\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{t25\_ftacell1 (TMQrYJXQCzf4ytDu89yRJH99nPW3CyfGtzy)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_gfacirc1 : {\iota}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_ftacell1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k36\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_twoscomp : {\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 $ k24\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k21\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k9\_facirc\_1 : {{\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 .  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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k3\_msafree2~\\
(k13\_ftacell1~X0~X1~X2~X3~X4)=k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~\\
(k2\_tarski~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k4\_gfacirc1)~(k36\_gfacirc1~\\
X0~X1~X2))~(k2\_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)~(k33\_gfacirc1~X0~X1~X2)))~(k2\_tarski~(k4\_tarski~\\
(k10\_finseq\_1~(k36\_gfacirc1~X0~X1~X2)~X4)~k4\_gfacirc1)~(k24\_gfacirc1~\\
(k36\_gfacirc1~X0~X1~X2)~X4~X3)))~(k2\_enumset1~(k4\_tarski~(k10\_finseq\_1~\\
(k36\_gfacirc1~X0~X1~X2)~X4)~k3\_gfacirc1)~(k4\_tarski~(k10\_finseq\_1~\\
X4~X3)~k3\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X3~(k36\_gfacirc1~\\
X0~X1~X2))~k2\_twoscomp)~(k21\_gfacirc1~(k36\_gfacirc1~X0~X1~X2)~X4~\\
X3))\end{array}
\label{hyp:ehcdbdpfggehbgdgfgmgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
k4\_enumset1~X0~X1~X2~X3~X4~X5=k2\_xboole\_0~(k2\_tarski~X0~X1)~(k2\_enumset1~\\
X2~X3~X4~X5)\end{array}
\label{hyp:ehbdcdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (X6=k4\_enumset1~X0~X1~X2~X3~X4~X5){\unicdbdjded}({\unicdcdadad} X7 .  (X7 \in X6){\unicdbdjded}\\
(\preoh (X7{\unicdcdgdad}X0){\unicdcdcdhd}((X7{\unicdcdgdad}X1){\unicdcdcdhd}((X7{\unicdcdgdad}X2){\unicdcdcdhd}((X7{\unicdcdgdad}X3){\unicdcdcdhd}((X7{\unicdcdgdad}X4){\unicdcdcdhd}(X7{\unicdcdgdad}X5)))))))\end{array}
\label{hyp:egedpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k36\_gfacirc1~X0~X1~X2=k9\_facirc\_1~\\
X0~X1~X2~k4\_gfacirc1\end{array}
\label{hyp:egddgdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k24\_gfacirc1~X0~X1~X2=k9\_facirc\_1~\\
X0~X1~X2~k4\_gfacirc1\end{array}
\label{hyp:egcdedpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfggehbgdgfgmgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~\\
(k10\_finseq\_1~X0~X1)~k4\_gfacirc1 \in k3\_msafree2~(k13\_ftacell1~X0~\\
X1~X2~X3~X4)){\unicdcdcdhd}((k36\_gfacirc1~X0~X1~X2 \in k3\_msafree2~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_twoscomp \in k3\_msafree2~\\
(k13\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X1~X2)~\\
k3\_gfacirc1 \in k3\_msafree2~(k13\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((k4\_tarski~\\
(k10\_finseq\_1~X2~X0)~k4\_twoscomp \in k3\_msafree2~(k13\_ftacell1~X0~\\
X1~X2~X3~X4)){\unicdcdcdhd}((k33\_gfacirc1~X0~X1~X2 \in k3\_msafree2~(k13\_ftacell1~\\
X0~X1~X2~X3~X4)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~(k36\_gfacirc1~X0~X1~X2)~\\
X4)~k4\_gfacirc1 \in k3\_msafree2~(k13\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((k24\_gfacirc1~\\
(k36\_gfacirc1~X0~X1~X2)~X4~X3 \in k3\_msafree2~(k13\_ftacell1~X0~X1~X2~\\
X3~X4)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~(k36\_gfacirc1~X0~X1~X2)~X4)~k3\_gfacirc1 \in \\
k3\_msafree2~(k13\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~\\
X4~X3)~k3\_twoscomp \in k3\_msafree2~(k13\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}(\\
(k4\_tarski~(k10\_finseq\_1~X3~(k36\_gfacirc1~X0~X1~X2))~k2\_twoscomp \in \\
k3\_msafree2~(k13\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}(k21\_gfacirc1~(k36\_gfacirc1~\\
X0~X1~X2)~X4~X3 \in k3\_msafree2~(k13\_ftacell1~X0~X1~X2~X3~X4))))))))))))\end{array}$$
\end{theorem}
\end{document}
