\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}
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\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{t53\_modelc\_3 (TMapQ3Zidp98cnZvyMzofoDHgv2sxv9yNmK)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\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 $ k23\_modelc\_3 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r6\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v7\_modelc\_2~X0){\unicdbdjdcd}(X0=k7\_modelc\_2~(k11\_modelc\_2~X0)~(k12\_modelc\_2~\\
X0)))\end{array}
\label{hyp:ehidpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(\\
m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(\\
m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_modelc\_2~X3){\unicdcdcdhd}(\\
m2\_finseq\_1~X3~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~k5\_numbers~(k23\_modelc\_3~X3)){\unicdcdcdhd}(m1\_subset\_1~X4~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k23\_modelc\_3~X3)))))){\unicdbdjdcd}\\
(((k7\_modelc\_2~X1~X2 \in u1\_modelc\_3~X3~(k10\_modelc\_3~(k3\_funct\_2~\\
k5\_numbers~(k23\_modelc\_3~X3)~X4~np\_\_1)~X3)){\unicdcdcdhd}(({\unicdcdadad} X5 .  (v7\_ordinal1~\\
X5){\unicdbdjdcd}(r6\_modelc\_3~X3~(k10\_modelc\_3~(k1\_funct\_1~X4~X5)~X3)~(k10\_modelc\_3~\\
(k3\_funct\_2~k5\_numbers~(k23\_modelc\_3~X3)~X4~(k1\_nat\_1~X5~np\_\_1))~\\
X3))){\unicdcdcdhd}({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X5){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X0~X5){\unicdcdcdhd}(X2 \in u1\_modelc\_3~X3~(k10\_modelc\_3~(k1\_funct\_1~\\
X4~X5)~X3))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}((r1\_xxreal\_0~\\
np\_\_1~X5){\unicdbdjdcd}((r1\_xxreal\_0~X0~X5){\unicdcdcdid}((X1 \in u1\_modelc\_3~X3~(k10\_modelc\_3~\\
(k1\_funct\_1~X4~X5)~X3)){\unicdcdcdhd}(k7\_modelc\_2~X1~X2 \in u1\_modelc\_3~X3~(k10\_modelc\_3~\\
(k1\_funct\_1~X4~X5)~X3)))))))))))\end{array}
\label{hyp:mgbdbdhdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v1\_modelc\_2~(k12\_modelc\_2~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k12\_modelc\_2~\\
X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgbdcdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v1\_modelc\_2~(k11\_modelc\_2~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k11\_modelc\_2~\\
X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgbdbdpfngpgegfgmgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdddpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(\\
m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(\\
m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((\\
v1\_funct\_2~X3~k5\_numbers~(k23\_modelc\_3~X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k23\_modelc\_3~X2)))))){\unicdbdjdcd}\\
(((v7\_modelc\_2~X1){\unicdcdcdhd}((X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~(k3\_funct\_2~\\
k5\_numbers~(k23\_modelc\_3~X2)~X3~np\_\_1)~X2)){\unicdcdcdhd}(({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}(r6\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X3~X4)~X2)~(k10\_modelc\_3~\\
(k3\_funct\_2~k5\_numbers~(k23\_modelc\_3~X2)~X3~(k1\_nat\_1~X4~np\_\_1))~\\
X2))){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X0~X4){\unicdcdcdhd}(k12\_modelc\_2~X1 \in u1\_modelc\_3~X2~(k10\_modelc\_3~\\
(k1\_funct\_1~X3~X4)~X2)))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(\\
(r1\_xxreal\_0~np\_\_1~X4){\unicdbdjdcd}((r1\_xxreal\_0~X0~X4){\unicdcdcdid}((k11\_modelc\_2~X1 \in \\
u1\_modelc\_3~X2~(k10\_modelc\_3~(k1\_funct\_1~X3~X4)~X2)){\unicdcdcdhd}(X1 \in u1\_modelc\_3~\\
X2~(k10\_modelc\_3~(k1\_funct\_1~X3~X4)~X2))))))))))\end{array}$$
\end{theorem}
\end{document}
