\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{t31\_gfacirc1 (TMLBoWdF1Ldsx8hfNzZbnnZa2FSY1UWMVgq)}
\maketitle
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_twoscomp : {\iota}$ be given.
Let $ k12\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k9\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k25\_twoscomp : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xboole\_0~(k2\_xboole\_0~X0~\\
X1)~X2=k2\_xboole\_0~X0~(k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:ehedpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}((v2\_circcomb~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}(k3\_msafree2~(k2\_circcomb~\\
X0~X1)=k2\_xboole\_0~(k3\_msafree2~X0)~(k3\_msafree2~X1)))\end{array}
\label{hyp:ehcdhdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_msafree2~(k10\_gfacirc1~X0~\\
X1~X2)=k2\_xboole\_0~(k1\_tarski~(k4\_tarski~(k10\_finseq\_1~X0~X1)~\\
k14\_twoscomp))~(k1\_tarski~(k12\_gfacirc1~X0~X1~X2))\end{array}
\label{hyp:ehcdedpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_msafree2~(k7\_gfacirc1~X0~\\
X1~X2)=k2\_xboole\_0~(k1\_enumset1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~\\
k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X1~X2)~k2\_twoscomp)~(k4\_tarski~\\
(k10\_finseq\_1~X2~X0)~k2\_twoscomp))~(k1\_tarski~(k9\_gfacirc1~X0~\\
X1~X2))\end{array}
\label{hyp:ehbdbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k7\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k7\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k7\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k7\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k7\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k7\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k7\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflghdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k10\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k10\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k10\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k10\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k10\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k10\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k10\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgbdadpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k7\_gfacirc1~X0~X1~X2=k2\_circcomb~\\
(k5\_gfacirc1~X0~X1~X2)~(k5\_circcomb~k25\_twoscomp~(k11\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X0~X1)~k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X2~X0)~k2\_twoscomp)))\end{array}
\label{hyp:eghdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k13\_gfacirc1~X0~X1~X2=k2\_circcomb~\\
(k10\_gfacirc1~X0~X1~X2)~(k7\_gfacirc1~X0~X1~X2)\end{array}
\label{hyp:egbdddpfhgggbgdgjgchdgbd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_msafree2~(k13\_gfacirc1~X0~\\
X1~X2)=k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(k1\_tarski~(k4\_tarski~\\
(k10\_finseq\_1~X0~X1)~k14\_twoscomp))~(k1\_tarski~(k12\_gfacirc1~\\
X0~X1~X2)))~(k1\_enumset1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k2\_twoscomp)~\\
(k4\_tarski~(k10\_finseq\_1~X1~X2)~k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~\\
X2~X0)~k2\_twoscomp)))~(k1\_tarski~(k9\_gfacirc1~X0~X1~X2))\end{array}$$
\end{theorem}
\end{document}
