\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{t12\_fsm\_3 (TMTzH8HZh5LHZEYh8Xh4CBKhZSkkFLHm7ch)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ k9\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~X5){\unicdcdcdhd}(l1\_rewrite3~\\
X5~X4)){\unicdbdjdcd}((r3\_rewrite3~X2~X4~X5~X0~(k3\_flang\_1~X2~X3)~X1~(k2\_flang\_1~\\
X2)){\unicdbdjdcd}((k2\_flang\_1~X2 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~\\
X4~X5))){\unicdcdcdid}(r2\_rewrite3~X2~X4~X5~X0~(k3\_flang\_1~X2~X3)~X1~(k2\_flang\_1~\\
X2)))))))\end{array}
\label{hyp:ehjdcdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_catalan2}~{X0}}={{k8\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdgbgehbgmgbgogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_rewrite3~\\
X2~X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k1\_fsm\_3~X0~X1~X2)){\unicdcdcdhd}((v1\_rewrite3~(\\
k1\_fsm\_3~X0~X1~X2)~(k9\_flang\_1~X0)){\unicdcdcdhd}(v2\_rewrite3~(k1\_fsm\_3~X0~X1~\\
X2)~X0~(k9\_flang\_1~X0))))\end{array}
\label{hyp:ggdgcdpfggdhngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k9\_flang\_1}~{X0}})}}~{({{k1\_zfmisc\_1}~{({{k3\_catalan2}~{X0}})}})}}}\label{hyp:egehpflgjdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_rewrite3~\\
X2~X1)))){\unicdbdjdcd}((v1\_rewrite3~(k1\_fsm\_3~X0~X1~X2)~(k9\_flang\_1~X0)){\unicdcdcdhd}(\\
l1\_rewrite3~(k1\_fsm\_3~X0~X1~X2)~(k9\_flang\_1~X0)))\end{array}
\label{hyp:egehpflgbdpfggdhngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_rewrite3~X2~X1){\unicdbdjdcd}((v2\_rewrite3~\\
X2~X0~X1){\unicdbdjded}(((v1\_relat\_1~(u1\_rewrite3~X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(u1\_rewrite3~\\
X1~X2))){\unicdcdcdhd}((\preoh k2\_flang\_1~X0 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~\\
X1~X2))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(k8\_afinsq\_1~X0)){\unicdbdjdcd}(((k4\_tarski~X3~X4 \in k9\_xtuple\_0~(u1\_rewrite3~\\
X1~X2)){\unicdcdcdhd}(k4\_tarski~X3~X5 \in k9\_xtuple\_0~(u1\_rewrite3~X1~X2))){\unicdbdjdcd}((\\
X4=X5){\unicdcdcdid}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((k1\_flang\_1~\\
X0~X4~X6{\unicdcdgdad}X5){\unicdcdcdhd}(k1\_flang\_1~X0~X5~X6{\unicdcdgdad}X4)))))))))))))\end{array}
\label{hyp:egbdpfchfghhchjgehfgdd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfggdhngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~X5){\unicdcdcdhd}(l1\_rewrite3~\\
X5~X4)){\unicdbdjdcd}((r3\_rewrite3~X2~(k9\_flang\_1~X2)~(k1\_fsm\_3~X2~X4~X5)~X0~(\\
k3\_flang\_1~X2~X3)~X1~(k2\_flang\_1~X2)){\unicdbdjdcd}(r2\_rewrite3~X2~(k9\_flang\_1~\\
X2)~(k1\_fsm\_3~X2~X4~X5)~X0~(k3\_flang\_1~X2~X3)~X1~(k2\_flang\_1~X2))))))\end{array}$$
\end{theorem}
\end{document}
