\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{t56\_graph\_5 (TMYxdqxJossAF5PudMAVzMq1UdpXJqE5TPG)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ v7\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r5\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\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 .  (m2\_finseq\_1~X3~(u4\_struct\_0~\\
X1)){\unicdbdjdcd}(((v2\_funct\_1~X2){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~X2)~(k10\_xtuple\_0~\\
X3)){\unicdcdcdhd}(r5\_graph\_5~X1~X0))){\unicdbdjdcd}(r1\_xxreal\_0~(k10\_graph\_5~X1~X2~X0)~\\
(k10\_graph\_5~X1~X3~X0))))))\end{array}
\label{hyp:ehfdfdpfhgchbgahigpffd}
\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 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}((v1\_graph\_4~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}\\
(v2\_funct\_1~X1))\end{array}
\label{hyp:ehbdhdpfhgchbgahigpffd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)){\unicdbdjdcd}(k6\_graph\_5~X0~X1=ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  (v7\_graph\_1~X2~X0){\unicdcdcdhd}((v1\_graph\_4~X2~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X2~X0))))~({\uniddcgcg} X2 : \iota .  (X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_funct\_1~(u1\_graph\_1~\\
X0)~(k1\_funct\_1~X2~np\_\_1)=k1\_funct\_1~(u1\_graph\_1~X0)~(k1\_funct\_1~\\
X1~np\_\_1)){\unicdcdcdhd}((k1\_funct\_1~(u2\_graph\_1~X0)~(k1\_funct\_1~X2~(k3\_finseq\_1~\\
X2))=k1\_funct\_1~(u2\_graph\_1~X0)~(k1\_funct\_1~X1~(k3\_finseq\_1~X1))){\unicdcdcdhd}\\
(r1\_tarski~(k10\_xtuple\_0~X2)~(k10\_xtuple\_0~X1)))))~({\uniddcgcg} X2 : \iota .  \\
X2)))\end{array}
\label{hyp:egbdadpfhgchbgahigpffd}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfhgchbgahigpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~\\
X2~(u4\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v7\_graph\_1~X3~X1){\unicdcdcdhd}(m2\_graph\_1~\\
X3~X1)){\unicdbdjdcd}(((X2 \in k6\_graph\_5~X1~X3){\unicdcdcdhd}(r5\_graph\_5~X1~X0)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k10\_graph\_5~X1~X2~X0)~(k10\_graph\_5~X1~X3~X0))))))\end{array}$$
\end{theorem}
\end{document}
