\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{t12\_yellow11 (TMTRxgpipm7hEh7myxCLmmsVQyH9PKDGNc7)}
\maketitle
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_yellow11 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_yellow11 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
((\preoh ({\unicdcdaddd} X1 .  ((v4\_yellow\_0~X1~X0){\unicdcdcdhd}((v5\_yellow\_0~X1~X0){\unicdcdcdhd}((v6\_yellow\_0~\\
X1~X0){\unicdcdcdhd}(m1\_yellow\_0~X1~X0)))){\unicdcdcdhd}(r5\_waybel\_1~k2\_yellow11~X1)){\unicdcdcdhd}\\
({\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\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X3){\unicdcdcdhd}((X1{\unicdcdgdad}\\
X4){\unicdcdcdhd}((X1{\unicdcdgdad}X5){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}((X2{\unicdcdgdad}X4){\unicdcdcdhd}((X2{\unicdcdgdad}X5){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}((X3{\unicdcdgdad}X5){\unicdcdcdhd}\\
((X4{\unicdcdgdad}X5){\unicdcdcdhd}((k12\_lattice3~X0~X1~X2=X1){\unicdcdcdhd}((k12\_lattice3~X0~X1~X3=\\
X1){\unicdcdcdhd}((k12\_lattice3~X0~X1~X4=X1){\unicdcdcdhd}((k12\_lattice3~X0~X2~X5=X2){\unicdcdcdhd}(\\
(k12\_lattice3~X0~X3~X5=X3){\unicdcdcdhd}((k12\_lattice3~X0~X4~X5=X4){\unicdcdcdhd}((k12\_lattice3~\\
X0~X2~X3=X1){\unicdcdcdhd}((k12\_lattice3~X0~X2~X4=X1){\unicdcdcdhd}((k12\_lattice3~X0~X3~X4=\\
X1){\unicdcdcdhd}((k13\_lattice3~X0~X2~X3=X5){\unicdcdcdhd}((k13\_lattice3~X0~X2~X4=X5){\unicdcdcdhd}(\\
k13\_lattice3~X0~X3~X4=X5)))))))))))))))))))))))))))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X3){\unicdcdcdhd}((X1{\unicdcdgdad}X4){\unicdcdcdhd}((X1{\unicdcdgdad}X5){\unicdcdcdhd}\\
((X2{\unicdcdgdad}X3){\unicdcdcdhd}((X2{\unicdcdgdad}X4){\unicdcdcdhd}((X2{\unicdcdgdad}X5){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}((X3{\unicdcdgdad}X5){\unicdcdcdhd}((X4{\unicdcdgdad}X5){\unicdcdcdhd}(\\
(k12\_lattice3~X0~X1~X2=X1){\unicdcdcdhd}((k12\_lattice3~X0~X1~X3=X1){\unicdcdcdhd}((k12\_lattice3~\\
X0~X1~X4=X1){\unicdcdcdhd}((k12\_lattice3~X0~X2~X5=X2){\unicdcdcdhd}((k12\_lattice3~X0~X3~X5=\\
X3){\unicdcdcdhd}((k12\_lattice3~X0~X4~X5=X4){\unicdcdcdhd}((k12\_lattice3~X0~X2~X3=X1){\unicdcdcdhd}(\\
(k12\_lattice3~X0~X2~X4=X1){\unicdcdcdhd}((k12\_lattice3~X0~X3~X4=X1){\unicdcdcdhd}((k13\_lattice3~\\
X0~X2~X3=X5){\unicdcdcdhd}((k13\_lattice3~X0~X2~X4=X5){\unicdcdcdhd}(k13\_lattice3~X0~X3~X4=\\
X5))))))))))))))))))))))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v4\_yellow\_0~X1~\\
X0){\unicdcdcdhd}((v5\_yellow\_0~X1~X0){\unicdcdcdhd}((v6\_yellow\_0~X1~X0){\unicdcdcdhd}(m1\_yellow\_0~X1~\\
X0)))){\unicdbdjdcd}(\preoh r5\_waybel\_1~k2\_yellow11~X1))))\end{array}
\label{hyp:ehbdadpfjhfgmgmgpghhbdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
((v1\_yellow11~X0){\unicdbdjdcd}((v2\_waybel\_1~X0){\unicdbdjded}({\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\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X3){\unicdcdcdhd}((X1{\unicdcdgdad}X4){\unicdcdcdhd}((X1{\unicdcdgdad}X5){\unicdcdcdhd}(\\
(X2{\unicdcdgdad}X3){\unicdcdcdhd}((X2{\unicdcdgdad}X4){\unicdcdcdhd}((X2{\unicdcdgdad}X5){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}((X3{\unicdcdgdad}X5){\unicdcdcdhd}((X4{\unicdcdgdad}X5){\unicdcdcdhd}((\\
k12\_lattice3~X0~X1~X2=X1){\unicdcdcdhd}((k12\_lattice3~X0~X1~X3=X1){\unicdcdcdhd}((k12\_lattice3~\\
X0~X1~X4=X1){\unicdcdcdhd}((k12\_lattice3~X0~X2~X5=X2){\unicdcdcdhd}((k12\_lattice3~X0~X3~X5=\\
X3){\unicdcdcdhd}((k12\_lattice3~X0~X4~X5=X4){\unicdcdcdhd}((k12\_lattice3~X0~X2~X3=X1){\unicdcdcdhd}(\\
(k12\_lattice3~X0~X2~X4=X1){\unicdcdcdhd}((k12\_lattice3~X0~X3~X4=X1){\unicdcdcdhd}((k13\_lattice3~\\
X0~X2~X3=X5){\unicdcdcdhd}((k13\_lattice3~X0~X2~X4=X5){\unicdcdcdhd}(k13\_lattice3~X0~X3~X4=\\
X5)))))))))))))))))))))))))))))\end{array}
\label{hyp:mgbdhdpfjhfgmgmgpghhbdbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfjhfgmgmgpghhbdbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
((v1\_yellow11~X0){\unicdbdjdcd}((v2\_waybel\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v4\_yellow\_0~\\
X1~X0){\unicdcdcdhd}((v5\_yellow\_0~X1~X0){\unicdcdcdhd}((v6\_yellow\_0~X1~X0){\unicdcdcdhd}(m1\_yellow\_0~\\
X1~X0)))){\unicdbdjdcd}(\preoh r5\_waybel\_1~k2\_yellow11~X1))))\end{array}$$
\end{theorem}
\end{document}
