\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{t3\_msscyc\_2 (TMWDMYa7YEhDZA4LbqcVE2ERz2Cwne7jRoa)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_msscyc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_msscyc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_msscyc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msscyc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msscyc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_msafree : {{\iota}{\unicdbdjdcd}{{\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.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (g1\_graph\_1~X0~X1~X2~X3=g1\_graph\_1~X4~X5~X6~\\
X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfhgchbgahigpfbd}
\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 v11\_struct\_0~X0){\unicdcdcdhd}(l5\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u4\_struct\_0~X0))\end{array}
\label{hyp:ggdgbdedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v11\_struct\_0~X0){\unicdcdcdhd}(l5\_struct\_0~X0)){\unicdbdjdcd}(v1\_xboole\_0~\\
(u4\_struct\_0~X0))\end{array}
\label{hyp:ggdgbdddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_graph\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k4\_msscyc\_2~X0)){\unicdcdcdhd}(l1\_graph\_1~(k4\_msscyc\_2~X0)))\end{array}
\label{hyp:egehpflgedpfngdhdhdgjhdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(k3\_msscyc\_2~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k3\_msscyc\_2~X0)~(k1\_msscyc\_2~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_msscyc\_2~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_msscyc\_2~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgddpfngdhdhdgjhdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(k2\_msscyc\_2~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k2\_msscyc\_2~X0)~(k1\_msscyc\_2~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_msscyc\_2~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_msscyc\_2~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgcdpfngdhdhdgjhdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)))))){\unicdbdjdcd}((v1\_graph\_1~(g1\_graph\_1~\\
X0~X1~X2~X3)){\unicdcdcdhd}(l1\_graph\_1~(g1\_graph\_1~X0~X1~X2~X3)))\end{array}
\label{hyp:egehpfhgbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}(k4\_msscyc\_2~\\
X0=g1\_graph\_1~(u1\_struct\_0~X0)~(k1\_msscyc\_2~X0)~(k2\_msscyc\_2~\\
X0)~(k3\_msscyc\_2~X0))\end{array}
\label{hyp:egedpfngdhdhdgjhdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=k1\_msscyc\_2~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  (X2=k4\_tarski~X3~\\
X4){\unicdcdcdhd}((X3 \in u4\_struct\_0~X0){\unicdcdcdhd}((X4 \in u1\_struct\_0~X0){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(v7\_ordinal1~X5){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(k13\_finseq\_1~(\\
u1\_struct\_0~X0))){\unicdcdcdhd}((k1\_funct\_1~(u1\_msualg\_1~X0)~X3=X6){\unicdcdcdhd}((X5 \in \\
k4\_finseq\_1~X6){\unicdcdcdhd}(k1\_funct\_1~X6~X5=X4))))))))))\end{array}
\label{hyp:egbdpfngdhdhdgjhdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}((v5\_msafree2~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v3\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdbdjdcd}(v4\_msafree2~X1~X0)))\end{array}
\label{hyp:egbdddpfngdhbgggchfgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}((v4\_msafree2~X1~X0){\unicdbdjded}(v2\_finset\_1~(u3\_msualg\_1~\\
X0~X1))))\end{array}
\label{hyp:egbdbdpfngdhbgggchfgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}(((\preoh v11\_struct\_0~X0){\unicdbdjdcd}((v3\_msafree2~X1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}(l1\_msualg\_1~\\
X2))){\unicdbdjdcd}((X2=X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~X2){\unicdbdjdcd}(\preoh (X3=X1){\unicdcdcdhd}(\\
{\unicdcdadad} X4 .  (m1\_msafree~X4~X2~X3){\unicdbdjdcd}(\preoh v2\_finset\_1~X4)))))))){\unicdcdcdhd}((\\
v11\_struct\_0~X0){\unicdbdjdcd}((v3\_msafree2~X1~X0){\unicdbdjded}(v2\_finset\_1~(u3\_msualg\_1~\\
X0~X1))))))\end{array}
\label{hyp:egbdadpfngdhbgggchfgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v11\_struct\_0~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_msscyc\_1~X0)))\end{array}
\label{hyp:dgdgddpfngdhdhdgjhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}((v1\_graph\_1~X0){\unicdbdjdcd}(X0=g1\_graph\_1~\\
(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfhgchbgahigpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddpfngdhdhdgjhdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}((v5\_msafree2~X0){\unicdbdjded}(v3\_msscyc\_1~(k4\_msscyc\_2~X0)))\end{array}$$
\end{theorem}
\end{document}
