\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{t66\_sheffer2 (TMH5tNfnNLkmkhQ4boSEGtounedL5K2F1EQ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sheffer2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_sheffer1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_sheffer2~X0){\unicdcdcdhd}(l1\_sheffer1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k5\_sheffer1~X0~(k5\_sheffer1~X0~X1~(k5\_sheffer1~\\
X0~X2~X2))~(k5\_sheffer1~X0~X1~(k5\_sheffer1~X0~X3~X3))=k5\_sheffer1~\\
X0~(k5\_sheffer1~X0~X1~(k5\_sheffer1~X0~X3~X2))~(k5\_sheffer1~X0~X1~(\\
k5\_sheffer1~X0~X3~X2))))))\end{array}
\label{hyp:ehgdfdpfdhigfgggggfgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_sheffer2~X0){\unicdcdcdhd}(l1\_sheffer1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k5\_sheffer1~X0~(k5\_sheffer1~X0~X1~X2)~X3=k5\_sheffer1~\\
X0~X3~(k5\_sheffer1~X0~X2~X1)))))\end{array}
\label{hyp:ehddhdpfdhigfgggggfgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_sheffer1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k5\_sheffer1~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgfdpfdhigfgggggfgchbd}
\end{equation}
\begin{theorem}\label{thm:ehgdgdpfdhigfgggggfgchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_sheffer2~X0){\unicdcdcdhd}(l1\_sheffer1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k5\_sheffer1~X0~(k5\_sheffer1~X0~(k5\_sheffer1~\\
X0~X1~X1)~X2)~(k5\_sheffer1~X0~(k5\_sheffer1~X0~X3~X3)~X2)=k5\_sheffer1~\\
X0~(k5\_sheffer1~X0~X2~(k5\_sheffer1~X0~X1~X3))~(k5\_sheffer1~X0~X2~(\\
k5\_sheffer1~X0~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
