\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{t32\_ec\_pf\_2 (TMdmrM5PSSUkWbG1K9SSrSzt3yN81VDMPxj)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\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\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ k5\_ec\_pf\_2 : {{\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 $ k6\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ 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 $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2)){\unicdbdjdcd}(X3=k3\_xtuple\_0~(k1\_mcart\_1~X0~X1~X2~X3)~(k2\_mcart\_1~\\
X0~X1~X2~X3)~(k3\_mcart\_1~X0~X1~X2~X3)))))\end{array}
\label{hyp:ehededpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0))~(k6\_ec\_pf\_1~X0~X1~X2)){\unicdbdjdcd}(X3=k4\_domain\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(k4\_ec\_pf\_2~X0~X1~X2~X3)~(k5\_ec\_pf\_2~X0~X1~X2~X3)~(k6\_ec\_pf\_2~\\
X0~X1~X2~X3)))))\end{array}
\label{hyp:ehddbdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\\
(m1\_subset\_1~X3~X0){\unicdcdcdhd}((m1\_subset\_1~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X5~X2)))))){\unicdbdjdcd}\\
(k4\_domain\_1~X0~X1~X2~X3~X4~X5=k3\_xtuple\_0~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2))))){\unicdbdjdcd}(k1\_mcart\_1~X0~X1~X2~X3=k4\_xtuple\_0~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xtuple\_0~(k3\_xtuple\_0~X0~\\
X1~X2)=X2\end{array}
\label{hyp:cheggdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k5\_xtuple\_0~(k3\_xtuple\_0~X0~\\
X1~X2)=X1\end{array}
\label{hyp:chegfdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k4\_xtuple\_0~(k3\_xtuple\_0~X0~\\
X1~X2)=X0\end{array}
\label{hyp:chegedpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v6\_struct\_0~\\
(k9\_int\_3~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k9\_int\_3~X0)){\unicdcdcdhd}((v33\_algstr\_0~\\
(k9\_int\_3~X0)){\unicdcdcdhd}((v3\_group\_1~(k9\_int\_3~X0)){\unicdcdcdhd}((v5\_group\_1~(k9\_int\_3~\\
X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k9\_int\_3~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_int\_3~X0)){\unicdcdcdhd}\\
((v4\_rlvect\_1~(k9\_int\_3~X0)){\unicdcdcdhd}((v4\_vectsp\_1~(k9\_int\_3~X0)){\unicdcdcdhd}(\\
v5\_vectsp\_1~(k9\_int\_3~X0)))))))))))\end{array}
\label{hyp:ggdghdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k9\_int\_3~X0)){\unicdcdcdhd}(v36\_algstr\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:ggdggdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{l6\_algstr\_0}~{({{k9\_int\_3}~{X0}})}})}}}\label{hyp:egehpflgjdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v7\_ordinal1~X0){\unicdcdcdhd}\\
(v1\_int\_2~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k6\_ec\_pf\_1~X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k6\_ec\_pf\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflggdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~(k9\_int\_3~X0))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_ec\_pf\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k6\_ec\_pf\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0)))))\end{array}
\label{hyp:egehpflggdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v7\_ordinal1~X0){\unicdcdcdhd}\\
(v1\_int\_2~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k6\_ec\_pf\_1~X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k5\_ec\_pf\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflgfdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v7\_ordinal1~X0){\unicdcdcdhd}\\
(v1\_int\_2~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k6\_ec\_pf\_1~X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_ec\_pf\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflgedpffgdgpfahggpfcd}
\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}((\preoh v1\_xboole\_0~\\
(k3\_ec\_pf\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k3\_ec\_pf\_1~X0)~(k1\_zfmisc\_1~(\\
k3\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpflgddpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)))\end{array}
\label{hyp:dgdgddpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpffgdgpfahggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0))~(k6\_ec\_pf\_1~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}\\
((X3=X4){\unicdbdjded}((k4\_ec\_pf\_2~X0~X1~X2~X3=k1\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X4){\unicdcdcdhd}\\
((k5\_ec\_pf\_2~X0~X1~X2~X3=k2\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~X0))~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X4){\unicdcdcdhd}(\\
k6\_ec\_pf\_2~X0~X1~X2~X3=k3\_mcart\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(\\
u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X4))))))))\end{array}$$
\end{theorem}
\end{document}
