\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{t31\_modelc\_2 (TMQegos5abh7n6rz61WjwYugVBDAgTwKQUq)}
\maketitle
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 $ v4\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(r1\_modelc\_2~X0~X1){\unicdbdjdcd}(r3\_modelc\_2~X0~X1)))\end{array}
\label{hyp:ehcdjdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(v8\_modelc\_2~X0){\unicdbdjdcd}((r1\_modelc\_2~X1~X0){\unicdbdjded}((X1=k11\_modelc\_2~X0){\unicdcdcdid}\\
(X1=k12\_modelc\_2~X0)))))\end{array}
\label{hyp:ehcdfdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(v7\_modelc\_2~X0){\unicdbdjdcd}((r1\_modelc\_2~X1~X0){\unicdbdjded}((X1=k11\_modelc\_2~X0){\unicdcdcdid}\\
(X1=k12\_modelc\_2~X0)))))\end{array}
\label{hyp:ehcdedpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(v5\_modelc\_2~X0){\unicdbdjdcd}((r1\_modelc\_2~X1~X0){\unicdbdjded}((X1=k11\_modelc\_2~X0){\unicdcdcdid}\\
(X1=k12\_modelc\_2~X0)))))\end{array}
\label{hyp:ehcdddpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(v4\_modelc\_2~X0){\unicdbdjdcd}((r1\_modelc\_2~X1~X0){\unicdbdjded}((X1=k11\_modelc\_2~X0){\unicdcdcdid}\\
(X1=k12\_modelc\_2~X0)))))\end{array}
\label{hyp:ehcdcdpfngpgegfgmgdgpfcd}
\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 .  ((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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(r3\_modelc\_2~X0~X1){\unicdbdjded}((r2\_modelc\_2~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}X1))))\end{array}
\label{hyp:egcdddpfngpgegfgmgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfngpgegfgmgdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(\preoh (\preoh v4\_modelc\_2~X0){\unicdcdcdhd}((\preoh v5\_modelc\_2~X0){\unicdcdcdhd}((\preoh v7\_modelc\_2~X0){\unicdcdcdhd}\\
(\preoh v8\_modelc\_2~X0)))){\unicdbdjdcd}((r2\_modelc\_2~(k11\_modelc\_2~X0)~X0){\unicdcdcdhd}(r2\_modelc\_2~\\
(k12\_modelc\_2~X0)~X0)))\end{array}$$
\end{theorem}
\end{document}
