\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=}
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\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\uniddcgcg{\lambda}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t43\_functor3 (TMakVypjb7doWwA25qfKowCKVMbethAELdq)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k9\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_functor2~\\
X0~X1~X2~X2~(k1\_functor2~X0~X1~X2)~X3=k8\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X3)))))\end{array}
\label{hyp:ehedpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_altcat\_3~X0~X1~X1~(k8\_altcat\_1~X0~X1)=\\
k8\_altcat\_1~X0~X1))\end{array}
\label{hyp:ehedpfbgmgehdgbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_functor0~X3~X0~X1){\unicdbdjdcd}((r1\_functor2~X0~X1~\\
X2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor2~X4~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_functor2~\\
X5~X0~X1~X2~X3){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k2\_functor2~X0~X1~X2~X3~X4~X6=k2\_functor2~X0~X1~X2~X3~X5~X6)){\unicdbdjdcd}(r8\_pboole~\\
(u1\_struct\_0~X0)~X4~X5))))))))\end{array}
\label{hyp:ehddpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X1~X0){\unicdcdcdhd}\\
(m2\_functor0~X2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X1~X0){\unicdcdcdhd}(\\
m2\_functor0~X3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor3~X4~X1~X0~X2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_functor3~\\
X1~X0~X2~X3){\unicdbdjdcd}(k2\_functor2~X1~X0~X3~X2~(k8\_functor3~X1~X0~X2~X3~X4)~X5=\\
k1\_altcat\_3~X0~(k3\_functor0~X1~X0~X2~X5)~(k3\_functor0~X1~X0~X3~X5)~\\
(k2\_functor2~X1~X0~X2~X3~X4~X5))))))))\end{array}
\label{hyp:ehddidpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}\\
((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}(r1\_functor3~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}((m2\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~\\
X1)))){\unicdbdjdcd}(r1\_functor2~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~\\
X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}(\\
(v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}((v15\_functor0~X2~X0~\\
X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)))){\unicdbdjdcd}(k9\_functor3~X0~X1~X2=k1\_functor2~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~\\
X0~X1)){\unicdcdcdhd}((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_functor2~X4~X0~X1~X2~X3){\unicdbdjdcd}(m1\_functor2~X4~X0~X1~X2~X3))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}(l2\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}\\
((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor3~\\
X4~X0~X1~X2~X3){\unicdbdjdcd}(m2\_functor2~X4~X0~X1~X2~X3))\end{array}
\label{hyp:egehpfngbdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (l2\_functor0~X2~X0~X1){\unicdbdjdcd}(l1\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfmgcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~\\
X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}(\\
(v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}((v15\_functor0~X2~X0~\\
X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)))){\unicdbdjdcd}(m1\_functor3~(k9\_functor3~X0~X1~\\
X2)~X0~X1~X2~X2)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}\\
((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}(((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1)){\unicdcdcdhd}(m1\_functor3~X4~X0~X1~X2~X3))))){\unicdbdjdcd}\\
(m1\_functor3~(k8\_functor3~X0~X1~X2~X3~X4)~X0~X1~X3~X2)\end{array}
\label{hyp:egehpflgidpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}\\
((l1\_functor0~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k3\_functor0~X0~X1~X2~X3)~(u1\_struct\_0~X1))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1))){\unicdbdjdcd}(m1\_functor2~(k1\_functor2~X0~X1~X2)~X0~\\
X1~X2~X2)\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpgchcd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfggfhogdgehpgchdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~X0)~(k8\_functor3~\\
X0~X1~X2~X2~(k9\_functor3~X0~X1~X2))~(k9\_functor3~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
