\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\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t47\_pnproc\_1 (TMZZDsnWLc2NGtjsZGB6tU7Y7twQFE2rosW)}
\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 $ k11\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k4\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_enumset1~X0~X2~X1~X3\end{array}
\label{hyp:ehgdcdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_xboole\_0~(k2\_tarski~X0~X1)~(k2\_tarski~X2~X3)\end{array}
\label{hyp:ehfdpffgogfhngdhfgehbd}
\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}({\unicdcdadad} X3 .  (m3\_pnproc\_1~X3~X0~X1){\unicdbdjdcd}(k11\_pnproc\_1~X0~X1~\\
(k6\_domain\_1~(k3\_finseq\_2~X1)~(k3\_pre\_poly~X1~X2))~(k6\_domain\_1~\\
(k3\_finseq\_2~X1)~(k3\_pre\_poly~X1~X3))=k7\_domain\_1~(k3\_finseq\_2~\\
X1)~(k4\_pre\_poly~X1~X2~X3)~(k4\_pre\_poly~X1~X3~X2))))\end{array}
\label{hyp:ehedgdpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}(k11\_pnproc\_1~X0~X1~(k4\_subset\_1~\\
(k3\_finseq\_2~X1)~X2~X3)~X4=k4\_subset\_1~(k3\_finseq\_2~X1)~(k11\_pnproc\_1~\\
X0~X1~X2~X4)~(k11\_pnproc\_1~X0~X1~X3~X4)))))\end{array}
\label{hyp:ehedfdpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_tarski~X0~X1=k2\_xboole\_0~(k1\_tarski~\\
X0)~(k1\_tarski~X1)\end{array}
\label{hyp:ehbdpffgogfhngdhfgehbd}
\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){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngddpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\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}((m1\_subset\_1~X1~X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X3~X0){\unicdcdcdhd}(m1\_subset\_1~X4~X0))))){\unicdbdjdcd}(k9\_domain\_1~X0~X1~X2~X3~X4=k2\_enumset1~\\
X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k7\_domain\_1~X0~X1~X2=k2\_tarski~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_finseq\_2}~{X0}}={{k13\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k13\_finseq\_1}~{X0}})}}}}}\label{hyp:ggdgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_pnproc\_1}~{X1}}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X1}}}})}}}}\label{hyp:egehpfngcdpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m1\_subset\_1~(k7\_domain\_1~X0~X1~X2)~\\
(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k6\_domain\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m2\_finseq\_2~(k4\_pre\_poly~X0~X1~X2)~\\
X0~(k3\_finseq\_2~X0))\end{array}
\label{hyp:egehpflgedpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m2\_finseq\_2~(k3\_pre\_poly~X0~X1)~X0~(k3\_finseq\_2~X0))\end{array}
\label{hyp:egehpflgddpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_finseq\_2}~{({{k3\_finseq\_2}~{X0}})}}~{X0}}}\label{hyp:egehpflgddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfahogahchpgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pnproc\_1~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m3\_pnproc\_1~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m3\_pnproc\_1~\\
X4~X0~X1){\unicdbdjdcd}(k11\_pnproc\_1~X0~X1~(k7\_domain\_1~(k3\_finseq\_2~X1)~(k3\_pre\_poly~\\
X1~X2)~(k3\_pre\_poly~X1~X3))~(k6\_domain\_1~(k3\_finseq\_2~X1)~(k3\_pre\_poly~\\
X1~X4))=k9\_domain\_1~(k3\_finseq\_2~X1)~(k4\_pre\_poly~X1~X2~X4)~(k4\_pre\_poly~\\
X1~X3~X4)~(k4\_pre\_poly~X1~X4~X2)~(k4\_pre\_poly~X1~X4~X3)))))\end{array}$$
\end{theorem}
\end{document}
