\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{t109\_sheffer2 (TMdYjC5i9RA12AeR3nr7fNtkyrhmLpTXqKm)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_sheffer1 : {{\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}((v10\_sheffer1~X0){\unicdcdcdhd}((v11\_sheffer1~\\
X0){\unicdcdcdhd}((v12\_sheffer1~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}(k5\_sheffer1~X0~X2~X1=k5\_sheffer1~X0~X1~X2)))\end{array}
\label{hyp:ehidddpfdhigfgggggfgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_sheffer1~X0){\unicdcdcdhd}((v11\_sheffer1~\\
X0){\unicdcdcdhd}((v12\_sheffer1~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}(k5\_sheffer1~X0~(k5\_sheffer1~X0~X2~(k5\_sheffer1~X0~X1~X1))~\\
(k5\_sheffer1~X0~X1~X2)=X2)))\end{array}
\label{hyp:ehbdadgdpfdhigfgggggfgchcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadjdpfdhigfgggggfgchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_sheffer1~X0){\unicdcdcdhd}((v11\_sheffer1~\\
X0){\unicdcdcdhd}((v12\_sheffer1~X0){\unicdcdcdhd}(l1\_sheffer1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k5\_sheffer1~X0~(k5\_sheffer1~X0~X2~(k5\_sheffer1~X0~X1~X1))~\\
(k5\_sheffer1~X0~X2~X1)=X2)))\end{array}$$
\end{theorem}
\end{document}
