\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{t34\_graph\_5 (TMJfRRsXgB2WdhAjFEyv5wSFht133Ak3mdV)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~(k4\_xboole\_0~X0~X1)~\\
X2){\unicdbdjdcd}(r1\_tarski~X0~(k2\_xboole\_0~X1~X2))\end{array}
\label{hyp:ehededpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_xboole\_0~(k2\_xboole\_0~X0~X1)~X1=k4\_xboole\_0~\\
X0~X1\end{array}
\label{hyp:ehedadpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{({{{k4\_xboole\_0}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ehddgdpfihcgpgpgmgfgpfbd}
\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~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\\
v7\_graph\_1~X5~X0){\unicdcdcdhd}(m2\_graph\_1~X5~X0)){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~\\
X5)){\unicdcdcdhd}((r1\_graph\_5~X0~X5~X2~X3){\unicdcdcdhd}((r1\_graph\_4~X0~X3~X4~(k1\_funct\_1~\\
X1~np\_\_1)){\unicdcdcdhd}((k3\_finseq\_1~X1=np\_\_1){\unicdcdcdhd}({\unicdcdadad} X6 .  ((v7\_graph\_1~\\
X6~X0){\unicdcdcdhd}(m2\_graph\_1~X6~X0)){\unicdbdjdcd}(\preoh (X6=k8\_finseq\_1~(u4\_struct\_0~X0)~\\
X5~X1){\unicdcdcdhd}(r1\_graph\_5~X0~X6~X2~X4))))))))))))\end{array}
\label{hyp:ehddddpfhgchbgahigpffd}
\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~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v7\_graph\_1~X2~\\
X0){\unicdcdcdhd}(m2\_graph\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v7\_graph\_1~X3~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X3~X0)){\unicdbdjdcd}(((X2=k8\_finseq\_1~(u4\_struct\_0~X0)~X3~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
np\_\_1~(k3\_finseq\_1~X3)){\unicdcdcdhd}(k3\_finseq\_1~X1=np\_\_1))){\unicdbdjdcd}(k2\_graph\_5~\\
X0~X2=k2\_xboole\_0~(k2\_graph\_5~X0~X3)~(k1\_tarski~(k1\_funct\_1~(u2\_graph\_1~\\
X0)~(k1\_funct\_1~X1~np\_\_1))))))))\end{array}
\label{hyp:ehcdhdpfhgchbgahigpffd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\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){\unicdbdjdcd}(m2\_finseq\_1~X1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpfngcdpfhgchbgahigpfbd}
\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}\\
(m1\_finseq\_1~X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k2\_graph\_5~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgcdpfhgchbgahigpffd}
\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\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v7\_graph\_1~X3~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (r2\_graph\_5~X0~X1~X2~X3~X4){\unicdbdjded}((r1\_graph\_5~X0~\\
X3~X1~X2){\unicdcdcdhd}(r1\_tarski~(k7\_subset\_1~(u1\_struct\_0~X0)~(k2\_graph\_5~\\
X0~X3)~(k1\_tarski~X2))~X4))))))\end{array}
\label{hyp:egedpfhgchbgahigpffd}
\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\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (r1\_graph\_4~X0~X1~X2~X3){\unicdbdjded}((k1\_funct\_1~\\
(u1\_graph\_1~X0)~X3=X1){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X0)~X3=X2)))))\end{array}
\label{hyp:egbdpfhgchbgahigpfed}
\end{equation}
\begin{theorem}\label{thm:ehddedpfhgchbgahigpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u4\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
((v7\_graph\_1~X6~X1){\unicdcdcdhd}(m2\_graph\_1~X6~X1)){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v7\_graph\_1~\\
X7~X1){\unicdcdcdhd}(m2\_graph\_1~X7~X1)){\unicdbdjdcd}(((X6=k8\_finseq\_1~(u4\_struct\_0~X1)~\\
X7~X2){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X7)){\unicdcdcdhd}((k3\_finseq\_1~X2=\\
np\_\_1){\unicdcdcdhd}((r2\_graph\_5~X1~X3~X4~X7~X0){\unicdcdcdhd}(r1\_graph\_4~X1~X4~X5~(k1\_funct\_1~\\
X2~np\_\_1)))))){\unicdbdjdcd}(r2\_graph\_5~X1~X3~X5~X6~(k2\_xboole\_0~X0~(k1\_tarski~\\
X4))))))))))\end{array}$$
\end{theorem}
\end{document}
