\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{t8\_sheffer1 (TMTMSGyewnL2wTP9CANndKXyTPXWzS4Vn7f)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_sheffer1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\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 $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_sheffer1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_lattices}~{X0}})}{\unicdbdjdcd}{({{({{l1\_lattices}~{X0}})}{\unicdcdcdhd}{({{l2\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lattices~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_lattices~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgcdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lattices~X0)){\unicdbdjdcd}((v5\_sheffer1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_lattices~\\
X0~X1~X1=X1)))\end{array}
\label{hyp:egjdpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((v3\_sheffer1~\\
X0){\unicdbdjded}({\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}(k1\_lattices~X0~X1~(k2\_lattices~X0~X2~X3)=k2\_lattices~\\
X0~(k1\_lattices~X0~X1~X2)~(k1\_lattices~X0~X1~X3))))))\end{array}
\label{hyp:egfdpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((v2\_sheffer1~\\
X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1=k2\_sheffer1~\\
X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_lattices~\\
X0~X1~X2=X2){\unicdcdcdhd}(k1\_lattices~X0~X2~X1=X2))))))\end{array}
\label{hyp:egedpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_lattices~X0)){\unicdbdjdcd}((v4\_lattices~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_lattices~X0~X1~X2=k1\_lattices~\\
X0~X2~X1))))\end{array}
\label{hyp:egedpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((v2\_sheffer1~\\
X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_lattices~X0~X1~X2=X2){\unicdcdcdhd}\\
(k1\_lattices~X0~X2~X1=X2)))))\end{array}
\label{hyp:egddpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((v1\_sheffer1~\\
X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k2\_lattices~X0~X1~X2=X2){\unicdcdcdhd}\\
(k2\_lattices~X0~X2~X1=X2)))))\end{array}
\label{hyp:egbdpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((v11\_lattices~\\
X0){\unicdbdjded}({\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}(k2\_lattices~X0~X1~(k1\_lattices~X0~X2~X3)=k1\_lattices~\\
X0~(k2\_lattices~X0~X1~X2)~(k2\_lattices~X0~X1~X3))))))\end{array}
\label{hyp:egbdbdpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehidpfdhigfgggggfgchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}((v11\_lattices~X0){\unicdcdcdhd}((v1\_sheffer1~X0){\unicdcdcdhd}((v2\_sheffer1~X0){\unicdcdcdhd}\\
((v3\_sheffer1~X0){\unicdcdcdhd}((v4\_sheffer1~X0){\unicdcdcdhd}(l3\_lattices~X0))))))))){\unicdbdjdcd}\\
(v5\_sheffer1~X0)\end{array}$$
\end{theorem}
\end{document}
