\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{t22\_sheffer1 (TMHW2Net1T6UDwnjP5JzQWtQk3r6isdFQ1P)}
\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 $ v7\_robbins1 : {{\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_sheffer1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sheffer1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_sheffer1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_lattices : {{\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}((v4\_lattices~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}((v11\_lattices~X0){\unicdcdcdhd}((v7\_robbins1~X0){\unicdcdcdhd}((v1\_sheffer1~X0){\unicdcdcdhd}\\
((v2\_sheffer1~X0){\unicdcdcdhd}((v3\_sheffer1~X0){\unicdcdcdhd}((v4\_sheffer1~X0){\unicdcdcdhd}(l3\_lattices~\\
X0)))))))))){\unicdbdjdcd}(k5\_lattices~X0=k2\_sheffer1~X0)\end{array}
\label{hyp:ehbdjdpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}((v11\_lattices~X0){\unicdcdcdhd}((v7\_robbins1~X0){\unicdcdcdhd}((v1\_sheffer1~X0){\unicdcdcdhd}\\
((v2\_sheffer1~X0){\unicdcdcdhd}((v3\_sheffer1~X0){\unicdcdcdhd}((v4\_sheffer1~X0){\unicdcdcdhd}(l3\_lattices~\\
X0)))))))))){\unicdbdjdcd}(k6\_lattices~X0=k1\_sheffer1~X0)\end{array}
\label{hyp:ehbdidpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_sheffer1~X0~X1~X2){\unicdbdjded}((k1\_lattices~X0~X2~\\
X1=k1\_sheffer1~X0){\unicdcdcdhd}((k1\_lattices~X0~X1~X2=k1\_sheffer1~X0){\unicdcdcdhd}((\\
k2\_lattices~X0~X2~X1=k2\_sheffer1~X0){\unicdcdcdhd}(k2\_lattices~X0~X1~X2=k2\_sheffer1~\\
X0)))))))\end{array}
\label{hyp:eggdpfdhigfgggggfgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_lattices~X0~X1~X2){\unicdbdjded}((k1\_lattices~X0~X1~\\
X2=k6\_lattices~X0){\unicdcdcdhd}((k1\_lattices~X0~X2~X1=k6\_lattices~X0){\unicdcdcdhd}((\\
k2\_lattices~X0~X1~X2=k5\_lattices~X0){\unicdcdcdhd}(k2\_lattices~X0~X2~X1=k5\_lattices~\\
X0)))))))\end{array}
\label{hyp:egbdidpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfdhigfgggggfgchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}((v11\_lattices~X0){\unicdcdcdhd}((v7\_robbins1~X0){\unicdcdcdhd}((v1\_sheffer1~X0){\unicdcdcdhd}\\
((v2\_sheffer1~X0){\unicdcdcdhd}((v3\_sheffer1~X0){\unicdcdcdhd}((v4\_sheffer1~X0){\unicdcdcdhd}(l3\_lattices~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_sheffer1~\\
X0~X1~X2){\unicdbdjded}(r2\_lattices~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
