\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{t36\_msualg\_6 (TMJaNJq9EFMAqBLvsNxrgeKv3f2K9tuSDJf)}
\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 $ 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 $ r2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
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}(m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)))){\unicdbdjdcd}((v3\_msualg\_6~(k8\_msualg\_6~X0~X1~X2)~X0~X1){\unicdcdcdhd}((v4\_msualg\_6~\\
(k8\_msualg\_6~X0~X1~X2)~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~(k8\_msualg\_6~X0~X1~X2)~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1))))\end{array}
\label{hyp:egehpflgidpfngdhfhbgmghgpfgd}
\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}(m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)))){\unicdbdjdcd}((v4\_msualg\_6~(k7\_msualg\_6~X0~X1~X2)~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
(k7\_msualg\_6~X0~X1~X2)~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflghdpfngdhfhbgmghgpfgd}
\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}(m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)))){\unicdbdjdcd}((v3\_msualg\_6~(k6\_msualg\_6~X0~X1~X2)~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
(k6\_msualg\_6~X0~X1~X2)~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflggdpfngdhfhbgmghgpfgd}
\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 .  (m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_msualg\_6~X3~X0~X1){\unicdcdcdhd}((v4\_msualg\_6~\\
X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(\\
u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}((X3=k8\_msualg\_6~X0~X1~X2){\unicdbdjded}((r2\_pboole~\\
(u1\_struct\_0~X0)~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v3\_msualg\_6~X4~X0~X1){\unicdcdcdhd}((\\
v4\_msualg\_6~X4~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~X4~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}((r2\_pboole~(u1\_struct\_0~X0)~X2~X4){\unicdbdjdcd}\\
(r2\_pboole~(u1\_struct\_0~X0)~X3~X4))))))))\end{array}
\label{hyp:egbdddpfngdhfhbgmghgpfgd}
\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 .  (m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msualg\_6~X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}(\\
(X3=k7\_msualg\_6~X0~X1~X2){\unicdbdjded}((r2\_pboole~(u1\_struct\_0~X0)~X2~X3){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  ((v4\_msualg\_6~X4~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~X4~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}((r2\_pboole~(u1\_struct\_0~\\
X0)~X2~X4){\unicdbdjdcd}(r2\_pboole~(u1\_struct\_0~X0)~X3~X4))))))))\end{array}
\label{hyp:egbdcdpfngdhfhbgmghgpfgd}
\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 .  (m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_msualg\_6~X3~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~\\
X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}(\\
(X3=k6\_msualg\_6~X0~X1~X2){\unicdbdjded}((r2\_pboole~(u1\_struct\_0~X0)~X2~X3){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  ((v3\_msualg\_6~X4~X0~X1){\unicdcdcdhd}(m1\_msualg\_4~X4~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}((r2\_pboole~(u1\_struct\_0~\\
X0)~X2~X4){\unicdbdjdcd}(r2\_pboole~(u1\_struct\_0~X0)~X3~X4))))))))\end{array}
\label{hyp:egbdbdpfngdhfhbgmghgpfgd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfngdhfhbgmghgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_msualg\_4~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}((r2\_pboole~(u1\_struct\_0~X0)~(k7\_msualg\_6~\\
X0~X1~X2)~(k8\_msualg\_6~X0~X1~X2)){\unicdcdcdhd}((r2\_pboole~(u1\_struct\_0~X0)~(\\
k6\_msualg\_6~X0~X1~X2)~(k8\_msualg\_6~X0~X1~X2)){\unicdcdcdhd}(r2\_pboole~(u1\_struct\_0~\\
X0)~(k7\_msualg\_6~X0~X1~(k6\_msualg\_6~X0~X1~X2))~(k8\_msualg\_6~X0~X1~\\
X2))))))\end{array}$$
\end{theorem}
\end{document}
