\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{t31\_facirc\_1 (TMbxVTtBbc3AtzWU96ZQARoasrVikxotkt4)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\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 $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_card\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~\\
X0){\unicdcdcdhd}((v2\_circcomb~X0){\unicdcdcdhd}((v3\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}((v3\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))))){\unicdbdjdcd}\\
((r1\_xboole\_0~(k3\_msafree2~X1)~(k2\_msafree2~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v4\_msafree2~X2~X0){\unicdcdcdhd}((v4\_circcomb~X2~X0){\unicdcdcdhd}((v6\_circcomb~X2~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X2~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msafree2~X3~X1){\unicdcdcdhd}((v4\_circcomb~\\
X3~X1){\unicdcdcdhd}((v6\_circcomb~X3~X1){\unicdcdcdhd}(l3\_msualg\_1~X3~X1)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k4\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~\\
X0~X1~X2~X3)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~(u3\_msualg\_1~\\
X0~X2))){\unicdbdjdcd}((X5=k11\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~\\
X0~X1~X2~X3))~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (v7\_ordinal1~X6){\unicdbdjdcd}\\
(k11\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~X0~X1~\\
X2~X3))~(k5\_facirc\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~X0~X1~X2~X3)~\\
X4~X6)~(u1\_struct\_0~X0)=k5\_facirc\_1~X0~X2~X5~X6)))))))))\end{array}
\label{hyp:ehddadpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~\\
X0){\unicdcdcdhd}((v2\_circcomb~X0){\unicdcdcdhd}((v3\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}((v3\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v4\_msafree2~X2~X0){\unicdcdcdhd}((v4\_circcomb~X2~X0){\unicdcdcdhd}((v6\_circcomb~\\
X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msafree2~X3~X1){\unicdcdcdhd}\\
((v4\_circcomb~X3~X1){\unicdcdcdhd}((v6\_circcomb~X3~X1){\unicdcdcdhd}(l3\_msualg\_1~X3~X1)))){\unicdbdjdcd}\\
(k3\_circcomb~X0~X1~X2~X3=k3\_circcomb~X1~X0~X3~X2))))\end{array}
\label{hyp:ehcdedpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}((v2\_circcomb~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}(k2\_circcomb~X0~X1=\\
k2\_circcomb~X1~X0))\end{array}
\label{hyp:ehcdddpfggbgdgjgchdgpfbd}
\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}((v6\_circcomb~X1~X0){\unicdbdjdcd}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}\\
(v4\_msafree2~X1~X0))))\end{array}
\label{hyp:dgdgddpfdgjgchdgdgpgngcg}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~\\
X0){\unicdcdcdhd}((v2\_circcomb~X0){\unicdcdcdhd}((v3\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}((v3\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))))){\unicdbdjdcd}\\
((r1\_xboole\_0~(k3\_msafree2~X0)~(k2\_msafree2~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v4\_msafree2~X2~X0){\unicdcdcdhd}((v4\_circcomb~X2~X0){\unicdcdcdhd}((v6\_circcomb~X2~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X2~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msafree2~X3~X1){\unicdcdcdhd}((v4\_circcomb~\\
X3~X1){\unicdcdcdhd}((v6\_circcomb~X3~X1){\unicdcdcdhd}(l3\_msualg\_1~X3~X1)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k4\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~\\
X0~X1~X2~X3)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~(u3\_msualg\_1~\\
X1~X3))){\unicdbdjdcd}((X5=k11\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~\\
X0~X1~X2~X3))~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  (v7\_ordinal1~X6){\unicdbdjdcd}\\
(k11\_card\_3~(u3\_msualg\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~X0~X1~\\
X2~X3))~(k5\_facirc\_1~(k2\_circcomb~X0~X1)~(k3\_circcomb~X0~X1~X2~X3)~\\
X4~X6)~(u1\_struct\_0~X1)=k5\_facirc\_1~X1~X3~X5~X6)))))))))\end{array}$$
\end{theorem}
\end{document}
