\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{t29\_ens\_1 (TMcYsVrjBE1e1deHGwdUriBoC6pWMqUkabJ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_ens\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_ens\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~(k11\_ens\_1~\\
X0))){\unicdbdjdcd}((k3\_graph\_1~(k11\_ens\_1~X0)~X1=k4\_graph\_1~(k11\_ens\_1~X0)~\\
X2){\unicdbdjdcd}(k1\_cat\_1~(k11\_ens\_1~X0)~X2~X1=k6\_ens\_1~X0~(k15\_ens\_1~X0~X2)~\\
(k15\_ens\_1~X0~X1)))))\end{array}
\label{hyp:ehcdidpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}((k3\_graph\_1~(k11\_ens\_1~X0)~X1=k3\_ens\_1~X0~(\\
k15\_ens\_1~X0~X1)){\unicdcdcdhd}(k4\_graph\_1~(k11\_ens\_1~X0)~X1=k4\_ens\_1~X0~(k15\_ens\_1~\\
X0~X1))))\end{array}
\label{hyp:ehcdgdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}(m1\_subset\_1~X1~(k2\_ens\_1~X0)))\end{array}
\label{hyp:ehcdfdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~X1~(u4\_struct\_0~(k11\_ens\_1~X0))))\end{array}
\label{hyp:ehcdedpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:ehcdddpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}((k3\_graph\_1~\\
X0~X2=X1){\unicdbdjdcd}(k1\_cat\_1~X0~(k4\_cat\_1~X0~X1)~X2=X2))))\end{array}
\label{hyp:ehcdcdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}((k6\_ens\_1~X0~(k5\_ens\_1~X0~(k3\_ens\_1~X0~X1))~X1=X1){\unicdcdcdhd}(k6\_ens\_1~\\
X0~X1~(k5\_ens\_1~X0~(k4\_ens\_1~X0~X1))=X1)))\end{array}
\label{hyp:ehbdedpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
((k2\_xtuple\_0~(k5\_ens\_1~X0~X1)=k6\_partfun1~X1){\unicdcdcdhd}((k3\_ens\_1~X0~\\
(k5\_ens\_1~X0~X1)=X1){\unicdcdcdhd}(k4\_ens\_1~X0~(k5\_ens\_1~X0~X1)=X1))))\end{array}
\label{hyp:ehbdbdpffgogdhpfbd}
\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}\\
((v2\_cat\_1~X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}\\
((v6\_cat\_1~X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(k4\_graph\_1~X0~(k4\_cat\_1~X0~X1)=X1)\end{array}
\label{hyp:chegedpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k11\_ens\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k11\_ens\_1~X0)){\unicdcdcdhd}((v1\_cat\_1~(k11\_ens\_1~X0)){\unicdcdcdhd}\\
((v2\_cat\_1~(k11\_ens\_1~X0)){\unicdcdcdhd}((v3\_cat\_1~(k11\_ens\_1~X0)){\unicdcdcdhd}((v4\_cat\_1~\\
(k11\_ens\_1~X0)){\unicdcdcdhd}((v5\_cat\_1~(k11\_ens\_1~X0)){\unicdcdcdhd}(v6\_cat\_1~(k11\_ens\_1~\\
X0)))))))))\end{array}
\label{hyp:ggdgedpffgogdhpfbd}
\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\_cat\_1~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_cat\_1~X3~X0~X1~X2){\unicdbdjdcd}(m1\_subset\_1~\\
X3~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpfngbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k5\_ens\_1~X0~X1)~(k2\_ens\_1~X0))\end{array}
\label{hyp:egehpflgfdpffgogdhpfbd}
\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}\\
((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~X0){\unicdcdcdhd}(l1\_cat\_1~X0))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_cat\_1~(k4\_cat\_1~X0~X1)~X0~X1~X1)\end{array}
\label{hyp:egehpflgedpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k11\_ens\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k11\_ens\_1~X0)){\unicdcdcdhd}((v1\_cat\_1~(k11\_ens\_1~X0)){\unicdcdcdhd}\\
(l1\_cat\_1~(k11\_ens\_1~X0)))))\end{array}
\label{hyp:egehpflgbdbdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}(k15\_ens\_1~X0~X1=X1))\end{array}
\label{hyp:egbdhdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}(k13\_ens\_1~X0~X1=X1))\end{array}
\label{hyp:egbdfdpffgogdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpffgogdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k11\_ens\_1~X0))){\unicdbdjdcd}(k4\_cat\_1~(k11\_ens\_1~X0)~X1=k5\_ens\_1~X0~(k13\_ens\_1~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
