\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{t25\_facirc\_1 (TMMkoNXepXGsBMXsyzyrEeZpU2SyKoGuQfr)}
\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 $ v4\_msafree2 : {{\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 $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u3\_msualg\_1 : {{\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}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~X1){\unicdbdjdcd}(((v6\_circcomb~X2~X0){\unicdcdcdhd}\\
(v6\_circcomb~X3~X1)){\unicdbdjdcd}(r1\_partfun1~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~\\
X1~X3))))))\end{array}
\label{hyp:ehfdjdpfdgjgchdgdgpgngcg}
\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 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_msualg\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msualg\_1~X3~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~X4~X1){\unicdcdcdhd}(l3\_msualg\_1~X4~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v4\_msualg\_1~X5~X2){\unicdcdcdhd}(l3\_msualg\_1~X5~X2)){\unicdbdjdcd}(((r1\_partfun1~\\
(u3\_msualg\_1~X0~X3)~(u3\_msualg\_1~X1~X4)){\unicdcdcdhd}((r1\_partfun1~(u3\_msualg\_1~\\
X1~X4)~(u3\_msualg\_1~X2~X5)){\unicdcdcdhd}(r1\_partfun1~(u3\_msualg\_1~X2~X5)~(u3\_msualg\_1~\\
X0~X3)))){\unicdbdjdcd}(k3\_circcomb~(k2\_circcomb~X0~X1)~X2~(k3\_circcomb~X0~X1~\\
X3~X4)~X5=k3\_circcomb~X0~(k2\_circcomb~X1~X2)~X3~(k3\_circcomb~X1~X2~\\
X4~X5))))))))\end{array}
\label{hyp:ehcdddpfdgjgchdgdgpgngcg}
\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:ehcdfdpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~\\
X0){\unicdcdcdhd}((v2\_circcomb~X0){\unicdcdcdhd}((v3\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}((v3\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((v1\_circcomb~\\
X2){\unicdcdcdhd}((v2\_circcomb~X2){\unicdcdcdhd}((v3\_circcomb~X2){\unicdcdcdhd}(l1\_msualg\_1~X2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v4\_msafree2~X3~X0){\unicdcdcdhd}((v6\_circcomb~X3~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msafree2~X4~X1){\unicdcdcdhd}((v6\_circcomb~X4~X1){\unicdcdcdhd}\\
(l3\_msualg\_1~X4~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msafree2~X5~X2){\unicdcdcdhd}((v6\_circcomb~\\
X5~X2){\unicdcdcdhd}(l3\_msualg\_1~X5~X2))){\unicdbdjdcd}(k3\_circcomb~(k2\_circcomb~X0~X1)~\\
X2~(k3\_circcomb~X0~X1~X3~X4)~X5=k3\_circcomb~X0~(k2\_circcomb~X1~X2)~\\
X3~(k3\_circcomb~X1~X2~X4~X5)))))))\end{array}$$
\end{theorem}
\end{document}
