\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{t53\_scmpds\_2 (TMUm8BREqZUYHVPM9qVca3m3j8fy3sRdta7)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k15\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_ami\_2~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
((k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k15\_scmpds\_2~X3~\\
X4~X1~X2)~X0)~(k4\_struct\_0~k1\_scmpds\_2)=k4\_card\_1~(k5\_memstr\_0~\\
np\_\_2~k1\_scmpds\_2~X0)){\unicdcdcdhd}(((k2\_scmpds\_2~(k1\_funct\_1~X0~X3)~X1{\unicdcdgdad}k2\_scmpds\_2~\\
(k1\_funct\_1~X0~X4)~X2){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
(k15\_scmpds\_2~X3~X4~X1~X2)~X0)~(k2\_scmpds\_2~(k1\_funct\_1~X0~X3)~X1)=\\
k5\_int\_1~(k1\_funct\_1~X0~(k2\_scmpds\_2~(k1\_funct\_1~X0~X3)~X1))~(k1\_funct\_1~\\
X0~(k2\_scmpds\_2~(k1\_funct\_1~X0~X4)~X2)))){\unicdcdcdhd}((k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_2~k1\_scmpds\_2~(k15\_scmpds\_2~X3~X4~X1~X2)~X0)~(k2\_scmpds\_2~(k1\_funct\_1~\\
X0~X4)~X2)=k6\_int\_1~(k1\_funct\_1~X0~(k2\_scmpds\_2~(k1\_funct\_1~X0~\\
X3)~X1))~(k1\_funct\_1~X0~(k2\_scmpds\_2~(k1\_funct\_1~X0~X4)~X2))){\unicdcdcdhd}(\\
{\unicdcdadad} X5 .  ((v1\_ami\_2~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
(\preoh (X5{\unicdcdgdad}k2\_scmpds\_2~(k1\_funct\_1~X0~X3)~X1){\unicdcdcdhd}((X5{\unicdcdgdad}k2\_scmpds\_2~(k1\_funct\_1~\\
X0~X4)~X2){\unicdcdcdhd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k15\_scmpds\_2~\\
X3~X4~X1~X2)~X0)~X5{\unicdcdgdad}k1\_funct\_1~X0~X5)))))))))))\end{array}
\label{hyp:ehfdcdpfdhdgngahegdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdddpfdhdgngahegdhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
k1\_scmpds\_2))){\unicdbdjdcd}((k1\_funct\_1~(k2\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
(k15\_scmpds\_2~X2~X2~X1~X1)~X0)~(k4\_struct\_0~k1\_scmpds\_2)=k4\_card\_1~\\
(k5\_memstr\_0~np\_\_2~k1\_scmpds\_2~X0)){\unicdcdcdhd}((k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_2~k1\_scmpds\_2~(k15\_scmpds\_2~X2~X2~X1~X1)~X0)~(k2\_scmpds\_2~(k1\_funct\_1~\\
X0~X2)~X1)=k6\_int\_1~(k1\_funct\_1~X0~(k2\_scmpds\_2~(k1\_funct\_1~X0~\\
X2)~X1))~(k1\_funct\_1~X0~(k2\_scmpds\_2~(k1\_funct\_1~X0~X2)~X1))){\unicdcdcdhd}(\\
{\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~k1\_scmpds\_2))){\unicdbdjdcd}\\
((X3{\unicdcdgdad}k2\_scmpds\_2~(k1\_funct\_1~X0~X2)~X1){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_2~k1\_scmpds\_2~(k15\_scmpds\_2~X2~X2~X1~X1)~X0)~X3=k1\_funct\_1~X0~\\
X3)))))))\end{array}$$
\end{theorem}
\end{document}
