\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t35\_pnproc\_1 (TMG1Y9pE2HExdre6B6kdPjt3oRMzhsxjPbs)}
\maketitle
Let $ m2\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k7\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(k3\_relat\_1~(k4\_relat\_1~(k9\_xtuple\_0~\\
X0))~X0=X0)\end{array}
\label{hyp:ehfdcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pnproc\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_pnproc\_1~X2~X0))\end{array}
\label{hyp:egehpfngddpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_pnproc\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~(k7\_pnproc\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k7\_pnproc\_1~X0~X1)))\end{array}
\label{hyp:egehpflghdpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X2=k7\_pnproc\_1~X0~X1){\unicdbdjded}((k9\_xtuple\_0~\\
X2=k9\_funct\_2~X0~k5\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(\\
(v1\_funct\_2~X3~X0~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k5\_numbers))))){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k6\_pnproc\_1~X0~X3~X1)))))\end{array}
\label{hyp:egidpfahogahchpgdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfahogahchpgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pnproc\_1~\\
X2~X0~X1){\unicdbdjdcd}(k3\_relat\_1~(k6\_partfun1~(k9\_funct\_2~X0~k5\_numbers))~\\
(k7\_pnproc\_1~X0~X2)=k7\_pnproc\_1~X0~X2))\end{array}$$
\end{theorem}
\end{document}
