\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{t35\_msualg\_9 (TMJ99sRU1pDTZFNRLp8yWEPc5H1eG5Wetyu)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k13\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ r2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k15\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ r1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v3\_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}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
(r2\_msualg\_3~X0~X1~(k13\_msualg\_4~X0~X1~X2)~(k15\_msualg\_4~X0~X1~X2))))\end{array}
\label{hyp:ehddpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v2\_msualg\_4~X3~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_pboole~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))){\unicdbdjdcd}(({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X2))~X5)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X5)){\unicdbdjdcd}((X6=k3\_msualg\_4~\\
X0~X1~X2~X5~X7){\unicdbdjdcd}(k3\_funct\_2~(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~X5)~(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~\\
X5)~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~X4~X5)~X6=k3\_msualg\_4~\\
X0~X1~X3~X5~X7))))){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~X0)~(k3\_msualg\_3~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X2))~\\
(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~(k15\_msualg\_4~X0~X1~X2)~\\
X4)~(k15\_msualg\_4~X0~X1~X3)))))))\end{array}
\label{hyp:ehddedpfngdhfhbgmghgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v4\_msualg\_1~X3~X0){\unicdcdcdhd}(l3\_msualg\_1~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_pboole~\\
X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m2\_pboole~X5~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X3)){\unicdbdjdcd}(((r2\_msualg\_3~X0~X1~X2~X4){\unicdcdcdhd}(r1\_msualg\_3~X0~X1~X3~X5)){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  (m2\_pboole~X6~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X2)~(\\
u3\_msualg\_1~X0~X3)){\unicdbdjdcd}((r8\_pboole~(u1\_struct\_0~X0)~(k3\_msualg\_3~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~\\
X0~X3)~X4~X6)~X5){\unicdbdjdcd}(r1\_msualg\_3~X0~X2~X3~X6)))))))))\end{array}
\label{hyp:ehbdjdpfngdhfhbgmghgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v2\_msualg\_4~X3~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_pboole~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))){\unicdbdjdcd}(({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X2))~X5)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X5)){\unicdbdjdcd}((X6=k3\_msualg\_4~\\
X0~X1~X2~X5~X7){\unicdbdjdcd}(k3\_funct\_2~(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~X5)~(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~\\
X5)~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~X4~X5)~X6=k3\_msualg\_4~\\
X0~X1~X3~X5~X7))))){\unicdbdjdcd}(v2\_msualg\_3~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~(k13\_msualg\_4~X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))))))))\end{array}
\label{hyp:mgddgdpfngdhfhbgmghgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~\\
X0)){\unicdcdcdhd}((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))))){\unicdbdjdcd}\\
((v3\_msualg\_1~(k13\_msualg\_4~X0~X1~X2)~X0){\unicdcdcdhd}(v4\_msualg\_1~(k13\_msualg\_4~\\
X0~X1~X2)~X0))\end{array}
\label{hyp:ggdgddpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~\\
X0)){\unicdcdcdhd}((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))))){\unicdbdjdcd}\\
(m2\_pboole~(k15\_msualg\_4~X0~X1~X2)~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X2)))\end{array}
\label{hyp:egehpflgbdfdpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~\\
X0)){\unicdcdcdhd}((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))))){\unicdbdjdcd}\\
(l3\_msualg\_1~(k13\_msualg\_4~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgbdddpfngdhfhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r2\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r1\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(v2\_msualg\_3~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X2)))))))\end{array}
\label{hyp:egidpfngdhfhbgmghgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfngdhfhbgmghgpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v2\_msualg\_4~X3~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_pboole~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))){\unicdbdjdcd}(({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X2))~X5)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_funct\_1~(u3\_msualg\_1~X0~X1)~X5)){\unicdbdjdcd}((X6=k3\_msualg\_4~\\
X0~X1~X2~X5~X7){\unicdbdjdcd}(k3\_funct\_2~(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~X5)~(k1\_funct\_1~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~\\
X5)~(k1\_msualg\_3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k13\_msualg\_4~\\
X0~X1~X2))~(u3\_msualg\_1~X0~(k13\_msualg\_4~X0~X1~X3))~X4~X5)~X6=k3\_msualg\_4~\\
X0~X1~X3~X5~X7))))){\unicdbdjdcd}(r2\_msualg\_3~X0~(k13\_msualg\_4~X0~X1~X2)~(k13\_msualg\_4~\\
X0~X1~X3)~X4))))))\end{array}$$
\end{theorem}
\end{document}
