\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{t44\_modelc\_1 (TMPbFXKMt7aQbcxpowPtMyqY9aWNFDpG2VT)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\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 $ k30\_modelc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k48\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k59\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k53\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k28\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}((r3\_modelc\_1~X0~\\
X1~X2~X6~X4){\unicdbdjdcd}(r3\_modelc\_1~X0~X1~X2~X6~X5))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~X0){\unicdbdjdcd}((r3\_modelc\_1~X0~X1~X2~X6~(k53\_modelc\_1~X0~X1~X2~X3~X4)){\unicdbdjdcd}(r3\_modelc\_1~\\
X0~X1~X2~X6~(k53\_modelc\_1~X0~X1~X2~X3~X5))))))))))\end{array}
\label{hyp:ehddgdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k30\_modelc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X3))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X3))){\unicdbdjdcd}((r3\_modelc\_1~X0~X1~X3~\\
X2~(k28\_modelc\_1~(k48\_modelc\_1~X0~X1~X3)~X4~X5)){\unicdbdjded}((r3\_modelc\_1~\\
X0~X1~X3~X2~X4){\unicdcdcdid}(r3\_modelc\_1~X0~X1~X3~X2~X5))))))))\end{array}
\label{hyp:ehbdhdpfngpgegfgmgdgpfbd}
\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}(((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k30\_modelc\_1~X0)))){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X2))))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k53\_modelc\_1~X0~X1~X2~X3~X4)~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2)))\end{array}
\label{hyp:egehpflgfdddpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}(k59\_modelc\_1~X0~X1~X2~X3~X4~X5=k28\_modelc\_1~(k48\_modelc\_1~\\
X0~X1~X2)~X4~(k53\_modelc\_1~X0~X1~X2~X3~X5)))))))\end{array}
\label{hyp:eghdbdpfngpgegfgmgdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehededpfngpgegfgmgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~(k48\_modelc\_1~\\
X0~X1~X2))){\unicdbdjdcd}(({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X0){\unicdbdjdcd}((r3\_modelc\_1~X0~\\
X1~X2~X7~X5){\unicdbdjdcd}(r3\_modelc\_1~X0~X1~X2~X7~X6))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~X0){\unicdbdjdcd}((r3\_modelc\_1~X0~X1~X2~X7~(k59\_modelc\_1~X0~X1~X2~X3~X4~X5)){\unicdbdjdcd}\\
(r3\_modelc\_1~X0~X1~X2~X7~(k59\_modelc\_1~X0~X1~X2~X3~X4~X6)))))))))))\end{array}$$
\end{theorem}
\end{document}
