\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{t18\_pcs\_0 (TMFn6ZDg3thaGfPfMpLKK4Q7pE6cuBNZSA2)}
\maketitle
Let $ v14\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ g2\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v8\_relat\_2~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_relat\_2~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)))){\unicdbdjdcd}((r1\_xboole\_0~\\
X0~X1){\unicdbdjdcd}(v8\_relat\_2~(k2\_pcs\_0~X0~X0~X1~X1~X2~X3))))\end{array}
\label{hyp:ehbdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_pcs\_0~X1){\unicdbdjdcd}(k18\_pcs\_0~\\
X0~X1=g2\_pcs\_0~(k2\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
(k2\_pcs\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(\\
u1\_struct\_0~X1)~(u1\_orders\_2~X0)~(u1\_orders\_2~X1))~(k2\_pcs\_0~(\\
u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1)~(u1\_pcs\_0~X0)~(u1\_pcs\_0~X1))))\end{array}
\label{hyp:ehbdfdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))){\unicdbdjdcd}(k2\_pcs\_0~X0~X1~X2~X3~X4~X5=\\
k2\_xboole\_0~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g2\_pcs\_0~X0~X1~X2=\\
g2\_pcs\_0~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgcdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}(v8\_relat\_2~(u1\_orders\_2~X0))\end{array}
\label{hyp:ggdgfdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pcs\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_pcs\_0~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_orders\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_pcs\_0}~{X0}})}{\unicdbdjdcd}{({{({{l1\_orders\_2}~{X0}})}{\unicdcdcdhd}{({{l1\_pcs\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pcs\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_pcs\_0~\\
X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_xboole\_0~X0~X2)~(\\
k2\_xboole\_0~X1~X3))))\end{array}
\label{hyp:egehpflgcdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))){\unicdbdjdcd}((v12\_pcs\_0~(g2\_pcs\_0~X0~X1~X2)){\unicdcdcdhd}(l2\_pcs\_0~(g2\_pcs\_0~\\
X0~X1~X2)))\end{array}
\label{hyp:egehpfhgcdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_struct\_0~X1){\unicdbdjdcd}((\\
r1\_tsep\_1~X0~X1){\unicdbdjded}(r1\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))\end{array}
\label{hyp:egddpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}((v14\_pcs\_0~X0){\unicdbdjdcd}((v3\_orders\_2~X0){\unicdcdcdhd}\\
((v4\_orders\_2~X0){\unicdcdcdhd}((v4\_pcs\_0~X0){\unicdcdcdhd}((v6\_pcs\_0~X0){\unicdcdcdhd}(v13\_pcs\_0~\\
X0))))))\end{array}
\label{hyp:dgdghdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v3\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{v2\_orders\_2}~{X0}})}})}}}\label{hyp:dgdgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}((v12\_pcs\_0~X0){\unicdbdjdcd}(X0=g2\_pcs\_0~(u1\_struct\_0~\\
X0)~(u1\_orders\_2~X0)~(u1\_pcs\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdcdpfahdgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfahdgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v14\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v14\_pcs\_0~\\
X1){\unicdcdcdhd}(l2\_pcs\_0~X1)){\unicdbdjdcd}((r1\_tsep\_1~X0~X1){\unicdbdjdcd}(v8\_relat\_2~(u1\_orders\_2~\\
(k18\_pcs\_0~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
