\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{t38\_abcmiz\_a (TMRQScktCuSCrmss2uFmXXW737x5skSmY5t)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_abcmiz\_1 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_abcmiz\_1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}((k1\_msualg\_1~X0~(k15\_abcmiz\_1~X0)=k3\_pre\_poly~(u1\_struct\_0~\\
X0)~(k13\_abcmiz\_1~X0)){\unicdcdcdhd}((k2\_msualg\_1~X0~(k15\_abcmiz\_1~X0)=k13\_abcmiz\_1~\\
X0){\unicdcdcdhd}((k1\_msualg\_1~X0~(k16\_abcmiz\_1~X0)=k4\_pre\_poly~(u1\_struct\_0~\\
X0)~(k13\_abcmiz\_1~X0)~(k12\_abcmiz\_1~X0)){\unicdcdcdhd}(k2\_msualg\_1~X0~(k16\_abcmiz\_1~\\
X0)=k12\_abcmiz\_1~X0))))\end{array}
\label{hyp:ehddidpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_abcmiz\_1~X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpfngcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k16\_abcmiz\_1~X0)~(u4\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdgdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k15\_abcmiz\_1~X0)~(u4\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k13\_abcmiz\_1~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdddpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k12\_abcmiz\_1~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_abcmiz\_1}={np\_\_1}}\label{hyp:egfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_abcmiz\_1}={k6\_numbers}}\label{hyp:egedpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdcdcdhd}(k2\_msualg\_1~X0~X2=X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}((m2\_abcmiz\_1~X2~X0~X1){\unicdbdjded}(k2\_msualg\_1~\\
X0~X2=X1)))))\end{array}
\label{hyp:egddcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(k13\_abcmiz\_1~X0=k7\_abcmiz\_1)\end{array}
\label{hyp:egbdedpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}((v4\_abcmiz\_a~\\
X1~X0){\unicdbdjded}(k1\_msualg\_1~X0~X1=k1\_xboole\_0)))\end{array}
\label{hyp:egbdddpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(k12\_abcmiz\_1~X0=k6\_abcmiz\_1)\end{array}
\label{hyp:egbdddpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}((v3\_abcmiz\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdcdcdhd}((k2\_msualg\_1~X0~X1=k6\_abcmiz\_1){\unicdcdcdhd}((k1\_msualg\_1~X0~X1=k1\_xboole\_0){\unicdcdcdhd}\\
((k2\_msualg\_1~X0~X2=k7\_abcmiz\_1){\unicdcdcdhd}(k1\_msualg\_1~X0~X2=k1\_xboole\_0)))))))\end{array}
\label{hyp:egbdcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}(((v1\_instalg1~X0){\unicdcdcdhd}(v1\_abcmiz\_1~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(v1\_instalg1~X0))))\end{array}
\label{hyp:dgdgedpfbgcgdgngjgkhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}((v3\_abcmiz\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m2\_abcmiz\_1~X1~X0~(k12\_abcmiz\_1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m2\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~X0)){\unicdcdcdhd}((v4\_abcmiz\_a~\\
X1~X0){\unicdcdcdhd}(v4\_abcmiz\_a~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
