\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{t80\_gfacirc1 (TMGKwe7JBYsPiHoFtY8W9ctJsjtS6aFsYoC)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_gfacirc1 : {\iota}$ be given.
Let $ k4\_twoscomp : {\iota}$ be given.
Let $ k33\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_msafree2~(k31\_gfacirc1~X0~\\
X1~X2)=k2\_xboole\_0~(k1\_enumset1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~\\
k3\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X1~X2)~k3\_gfacirc1)~(k4\_tarski~\\
(k10\_finseq\_1~X2~X0)~k4\_twoscomp))~(k1\_tarski~(k33\_gfacirc1~X0~\\
X1~X2))\end{array}
\label{hyp:ehhdedpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_xboole\_0~(k1\_enumset1~X0~X1~X2)~(k1\_tarski~X3)\end{array}
\label{hyp:ehgdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (X4=k2\_enumset1~\\
X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (X5 \in X4){\unicdbdjded}(\preoh (X5{\unicdcdgdad}X0){\unicdcdcdhd}((X5{\unicdcdgdad}X1){\unicdcdcdhd}((X5{\unicdcdgdad}X2){\unicdcdcdhd}\\
(X5{\unicdcdgdad}X3)))))\end{array}
\label{hyp:egcdpffgogfhngdhfgehbd}
\end{equation}
\begin{theorem}\label{thm:ehidadpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k4\_tarski~(k10\_finseq\_1~X0~\\
X1)~k3\_twoscomp \in k3\_msafree2~(k31\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~\\
(k10\_finseq\_1~X1~X2)~k3\_gfacirc1 \in k3\_msafree2~(k31\_gfacirc1~X0~\\
X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X2~X0)~k4\_twoscomp \in k3\_msafree2~\\
(k31\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}(k33\_gfacirc1~X0~X1~X2 \in k3\_msafree2~(k31\_gfacirc1~\\
X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
