\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{t101\_chord (TMVV14MUjCJt2Z8b2CdrUFHcT8f3YRy9c8s)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_chord : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_chord : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_chord : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v4\_chord : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m2\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_glib\_002 : {{\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~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v2\_glib\_000~X0){\unicdcdcdhd}\\
(v6\_chord~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k6\_glib\_000~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}\\
((\preoh r1\_chord~X0~X1~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_chord~X3~X0~X1~X2){\unicdcdcdhd}((v4\_chord~\\
X3~X0~X1~X2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_glib\_000~X4~X0~(k6\_subset\_1~(k6\_glib\_000~\\
X0)~X3)~(k21\_glib\_000~X0~(k6\_subset\_1~(k6\_glib\_000~X0)~X3))){\unicdcdcdhd}(\\
{\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k6\_glib\_000~X4)){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k6\_glib\_000~X0)){\unicdbdjdcd}(\preoh (X6 \in k1\_glib\_002~X4~X5){\unicdcdcdhd}(\\
{\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k6\_glib\_000~X0)){\unicdbdjdcd}((X7 \in X3){\unicdbdjdcd}(r1\_chord~\\
X0~X6~X7))))))))))))))\end{array}
\label{hyp:ehbdadadpfdgigpgcheg}
\end{equation}
\begin{theorem}\label{thm:ehbdadbdpfdgigpgcheg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v2\_glib\_000~X0){\unicdcdcdhd}\\
(v6\_chord~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k6\_glib\_000~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}\\
((\preoh r1\_chord~X0~X1~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_chord~X3~X0~X1~X2){\unicdcdcdhd}((v4\_chord~\\
X3~X0~X1~X2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_glib\_000~X4~X0~(k6\_subset\_1~(k6\_glib\_000~\\
X0)~X3)~(k21\_glib\_000~X0~(k6\_subset\_1~(k6\_glib\_000~X0)~X3))){\unicdcdcdhd}(\\
{\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k6\_glib\_000~X4)){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~(k6\_glib\_000~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~\\
(k6\_glib\_000~X0)){\unicdcdcdhd}((X6 \in X3){\unicdcdcdhd}((X7 \in X3){\unicdcdcdhd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(k6\_glib\_000~X0)){\unicdbdjdcd}(\preoh (X8 \in k1\_glib\_002~X4~X5){\unicdcdcdhd}((r1\_chord~X0~X8~\\
X6){\unicdcdcdhd}(r1\_chord~X0~X8~X7)))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
