\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=}
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\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t3\_algstr\_3 (TMPqzu6GCCyMWfvnvdM6VixTHSokQoeMXyH)}
\maketitle
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_algstr\_3 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_algstr\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_algstr\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_algstr\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_algstr\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_algstr\_3 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X1~\\
X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k3\_zfmisc\_1~\\
X0~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_zfmisc\_1~\\
X0~X0~X0)~X0))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  \\
(g1\_algstr\_3~X0~X1~X2~X3=g1\_algstr\_3~X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=\\
X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(u2\_struct\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpffhcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_3~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_algstr\_3~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_algstr\_3~X0)~(k3\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(u1\_algstr\_3~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_3}~{X0}})}{\unicdbdjdcd}{({{l4\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k5\_struct\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_algstr\_3}~{k3\_algstr\_3}})}{\unicdcdcdhd}{({{l1\_algstr\_3}~{k3\_algstr\_3}})}}\label{hyp:egehpflgddpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k5\_struct\_0}~{X0}}={{u3\_struct\_0}~{X0}}})}}}\label{hyp:eghdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_algstr\_3}={{{{{g1\_algstr\_3}~{k1\_numbers}}~{k6\_numbers}}~{np\_\_1}}~{k2\_algstr\_3}}}\label{hyp:egddpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_3~X0){\unicdbdjdcd}((v1\_algstr\_3~X0){\unicdbdjdcd}(X0=g1\_algstr\_3~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u3\_struct\_0~X0)~(u1\_algstr\_3~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfbgmghgdhehchpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddpfbgmghgdhehchpfdd}
${{np\_\_1}={{k5\_struct\_0}~{k3\_algstr\_3}}}$.
\end{theorem}
\end{document}
