gate\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_gate\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~\\
(k21\_gate\_1~X0~X1~X2~X3~X4)){\unicdbdjded}((v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}(v1\_xboole\_0~X4)))))\end{array}
\label{hyp:ehcdhdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~\\
X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_xboole\_0~X5){\unicdcdcdhd}\\
((v1\_xboole\_0~X6){\unicdcdcdhd}(k29\_gate\_1~X0~X1~X2~X3~X4~X5~X6{\unicdcdgdad}k1\_gate\_1~k1\_xboole\_0)))))))){\unicdcdcdhd}\\
((\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}((\\
v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_xboole\_0~X5){\unicdcdcdhd}(v1\_xboole\_0~\\
X6))))))){\unicdbdjdcd}(k29\_gate\_1~X0~X1~X2~X3~X4~X5~X6=k1\_xboole\_0))\end{array}
\label{hyp:egcdjdpfhgbgehfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\preoh (v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}\\
((v1\_xboole\_0~X4){\unicdcdcdhd}(k21\_gate\_1~X0~X1~X2~X3~X4{\unicdcdgdad}k1\_gate\_1~k1\_xboole\_0)))))){\unicdcdcdhd}\\
((\preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}((\\
v1\_xboole\_0~X3){\unicdcdcdhd}(v1\_xboole\_0~X4))))){\unicdbdjdcd}(k21\_gate\_1~X0~X1~X2~X3~X4=\\
k1\_xboole\_0))\end{array}
\label{hyp:egcdbdpfhgbgehfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfhgbgehfgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (\preoh v1\_xboole\_0~(k29\_gate\_1~X0~X1~X2~X3~X4~X5~X6)){\unicdbdjded}((v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_xboole\_0~X3){\unicdcdcdhd}\\
((v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_xboole\_0~X5){\unicdcdcdhd}(v1\_xboole\_0~X6)))))))\end{array}$$
\end{theorem}
\end{document}
