\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{t8\_fscirc\_1 (TMG4BNk1MoqVGSHn9csMScCkHsmgbBJQ2fv)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_fscirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in u1\_struct\_0~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}(X2 \in u1\_struct\_0~\\
(k4\_fscirc\_1~X0~X1~X2)))\end{array}
\label{hyp:ehgdpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(\preoh \\
X0 \in X1))\end{array}
\label{hyp:ehfdadpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  v1\_relat\_1~(k3\_msafree2~(k4\_fscirc\_1~\\
X0~X1~X2))\end{array}
\label{hyp:ehbdpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k4\_fscirc\_1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgedpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k4\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(\preoh X3 \in X1)))\end{array}
\label{hyp:egfdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}(k3\_msafree2~\\
X0=k2\_relset\_1~(u1\_struct\_0~X0)~(u2\_msualg\_1~X0))\end{array}
\label{hyp:egddpfngdhbgggchfgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}(k2\_msafree2~\\
X0=k6\_subset\_1~(u1\_struct\_0~X0)~(k2\_relset\_1~(u1\_struct\_0~X0)~\\
(u2\_msualg\_1~X0)))\end{array}
\label{hyp:egcdpfngdhbgggchfgfgcd}
\end{equation}
\begin{theorem}\label{thm:ehidpfggdhdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}((X0 \in k2\_msafree2~(k4\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((X1 \in k2\_msafree2~(k4\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}(X2 \in k2\_msafree2~\\
(k4\_fscirc\_1~X0~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
