\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{t26\_cat\_4 (TMNsJLJbBUNS6hbesKcaerEwUh5xbPFPvxx)}
\maketitle
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 $ v3\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_4 : {{\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 $ m1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k7\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\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}((v3\_cat\_4~\\
X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((m1\_cat\_1~X4~X0~X3~X1){\unicdcdcdhd}(m1\_cat\_1~X5~X0~X3~X2)))))){\unicdbdjdcd}(m1\_cat\_1~\\
(k9\_cat\_4~X0~X1~X2~X3~X4~X5)~X0~X3~(k2\_cat\_4~X0~X1~X2))\end{array}
\label{hyp:egehpflgjdpfdgbgehpfed}
\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}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_cat\_1~X4~X0~X3~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~X3~X2){\unicdbdjdcd}(\preoh (k2\_cat\_1~\\
X0~X3~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~X0~X3~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(\preoh {\unicdcdadad} X6 .  \\
(m1\_cat\_1~X6~X0~X3~(k2\_cat\_4~X0~X1~X2)){\unicdbdjdcd}((X6=k9\_cat\_4~X0~X1~X2~X3~X4~\\
X5){\unicdbdjded}((k5\_cat\_1~X0~X3~(k2\_cat\_4~X0~X1~X2)~X1~X6~(k7\_cat\_4~X0~X1~X2)=\\
X4){\unicdcdcdhd}(k5\_cat\_1~X0~X3~(k2\_cat\_4~X0~X1~X2)~X2~X6~(k8\_cat\_4~X0~X1~X2)=X5)))))))))))\end{array}
\label{hyp:egbdadpfdgbgehpfed}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfdgbgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_cat\_1~X4~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_cat\_1~X6~X0~X1~X3){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_cat\_1~X7~X0~X1~X3){\unicdbdjdcd}((k9\_cat\_4~\\
X0~X2~X3~X1~X4~X6=k9\_cat\_4~X0~X2~X3~X1~X5~X7){\unicdbdjdcd}((k2\_cat\_1~X0~X1~X2=k1\_xboole\_0){\unicdcdcdid}\\
((k2\_cat\_1~X0~X1~X3=k1\_xboole\_0){\unicdcdcdid}((X4=X5){\unicdcdcdhd}(X6=X7))))))))))))\end{array}$$
\end{theorem}
\end{document}
