\documentclass{article}
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\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{t9\_freealg (TMZNPQEULxG4PmqjbdEDDeyhEouq9Lj3iCi)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_freealg : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_unialg\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_freealg : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v2\_unialg\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v2\_relat\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~\\
X0~k5\_numbers))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_freealg~X1){\unicdbdjdcd}(v2\_unialg\_2~(\\
k15\_freealg~X0~X1)))\end{array}
\label{hyp:ehidpfggchfgfgbgmghg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v2\_unialg\_2~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)))))){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k6\_unialg\_2~X0))\end{array}
\label{hyp:ggdgbdpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v2\_relat\_1~X0){\unicdcdcdhd}\\
(m1\_finseq\_1~X0~k5\_numbers))){\unicdcdcdhd}(v1\_freealg~X1)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k15\_freealg~X0~X1)){\unicdcdcdhd}((v1\_unialg\_1~(k15\_freealg~X0~X1)){\unicdcdcdhd}((v2\_unialg\_1~\\
(k15\_freealg~X0~X1)){\unicdcdcdhd}((v3\_unialg\_1~(k15\_freealg~X0~X1)){\unicdcdcdhd}((v4\_unialg\_1~\\
(k15\_freealg~X0~X1)){\unicdcdcdhd}(l1\_unialg\_1~(k15\_freealg~X0~X1)))))))\end{array}
\label{hyp:egehpflgbdfdpfggchfgfgbgmghg}
\end{equation}
\begin{theorem}\label{thm:ehjdpfggchfgfgbgmghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v2\_relat\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~\\
X0~k5\_numbers))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_freealg~X1){\unicdbdjdcd}(k6\_unialg\_2~(\\
k15\_freealg~X0~X1){\unicdcdgdad}k1\_xboole\_0))\end{array}$$
\end{theorem}
\end{document}
