\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\_parsp\_1 (TMQ9H4e6j9tdpguvSi6GwCx9xeToymWCLSW)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_parsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_parsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_parsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}((r1\_parsp\_1~(k9\_parsp\_1~X0)~\\
X1~X2~X3~X4){\unicdbdjded}((k5\_domain\_1~(u1\_struct\_0~(k9\_parsp\_1~X0))~(u1\_struct\_0~\\
(k9\_parsp\_1~X0))~(u1\_struct\_0~(k9\_parsp\_1~X0))~(u1\_struct\_0~(\\
k9\_parsp\_1~X0))~X1~X2~X3~X4 \in k6\_parsp\_1~X0){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~\\
X7~(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}((k5\_domain\_1~(u1\_struct\_0~\\
(k9\_parsp\_1~X0))~(u1\_struct\_0~(k9\_parsp\_1~X0))~(u1\_struct\_0~(\\
k9\_parsp\_1~X0))~(u1\_struct\_0~(k9\_parsp\_1~X0))~X1~X2~X3~X4=k5\_domain\_1~\\
(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
X5~X6~X7~X8){\unicdcdcdhd}((k5\_algstr\_0~X0~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k1\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6))~(k5\_algstr\_0~\\
X0~(k2\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X7)~(k2\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X8)))~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X7)~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X8))~(k5\_algstr\_0~X0~(k2\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k2\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6)))=k4\_struct\_0~\\
X0){\unicdcdcdhd}((k5\_algstr\_0~X0~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k1\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6))~(k5\_algstr\_0~\\
X0~(k3\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X7)~(k3\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X8)))~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X7)~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X8))~(k5\_algstr\_0~X0~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6)))=k4\_struct\_0~\\
X0){\unicdcdcdhd}(k5\_algstr\_0~X0~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k2\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k2\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6))~(k5\_algstr\_0~\\
X0~(k3\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X7)~(k3\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X8)))~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k2\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X7)~(k2\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X8))~(k5\_algstr\_0~X0~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6)))=k4\_struct\_0~\\
X0))))))))))))))\end{array}
\label{hyp:ehjdpfahbgchdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}(k5\_domain\_1~(u1\_struct\_0~(k9\_parsp\_1~\\
X0))~(u1\_struct\_0~(k9\_parsp\_1~X0))~(u1\_struct\_0~(k9\_parsp\_1~X0))~\\
(u1\_struct\_0~(k9\_parsp\_1~X0))~X1~X2~X3~X4 \in k6\_parsp\_1~X0)))))\end{array}
\label{hyp:ehbdbdpfahbgchdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}(u1\_struct\_0~\\
(k9\_parsp\_1~X0)=k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ehbdadpfahbgchdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfahbgchdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k9\_parsp\_1~X0))){\unicdbdjdcd}((r1\_parsp\_1~(k9\_parsp\_1~X0)~\\
X1~X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}((k5\_domain\_1~(u1\_struct\_0~(k9\_parsp\_1~X0))~(u1\_struct\_0~\\
(k9\_parsp\_1~X0))~(u1\_struct\_0~(k9\_parsp\_1~X0))~(u1\_struct\_0~(\\
k9\_parsp\_1~X0))~X1~X2~X3~X4=k5\_domain\_1~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~X5~X6~X7~X8){\unicdcdcdhd}((k5\_algstr\_0~\\
X0~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6))~(k5\_algstr\_0~X0~(k2\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X7)~(k2\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X8)))~(k8\_group\_1~\\
X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~X7)~(k1\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~X8))~(k5\_algstr\_0~X0~(k2\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k2\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6)))=k4\_struct\_0~X0){\unicdcdcdhd}(\\
(k5\_algstr\_0~X0~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k1\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6))~(k5\_algstr\_0~X0~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X7)~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X8)))~(k8\_group\_1~\\
X0~(k5\_algstr\_0~X0~(k1\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~X7)~(k1\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~X8))~(k5\_algstr\_0~X0~(k3\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k3\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6)))=k4\_struct\_0~X0){\unicdcdcdhd}(\\
k5\_algstr\_0~X0~(k8\_group\_1~X0~(k5\_algstr\_0~X0~(k2\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k2\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6))~(k5\_algstr\_0~X0~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X7)~(k3\_mcart\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X8)))~(k8\_group\_1~\\
X0~(k5\_algstr\_0~X0~(k2\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~X7)~(k2\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~X8))~(k5\_algstr\_0~X0~(k3\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X5)~(k3\_mcart\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X6)))=k4\_struct\_0~X0)))))))))))))\end{array}$$
\end{theorem}
\end{document}
