\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{t13\_graph\_5 (TMYviXv3UyYd9z6F3MZG9xPww8kgjad1XHN)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_graph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_graph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_graph\_1~X2~\\
X0){\unicdbdjdcd}(\preoh (r1\_graph\_2~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v3\_graph\_2~X5~X0){\unicdcdcdhd}(m2\_graph\_1~X5~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k15\_finseq\_1~X3=X5){\unicdcdcdhd}((k15\_finseq\_1~\\
X4=X6){\unicdcdcdhd}((r1\_graph\_2~X0~X6~X5){\unicdcdcdhd}((k1\_funct\_1~X1~np\_\_1=k1\_funct\_1~\\
X6~np\_\_1){\unicdcdcdhd}(k1\_funct\_1~X1~(k3\_finseq\_1~X1)=k1\_funct\_1~X6~(k3\_finseq\_1~\\
X6)))))))))))))\end{array}
\label{hyp:ehedjdpfhgchbgahigpfcd}
\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 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v1\_graph\_4~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)))){\unicdcdcdhd}((((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v1\_graph\_4~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)))){\unicdcdcdhd}(((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}((v2\_funct\_1~\\
X1){\unicdcdcdhd}((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)))))))\end{array}
\label{hyp:ehcdedpfhgchbgahigpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}(m2\_graph\_1~\\
k1\_xboole\_0~X0)\end{array}
\label{hyp:ehbdedpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_finseq\_1~X0))){\unicdbdjdcd}\\
(((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}(k15\_finseq\_1~\\
X0=X0))\end{array}
\label{hyp:ehbdbdgdpfggjgogdhfgbhpfdd}
\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 .  \\
(m2\_graph\_1~X1~X0){\unicdbdjded}(m1\_graph\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X1 .  \\
(m1\_graph\_1~X1~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X1~(u4\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_xboole\_0~\\
X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}(v2\_finseq\_1~X1)))))))))\end{array}
\label{hyp:chdgfdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}(m1\_graph\_1~\\
k1\_xboole\_0~X0)\end{array}
\label{hyp:mgbdfdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\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 .  \\
(m1\_graph\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))))\end{array}
\label{hyp:egehpfngbdpfhgchbgahigpfbd}
\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 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((m1\_graph\_1~\\
X1~X0){\unicdbdjded}((m2\_finseq\_1~X1~(u4\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m2\_finseq\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(r1\_graph\_2~X0~X2~X1)))))\end{array}
\label{hyp:egbdpfngdhdhdgjhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_finseq\_1~X0)))\end{array}
\label{hyp:dgdggdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\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 .  \\
(m1\_graph\_1~X1~X0){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdbdjdcd}(v7\_graph\_1~X1~X0)))\end{array}
\label{hyp:dgdgbdpfhgchbgahigpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfhgchbgahigpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}((v7\_graph\_1~\\
k1\_xboole\_0~X0){\unicdcdcdhd}((v1\_graph\_4~k1\_xboole\_0~X0){\unicdcdcdhd}(m2\_graph\_1~k1\_xboole\_0~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
