\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{t125\_gfacirc1 (TML9GY1WfX7cs8fC37Dx6v3x1cJB1ba8ViQ)}
\maketitle
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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k46\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k47\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k48\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_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 .  (X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k14\_twoscomp){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(\\
u3\_msualg\_1~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~X1~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}((\\
(X4=k1\_funct\_1~X3~X0){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X1){\unicdcdcdhd}(X6=k1\_funct\_1~\\
X3~X2))){\unicdbdjdcd}((k1\_twoscomp~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~\\
X1~X2)~(k5\_facirc\_1~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~X1~X2)~\\
X3~np\_\_2)~(k12\_gfacirc1~X0~X1~X2)=k2\_binarith~(k2\_binarith~X4~X5)~\\
X6){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~\\
X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k14\_twoscomp)=\\
k2\_binarith~X4~X5){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k10\_gfacirc1~X0~\\
X1~X2)~(k11\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~X0=X4){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~\\
(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~X1=X5){\unicdcdcdhd}\\
(k1\_funct\_1~(k5\_facirc\_1~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~\\
X0~X1~X2)~X3~np\_\_2)~X2=X6))))))))))\end{array}
\label{hyp:ehddadpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k48\_gfacirc1~X0~X1~X2=k9\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egedidpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k47\_gfacirc1~X0~X1~X2=k10\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egedhdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k46\_gfacirc1~X0~X1~X2=k8\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egedgdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k12\_gfacirc1~X0~X1~X2=k9\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egbdcdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k11\_gfacirc1~X0~X1~X2=k10\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egbdbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k10\_gfacirc1~X0~X1~X2=k8\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egbdadpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehbdcdfdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k14\_twoscomp){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(\\
u3\_msualg\_1~(k46\_gfacirc1~X0~X1~X2)~(k47\_gfacirc1~X0~X1~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}((\\
(X4=k1\_funct\_1~X3~X0){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X1){\unicdcdcdhd}(X6=k1\_funct\_1~\\
X3~X2))){\unicdbdjdcd}((k1\_twoscomp~(k46\_gfacirc1~X0~X1~X2)~(k47\_gfacirc1~X0~\\
X1~X2)~(k5\_facirc\_1~(k46\_gfacirc1~X0~X1~X2)~(k47\_gfacirc1~X0~X1~X2)~\\
X3~np\_\_2)~(k48\_gfacirc1~X0~X1~X2)=k2\_binarith~(k2\_binarith~X4~X5)~\\
X6){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k46\_gfacirc1~X0~X1~X2)~(k47\_gfacirc1~\\
X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k14\_twoscomp)=\\
k2\_binarith~X4~X5){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(k46\_gfacirc1~X0~\\
X1~X2)~(k47\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~X0=X4){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~\\
(k46\_gfacirc1~X0~X1~X2)~(k47\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~X1=X5){\unicdcdcdhd}\\
(k1\_funct\_1~(k5\_facirc\_1~(k46\_gfacirc1~X0~X1~X2)~(k47\_gfacirc1~\\
X0~X1~X2)~X3~np\_\_2)~X2=X6))))))))))\end{array}$$
\end{theorem}
\end{document}
