\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\begin{document}
\title{t13\_twoscomp (TMMVFS6c1vwMaUFfDm55TPnsZ6kMzFiQoer)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_twoscomp : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k22\_twoscomp : {\iota}$ be given.
Let $ k23\_twoscomp : {\iota}$ be given.
Let $ k24\_twoscomp : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k24\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k24\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k24\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdedpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k23\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k23\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k23\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdddpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k22\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k22\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k22\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdcdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k21\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k21\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k21\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdbdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0=k24\_twoscomp){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}(k1\_funct\_1~\\
X0~(k11\_finseq\_1~X1~X2~X3)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~\\
(k9\_margrel1~X1)~(k9\_margrel1~X2))~(k9\_margrel1~X3)))))))\end{array}
\label{hyp:egcdddpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0=k23\_twoscomp){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}(k1\_funct\_1~\\
X0~(k11\_finseq\_1~X1~X2~X3)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~\\
(k9\_margrel1~X1)~(k9\_margrel1~X2))~X3))))))\end{array}
\label{hyp:egcdcdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0=k22\_twoscomp){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}(k1\_funct\_1~\\
X0~(k11\_finseq\_1~X1~X2~X3)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~\\
(k9\_margrel1~X1)~X2)~X3))))))\end{array}
\label{hyp:egcdbdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0=k21\_twoscomp){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}(k1\_funct\_1~\\
X0~(k11\_finseq\_1~X1~X2~X3)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~\\
X1~X2)~X3))))))\end{array}
\label{hyp:egcdadpfehhhpgdhdgpgngah}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfehhhpgdhdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k6\_margrel1){\unicdbdjdcd}((\\
k1\_funct\_1~k21\_twoscomp~(k11\_finseq\_1~X0~X1~X2)=k9\_margrel1~(\\
k10\_margrel1~(k10\_margrel1~X0~X1)~X2)){\unicdcdcdhd}((k1\_funct\_1~k22\_twoscomp~\\
(k11\_finseq\_1~X0~X1~X2)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~\\
(k9\_margrel1~X0)~X1)~X2)){\unicdcdcdhd}((k1\_funct\_1~k23\_twoscomp~(k11\_finseq\_1~\\
X0~X1~X2)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~(k9\_margrel1~\\
X0)~(k9\_margrel1~X1))~X2)){\unicdcdcdhd}(k1\_funct\_1~k24\_twoscomp~(k11\_finseq\_1~\\
X0~X1~X2)=k9\_margrel1~(k10\_margrel1~(k10\_margrel1~(k9\_margrel1~\\
X0)~(k9\_margrel1~X1))~(k9\_margrel1~X2))))))))\end{array}$$
\end{theorem}
\end{document}
