\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{t12\_twoscomp (TMJHYLWzpZRVAZdmBtAGA91pro7AcDdeUeG)}
\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 $ k17\_twoscomp : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_twoscomp : {\iota}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_twoscomp : {\iota}$ be given.
Let $ k20\_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~k20\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k20\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k20\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdadpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k19\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k19\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k19\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdjdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k18\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k18\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k18\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdidpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k17\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k17\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k17\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdhdpfehhhpgdhdgpgngah}
\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=k20\_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)=k10\_margrel1~(k10\_margrel1~(k9\_margrel1~\\
X1)~(k9\_margrel1~X2))~(k9\_margrel1~X3))))))\end{array}
\label{hyp:egbdjdpfehhhpgdhdgpgngah}
\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=k19\_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)=k10\_margrel1~(k10\_margrel1~(k9\_margrel1~\\
X1)~(k9\_margrel1~X2))~X3)))))\end{array}
\label{hyp:egbdidpfehhhpgdhdgpgngah}
\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=k18\_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)=k10\_margrel1~(k10\_margrel1~(k9\_margrel1~\\
X1)~X2)~X3)))))\end{array}
\label{hyp:egbdhdpfehhhpgdhdgpgngah}
\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=k17\_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)=k10\_margrel1~(k10\_margrel1~X1~X2)~X3)))))\end{array}
\label{hyp:egbdgdpfehhhpgdhdgpgngah}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfehhhpgdhdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k6\_margrel1){\unicdbdjdcd}((\\
k1\_funct\_1~k17\_twoscomp~(k11\_finseq\_1~X0~X1~X2)=k10\_margrel1~\\
(k10\_margrel1~X0~X1)~X2){\unicdcdcdhd}((k1\_funct\_1~k18\_twoscomp~(k11\_finseq\_1~\\
X0~X1~X2)=k10\_margrel1~(k10\_margrel1~(k9\_margrel1~X0)~X1)~X2){\unicdcdcdhd}\\
((k1\_funct\_1~k19\_twoscomp~(k11\_finseq\_1~X0~X1~X2)=k10\_margrel1~\\
(k10\_margrel1~(k9\_margrel1~X0)~(k9\_margrel1~X1))~X2){\unicdcdcdhd}(k1\_funct\_1~\\
k20\_twoscomp~(k11\_finseq\_1~X0~X1~X2)=k10\_margrel1~(k10\_margrel1~\\
(k9\_margrel1~X0)~(k9\_margrel1~X1))~(k9\_margrel1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
