\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{l29\_modelc\_2 (TMUJb6bezSNZrrvMuLkkbNNSchPiZsC2AwW)}
\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 $ v2\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ v3\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
\preoh (\preoh v2\_modelc\_2~X0){\unicdcdcdhd}((\preoh v3\_modelc\_2~X0){\unicdcdcdhd}((\preoh v4\_modelc\_2~X0){\unicdcdcdhd}(\\
(\preoh v5\_modelc\_2~X0){\unicdcdcdhd}((\preoh v6\_modelc\_2~X0){\unicdcdcdhd}((\preoh v7\_modelc\_2~X0){\unicdcdcdhd}(\preoh \\
v8\_modelc\_2~X0)))))))\end{array}
\label{hyp:ehcdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v2\_modelc\_2~X0){\unicdbdjdcd}((k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~\\
X0~np\_\_1{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((k1\_funct\_1~X0~\\
np\_\_1{\unicdcdgdad}np\_\_3){\unicdcdcdhd}((k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}np\_\_4){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}\\
np\_\_5)))))))\end{array}
\label{hyp:mgcdidpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v8\_modelc\_2~X0){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1=np\_\_5))\end{array}
\label{hyp:mgcdhdpfngpgegfgmgdgpfcd}
\end{equation}
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}(k1\_funct\_1~X0~np\_\_1=np\_\_4))\end{array}
\label{hyp:mgcdgdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v6\_modelc\_2~X0){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1=np\_\_3))\end{array}
\label{hyp:mgcdfdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v5\_modelc\_2~X0){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1=np\_\_2))\end{array}
\label{hyp:mgcdedpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v4\_modelc\_2~X0){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1=np\_\_1))\end{array}
\label{hyp:mgcdddpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v3\_modelc\_2~X0){\unicdbdjdcd}(k1\_funct\_1~X0~np\_\_1=k6\_numbers))\end{array}
\label{hyp:mgcdcdpfngpgegfgmgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:mgcdjdpfngpgegfgmgdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
\preoh (\preoh (v2\_modelc\_2~X0){\unicdcdcdhd}((k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~\\
X0~np\_\_1{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((k1\_funct\_1~X0~\\
np\_\_1{\unicdcdgdad}np\_\_3){\unicdcdcdhd}((k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}np\_\_4){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1{\unicdcdgdad}\\
np\_\_5))))))){\unicdcdcdhd}((\preoh (v3\_modelc\_2~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=k6\_numbers)){\unicdcdcdhd}\\
((\preoh (v4\_modelc\_2~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_1)){\unicdcdcdhd}((\preoh (v5\_modelc\_2~\\
X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_2)){\unicdcdcdhd}((\preoh (v6\_modelc\_2~X0){\unicdcdcdhd}(k1\_funct\_1~\\
X0~np\_\_1=np\_\_3)){\unicdcdcdhd}((\preoh (v7\_modelc\_2~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_4)){\unicdcdcdhd}\\
(\preoh (v8\_modelc\_2~X0){\unicdcdcdhd}(k1\_funct\_1~X0~np\_\_1=np\_\_5))))))))\end{array}$$
\end{theorem}
\end{document}
