\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{t23\_modelc\_2 (TMSv3NHCXkXA6xVjXstsHRhnAsZBKykWvf5)}
\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 $ v5\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_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 $ k5\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_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 $ k4\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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}(\\
{\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(\\
(r1\_modelc\_2~X0~(k5\_modelc\_2~X1~X2)){\unicdbdjded}((X0=X1){\unicdcdcdid}(X0=X2)))))\end{array}
\label{hyp:ehbdgdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\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}({\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(((v4\_modelc\_2~X0){\unicdbdjdcd}((X1=k12\_modelc\_2~X0){\unicdbdjded}(\\
{\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}(\\
k4\_modelc\_2~X2~X1=X0)))){\unicdcdcdhd}(((v5\_modelc\_2~X0){\unicdbdjdcd}((X1=k12\_modelc\_2~\\
X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}\\
(k5\_modelc\_2~X2~X1=X0)))){\unicdcdcdhd}(((v7\_modelc\_2~X0){\unicdbdjdcd}((X1=k12\_modelc\_2~\\
X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}\\
(k7\_modelc\_2~X2~X1=X0)))){\unicdcdcdhd}(\preoh (\preoh v4\_modelc\_2~X0){\unicdcdcdhd}((\preoh v5\_modelc\_2~\\
X0){\unicdcdcdhd}((\preoh v7\_modelc\_2~X0){\unicdcdcdhd}(\preoh (X1=k12\_modelc\_2~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}(k8\_modelc\_2~\\
X2~X1=X0)))))))))))\end{array}
\label{hyp:egcdadpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\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}({\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(((v4\_modelc\_2~X0){\unicdbdjdcd}((X1=k11\_modelc\_2~X0){\unicdbdjded}(\\
{\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}(\\
k4\_modelc\_2~X1~X2=X0)))){\unicdcdcdhd}(((v5\_modelc\_2~X0){\unicdbdjdcd}((X1=k11\_modelc\_2~\\
X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}\\
(k5\_modelc\_2~X1~X2=X0)))){\unicdcdcdhd}(((v7\_modelc\_2~X0){\unicdbdjdcd}((X1=k11\_modelc\_2~\\
X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}\\
(k7\_modelc\_2~X1~X2=X0)))){\unicdcdcdhd}(\preoh (\preoh v4\_modelc\_2~X0){\unicdcdcdhd}((\preoh v5\_modelc\_2~\\
X0){\unicdcdcdhd}((\preoh v7\_modelc\_2~X0){\unicdcdcdhd}(\preoh (X1=k11\_modelc\_2~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}(k8\_modelc\_2~\\
X1~X2=X0)))))))))))\end{array}
\label{hyp:egbdjdpfngpgegfgmgdgpfcd}
\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){\unicdbdjded}({\unicdcdaddd} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)){\unicdcdcdhd}({\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~\\
X2~k5\_numbers)){\unicdcdcdhd}(X0=k5\_modelc\_2~X1~X2))))\end{array}
\label{hyp:egbdedpfngpgegfgmgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfngpgegfgmgdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(v5\_modelc\_2~X0){\unicdbdjdcd}((r1\_modelc\_2~X1~X0){\unicdbdjded}((X1=k11\_modelc\_2~X0){\unicdcdcdid}\\
(X1=k12\_modelc\_2~X0)))))\end{array}$$
\end{theorem}
\end{document}
