\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t52\_twoscomp (TMRBbV5ihcV5X2kjEtiXuNuovn86WZZJy3u)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k40\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k41\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k36\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k39\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}(((X3=k1\_funct\_1~X2~\\
X0){\unicdcdcdhd}(X4=k1\_funct\_1~X2~X1)){\unicdbdjdcd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~(k39\_twoscomp~X0~X1)=k10\_margrel1~\\
(k9\_margrel1~X3)~X4){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~X0=X3){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~\\
(k40\_twoscomp~X0~X1)~(k41\_twoscomp~X0~X1)~X2)~X1=X4))))))))\end{array}
\label{hyp:ehfdadpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}(((X3=k1\_funct\_1~X2~\\
X0){\unicdcdcdhd}(X4=k1\_funct\_1~X2~X1)){\unicdbdjdcd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~(k36\_twoscomp~X0~X1)=k2\_binarith~\\
(k9\_margrel1~X3)~X4){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~X0=X3){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~\\
(k40\_twoscomp~X0~X1)~(k41\_twoscomp~X0~X1)~X2)~X1=X4))))))))\end{array}
\label{hyp:ehedgdpfehhhpgdhdgpgngah}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfehhhpgdhdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k6\_margrel1){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}(((X3=k1\_funct\_1~X2~\\
X0){\unicdcdcdhd}(X4=k1\_funct\_1~X2~X1)){\unicdbdjdcd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~(k36\_twoscomp~X0~X1)=k2\_binarith~\\
(k9\_margrel1~X3)~X4){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~(k39\_twoscomp~X0~X1)=k10\_margrel1~\\
(k9\_margrel1~X3)~X4){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k40\_twoscomp~\\
X0~X1)~(k41\_twoscomp~X0~X1)~X2)~X0=X3){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~\\
(k40\_twoscomp~X0~X1)~(k41\_twoscomp~X0~X1)~X2)~X1=X4)))))))))\end{array}$$
\end{theorem}
\end{document}
