\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{t16\_msualg\_9 (TMZtq2m8BVLfvKXCEok2u5ZjzrRV4K4PiTV)}
\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 $ m2\_pboole : {{\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 $ r3\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r6\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_msualg\_3 : {{\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 $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_msualg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r4\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\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}((\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 .  \\
(m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X2)){\unicdbdjdcd}(\preoh (r1\_msualg\_3~X0~X1~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_pboole~X4~(\\
u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~(k6\_msualg\_3~\\
X0~X1~X2~X3))){\unicdbdjdcd}(\preoh (r8\_pboole~(u1\_struct\_0~X0)~X3~X4){\unicdcdcdhd}(r2\_msualg\_3~\\
X0~X1~(k6\_msualg\_3~X0~X1~X2~X3)~X4)))))))\end{array}
\label{hyp:ehcdbdpfngdhfhbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~\\
X2~X0)))))){\unicdbdjdcd}((r8\_pboole~X0~X1~X2){\unicdbdjded}(X1=X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchidpfahcgpgpgmgfg}
\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}((l3\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~\\
X0))){\unicdbdjdcd}((r6\_msualg\_3~X0~X1~X2){\unicdbdjded}(r5\_msualg\_3~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchgdpfngdhfhbgmghgpfdd}
\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 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l2\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_pboole~X3~X0~X1~X2){\unicdbdjdcd}((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~X0)))))\end{array}
\label{hyp:egehpfngcdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_msualg\_2~\\
X2~X0~X1){\unicdbdjdcd}(l3\_msualg\_1~X2~X0))\end{array}
\label{hyp:egehpfngbdpfngdhfhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\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}(l2\_msualg\_1~X1~X0))\end{array}
\label{hyp:egehpfmgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\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}(((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X2~X0)){\unicdcdcdhd}(m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X2))))){\unicdbdjdcd}((v3\_msualg\_1~(k6\_msualg\_3~X0~X1~X2~X3)~X0){\unicdcdcdhd}((v4\_msualg\_1~\\
(k6\_msualg\_3~X0~X1~X2~X3)~X0){\unicdcdcdhd}(m1\_msualg\_2~(k6\_msualg\_3~X0~X1~X2~\\
X3)~X0~X2)))\end{array}
\label{hyp:egehpflggdpfngdhfhbgmghgpfdd}
\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}((r3\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r1\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(v1\_msualg\_3~X3))))))\end{array}
\label{hyp:egjdpfngdhfhbgmghgpfdd}
\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}
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}((r5\_msualg\_3~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_pboole~X3~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdcdcdhd}(r4\_msualg\_3~X0~X1~\\
X2~X3)))))\end{array}
\label{hyp:egbdbdpfngdhfhbgmghgpfdd}
\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}((r4\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r2\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(r3\_msualg\_3~X0~X1~X2~X3))))))\end{array}
\label{hyp:egbdadpfngdhfhbgmghgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfngdhfhbgmghgpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X2)){\unicdbdjdcd}((r3\_msualg\_3~X0~X1~X2~X3){\unicdbdjdcd}(r6\_msualg\_3~X0~X1~(k6\_msualg\_3~\\
X0~X1~X2~X3))))))\end{array}$$
\end{theorem}
\end{document}
