\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{t1\_msinst\_1 (TMJaPXnsZnSNxK8MGgXJWsnQK4f7FKnTZcn)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k1\_msinst\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_msalimit : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_msalimit : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_msalimit : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_msalimit : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v2\_msalimit~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_msalimit~X1~X0){\unicdbdjded}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngddpfngdhbgmgjgngjgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k5\_msalimit~X0)){\unicdcdcdhd}\\
(v2\_msalimit~(k5\_msalimit~X0)))\end{array}
\label{hyp:ggdgfdpfngdhbgmgjgngjgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k1\_msinst\_1~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k1\_msinst\_1~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k1\_msinst\_1~\\
X0)){\unicdcdcdhd}((v11\_altcat\_1~(k1\_msinst\_1~X0)){\unicdcdcdhd}(v12\_altcat\_1~(k1\_msinst\_1~\\
X0))))))\end{array}
\label{hyp:ggdgbdpfngdhjgogdhehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v2\_msalimit~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_msalimit~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}\\
((v1\_msualg\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))))\end{array}
\label{hyp:egehpfngddpfngdhbgmgjgngjgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v6\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))){\unicdbdjdcd}((X1=k1\_msinst\_1~X0){\unicdbdjded}\\
((u1\_struct\_0~X1=k5\_msalimit~X0){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m3\_msalimit~\\
X2~(k5\_msalimit~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m3\_msalimit~X3~(k5\_msalimit~\\
X0)){\unicdbdjdcd}(k1\_binop\_1~(u1\_altcat\_1~X1)~X2~X3=k6\_msalimit~X2~X3))){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(((X2 \in k5\_msalimit~X0){\unicdcdcdhd}((X3 \in k5\_msalimit~X0){\unicdcdcdhd}(X4 \in k5\_msalimit~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(v1\_funct\_1~X5)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_relat\_1~\\
X7){\unicdcdcdhd}(v1\_funct\_1~X7)){\unicdbdjdcd}({\unicdcdadad} X8 .  ((v1\_relat\_1~X8){\unicdcdcdhd}(v1\_funct\_1~\\
X8)){\unicdbdjdcd}(((k4\_tarski~X5~X6 \in k1\_binop\_1~(u1\_altcat\_1~X1)~X2~X3){\unicdcdcdhd}(k4\_tarski~\\
X7~X8 \in k1\_binop\_1~(u1\_altcat\_1~X1)~X3~X4)){\unicdbdjdcd}(k1\_binop\_1~(k4\_altcat\_1~\\
(u1\_struct\_0~X1)~(u1\_altcat\_1~X1)~(u2\_altcat\_1~X1)~X2~X3~X4)~(k4\_tarski~\\
X7~X8)~(k4\_tarski~X5~X6)=k4\_tarski~(k3\_relat\_1~X5~X7)~(k3\_relat\_1~\\
X6~X8)))))))))))))))\end{array}
\label{hyp:egbdpfngdhjgogdhehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfngdhjgogdhehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))))){\unicdbdjdcd}((X1=k1\_msinst\_1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}(l1\_msualg\_1~X2))))))\end{array}$$
\end{theorem}
\end{document}
