\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{t15\_pcs\_0 (TMYiR82iZBtyzVsS7m53m7aucKo9t7kPJi5)}
\maketitle
Let $ l2\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_pcs\_0 : {{\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 $ k2\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v12\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_pcs\_0~X1){\unicdbdjdcd}((u1\_struct\_0~\\
(k18\_pcs\_0~X0~X1)=k2\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
((u1\_orders\_2~(k18\_pcs\_0~X0~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)){\unicdcdcdhd}(u1\_pcs\_0~(k18\_pcs\_0~X0~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:ehbdedpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k6\_afinsq\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k6\_afinsq\_1~X0~X1))\end{array}
\label{hyp:ggdgjdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X1)){\unicdbdjdcd}(v16\_pcs\_0~\\
(k6\_afinsq\_1~X0~X1))\end{array}
\label{hyp:ggdgedidpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  v1\_partfun1~(k6\_afinsq\_1~X0~X1)~(k2\_tarski~\\
k6\_numbers~np\_\_1)\end{array}
\label{hyp:ggdgededpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  v4\_relat\_1~(k6\_afinsq\_1~X0~X1)~(k2\_tarski~\\
k6\_numbers~np\_\_1)\end{array}
\label{hyp:ggdgedddpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X1)){\unicdbdjdcd}(l2\_pcs\_0~\\
(k18\_pcs\_0~X0~X1))\end{array}
\label{hyp:egehpflgbdidpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v16\_pcs\_0~X1))))){\unicdbdjdcd}((v12\_pcs\_0~\\
(k17\_pcs\_0~X0~X1)){\unicdcdcdhd}(l2\_pcs\_0~(k17\_pcs\_0~X0~X1)))\end{array}
\label{hyp:egehpflgbdhdpfahdgdhpfad}
\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=k17\_pcs\_0~(k2\_tarski~k6\_numbers~np\_\_1)~(k6\_afinsq\_1~X0~X1)))\end{array}
\label{hyp:egddidpfahdgdhpfad}
\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:ehbdfdpfahdgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_pcs\_0~X1){\unicdbdjdcd}(k18\_pcs\_0~\\
X0~X1=g2\_pcs\_0~(k2\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
(k2\_pcs\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(\\
u1\_struct\_0~X1)~(u1\_orders\_2~X0)~(u1\_orders\_2~X1))~(k2\_pcs\_0~(\\
u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1)~(u1\_pcs\_0~X0)~(u1\_pcs\_0~X1))))\end{array}$$
\end{theorem}
\end{document}
