\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{t32\_graph\_1 (TMFTZHXPKNx5vUtmSJD2HoYxU2bNKTNo7SA)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{X1}})}{\unicdbdjded}{({{X0} \in {X1}})}}}}\label{hyp:ehddbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}(r1\_tarski~(k1\_tarski~X0)~(k11\_graph\_1~X0))\end{array}
\label{hyp:ehddbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_graph\_1~X1){\unicdcdcdhd}(l1\_graph\_1~X1))){\unicdbdjdcd}((X1 \in \\
k11\_graph\_1~X0){\unicdbdjded}(r4\_graph\_1~X1~X0)))\end{array}
\label{hyp:ehcdidpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(((r1\_partfun1~(u1\_graph\_1~\\
X0)~(u1\_graph\_1~X1)){\unicdcdcdhd}(r1\_partfun1~(u2\_graph\_1~X0)~(u2\_graph\_1~\\
X1))){\unicdbdjdcd}(((k5\_graph\_1~X0~X1{\unicdcdgdad}X1){\unicdcdcdhd}(k5\_graph\_1~X1~X0{\unicdcdgdad}X1)){\unicdcdcdid}(r4\_graph\_1~\\
X0~X1))))\end{array}
\label{hyp:ehcdedpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(((r1\_partfun1~(u1\_graph\_1~\\
X0)~(u1\_graph\_1~X1)){\unicdcdcdhd}(r1\_partfun1~(u2\_graph\_1~X0)~(u2\_graph\_1~\\
X1))){\unicdbdjdcd}((r4\_graph\_1~X0~(k5\_graph\_1~X0~X1)){\unicdcdcdhd}(r4\_graph\_1~X1~(k5\_graph\_1~\\
X0~X1)))))\end{array}
\label{hyp:ehbdjdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_graph\_1~X1){\unicdcdcdhd}(l1\_graph\_1~\\
X1))){\unicdbdjdcd}(((r4\_graph\_1~X0~X1){\unicdcdcdhd}(r4\_graph\_1~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdgdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_graph\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_graph\_1~(k5\_graph\_1~X0~X1)){\unicdcdcdhd}(l1\_graph\_1~(k5\_graph\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgfdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfhgchbgahigpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_graph\_1~X1){\unicdcdcdhd}(l1\_graph\_1~\\
X1))){\unicdbdjdcd}(\preoh (r1\_partfun1~(u1\_graph\_1~X0)~(u1\_graph\_1~X1)){\unicdcdcdhd}((r1\_partfun1~\\
(u2\_graph\_1~X0)~(u2\_graph\_1~X1)){\unicdcdcdhd}((r1\_tarski~(k11\_graph\_1~(k5\_graph\_1~\\
X0~X1))~(k2\_xboole\_0~(k11\_graph\_1~X0)~(k11\_graph\_1~X1))){\unicdcdcdhd}((\preoh r4\_graph\_1~\\
X0~X1){\unicdcdcdhd}(\preoh r4\_graph\_1~X1~X0))))))\end{array}$$
\end{theorem}
\end{document}
