\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{t28\_modelc\_3 (TMNBiNGnrRpW45mKSeNr5tq8vJ7ejfioMud)}
\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 $ v1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r4\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u2\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k6\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in k2\_xboole\_0~X2~(k1\_tarski~\\
X1)){\unicdbdjded}((X0 \in X2){\unicdcdcdid}(X0=X1))\end{array}
\label{hyp:ehbdddgdpfkhggngjgdhdgpfbd}
\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 .  (l1\_modelc\_3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_modelc\_3~X2~X0){\unicdbdjdcd}\\
((r4\_modelc\_3~X0~X1~X2){\unicdbdjded}((r2\_modelc\_3~X0~X1~X2){\unicdcdcdid}(r3\_modelc\_3~X0~\\
X1~X2)))))\end{array}
\label{hyp:egjdpfngpgegfgmgdgpfdd}
\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 .  (l1\_modelc\_3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_modelc\_3~X2~X0){\unicdbdjdcd}\\
((r3\_modelc\_3~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_modelc\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~\\
X3~k5\_numbers)){\unicdcdcdhd}((X3 \in u2\_modelc\_3~X0~X1){\unicdcdcdhd}((\preoh (\preoh v5\_modelc\_2~X3){\unicdcdcdhd}\\
((\preoh v7\_modelc\_2~X3){\unicdcdcdhd}(\preoh v8\_modelc\_2~X3))){\unicdcdcdhd}(X2=k6\_modelc\_3~X0~X1~\\
X3)))))))\end{array}
\label{hyp:egidpfngpgegfgmgdgpfdd}
\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 .  (l1\_modelc\_3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_modelc\_3~X2~X0){\unicdbdjdcd}\\
((r2\_modelc\_3~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_modelc\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~\\
X3~k5\_numbers)){\unicdcdcdhd}((X3 \in u2\_modelc\_3~X0~X1){\unicdcdcdhd}(X2=k5\_modelc\_3~X0~X1~\\
X3))))))\end{array}
\label{hyp:eghdpfngpgegfgmgdgpfdd}
\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 .  (l1\_modelc\_3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_modelc\_3~X2~X0){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_modelc\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~k5\_numbers)){\unicdbdjdcd}\\
((r1\_modelc\_3~X0~X1~X2~X3){\unicdbdjded}((X3 \in u2\_modelc\_3~X0~X1){\unicdcdcdhd}((X2=k5\_modelc\_3~\\
X0~X1~X3){\unicdcdcdid}((\preoh (\preoh v5\_modelc\_2~X3){\unicdcdcdhd}((\preoh v7\_modelc\_2~X3){\unicdcdcdhd}(\preoh v8\_modelc\_2~\\
X3))){\unicdcdcdhd}(X2=k6\_modelc\_3~X0~X1~X3))))))))\end{array}
\label{hyp:eggdpfngpgegfgmgdgpfdd}
\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 .  (l1\_modelc\_3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}\\
(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}((X2 \in u2\_modelc\_3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_modelc\_3~X3~X0){\unicdcdcdhd}(l1\_modelc\_3~X3~X0)){\unicdbdjdcd}((X3=k6\_modelc\_3~X0~\\
X1~X2){\unicdbdjded}((u1\_modelc\_3~X0~X3=k2\_xboole\_0~(u1\_modelc\_3~X0~X1)~(k1\_tarski~\\
X2)){\unicdcdcdhd}((u2\_modelc\_3~X0~X3=k2\_xboole\_0~(k7\_subset\_1~(k1\_modelc\_3~\\
X0)~(u2\_modelc\_3~X0~X1)~(k1\_tarski~X2))~(k7\_subset\_1~(k1\_modelc\_3~\\
X2)~(k3\_modelc\_3~X2)~(u1\_modelc\_3~X0~X1))){\unicdcdcdhd}(u3\_modelc\_3~X0~X3=\\
u3\_modelc\_3~X0~X1))))))))\end{array}
\label{hyp:egfdpfngpgegfgmgdgpfdd}
\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 .  (l1\_modelc\_3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}\\
(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}((X2 \in u2\_modelc\_3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_modelc\_3~X3~X0){\unicdcdcdhd}(l1\_modelc\_3~X3~X0)){\unicdbdjdcd}((X3=k5\_modelc\_3~X0~\\
X1~X2){\unicdbdjded}((u1\_modelc\_3~X0~X3=k2\_xboole\_0~(u1\_modelc\_3~X0~X1)~(k1\_tarski~\\
X2)){\unicdcdcdhd}((u2\_modelc\_3~X0~X3=k2\_xboole\_0~(k7\_subset\_1~(k1\_modelc\_3~\\
X0)~(u2\_modelc\_3~X0~X1)~(k1\_tarski~X2))~(k7\_subset\_1~(k1\_modelc\_3~\\
X2)~(k2\_modelc\_3~X2)~(u1\_modelc\_3~X0~X1))){\unicdcdcdhd}(u3\_modelc\_3~X0~X3=\\
k2\_xboole\_0~(u3\_modelc\_3~X0~X1)~(k4\_modelc\_3~X2)))))))))\end{array}
\label{hyp:egedpfngpgegfgmgdgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_modelc\_3~X2~X1){\unicdcdcdhd}(l1\_modelc\_3~X2~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_modelc\_3~X3~X1){\unicdcdcdhd}(l1\_modelc\_3~X3~X1)){\unicdbdjdcd}(((r4\_modelc\_3~X1~X3~\\
X2){\unicdcdcdhd}(X0 \in u1\_modelc\_3~X1~X2)){\unicdbdjdcd}((X0 \in u1\_modelc\_3~X1~X3){\unicdcdcdid}(r1\_modelc\_3~\\
X1~X3~X2~X0))))))\end{array}$$
\end{theorem}
\end{document}
