\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{t18\_zfmodel1 (TMHySCpVR2AKAKMBWAmuFwaSG3TwjX4h6wm)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zf\_lang : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_zf\_model : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_zf\_model : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k13\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k12\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_zfmodel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_zf\_model : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_zf\_model : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_zf\_model : {\iota}$ be given.
Let $ k9\_zf\_model : {\iota}$ be given.
Let $ k8\_zf\_model : {\iota}$ be given.
Let $ k7\_zf\_model : {\iota}$ be given.
Let $ k11\_zf\_model : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_ordinal1~X0){\unicdbdjdcd}((r2\_zf\_model~\\
X0~k10\_zf\_model){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(k3\_xboole\_0~\\
X0~(k1\_zfmisc\_1~X1) \in X0))))\end{array}
\label{hyp:ehidpfkhggngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_ordinal1~X0){\unicdbdjdcd}((r2\_zf\_model~\\
X0~k9\_zf\_model){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~X0){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X0){\unicdbdjdcd}(\preoh (r2\_xboole\_0~X2~X3){\unicdcdcdhd}(X3 \in X1)))))))))\end{array}
\label{hyp:ehgdpfkhggngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_ordinal1~X0){\unicdbdjdcd}((r2\_zf\_model~\\
X0~k8\_zf\_model){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(k3\_tarski~X1 \in \\
X0))))\end{array}
\label{hyp:ehedpfkhggngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_ordinal1~X0){\unicdbdjdcd}((r2\_zf\_model~\\
X0~k7\_zf\_model){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}(k2\_tarski~X1~X2 \in X0)))))\end{array}
\label{hyp:ehcdpfkhggngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_ordinal1~X0){\unicdbdjdcd}(({\unicdcdadad} X1 .  \\
((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}((r1\_xboole\_0~\\
(k1\_enumset1~(k2\_zf\_lang~k6\_numbers)~(k2\_zf\_lang~np\_\_1)~(k2\_zf\_lang~\\
np\_\_2))~(k2\_zf\_model~X1)){\unicdbdjdcd}(r2\_zf\_model~X0~(k11\_zf\_model~X1)))){\unicdbdjded}\\
({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k1\_zf\_lang~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_zf\_lang~X0))))){\unicdbdjdcd}\\
(((r1\_xboole\_0~(k1\_enumset1~(k2\_zf\_lang~k6\_numbers)~(k2\_zf\_lang~\\
np\_\_1)~(k2\_zf\_lang~np\_\_2))~(k2\_zf\_model~X1)){\unicdcdcdhd}(r1\_zf\_model~X0~\\
X2~(k8\_zf\_lang~(k2\_zf\_lang~np\_\_3)~(k13\_zf\_lang~(k2\_zf\_lang~k6\_numbers)~\\
(k8\_zf\_lang~(k2\_zf\_lang~np\_\_4)~(k12\_zf\_lang~X1~(k4\_zf\_lang~(k2\_zf\_lang~\\
np\_\_4)~(k2\_zf\_lang~k6\_numbers)))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X0){\unicdbdjdcd}(k7\_relset\_1~X0~X0~(k1\_zfmodel1~X1~X0~X2)~X3 \in X0)))))))\end{array}
\label{hyp:ehbdfdpfkhggngpgegfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_zf\_model~X0){\unicdbdjded}((v1\_ordinal1~\\
X0){\unicdcdcdhd}((r2\_zf\_model~X0~k7\_zf\_model){\unicdcdcdhd}((r2\_zf\_model~X0~k8\_zf\_model){\unicdcdcdhd}\\
((r2\_zf\_model~X0~k9\_zf\_model){\unicdcdcdhd}((r2\_zf\_model~X0~k10\_zf\_model){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
(r1\_xboole\_0~(k1\_enumset1~(k2\_zf\_lang~k6\_numbers)~(k2\_zf\_lang~\\
np\_\_1)~(k2\_zf\_lang~np\_\_2))~(k2\_zf\_model~X1)){\unicdbdjdcd}(r2\_zf\_model~X0~\\
(k11\_zf\_model~X1))))))))))\end{array}
\label{hyp:egbdcdpfkhggpfngpgegfgmg}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfkhggngpgegfgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(((v1\_ordinal1~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(k2\_tarski~\\
X1~X2 \in X0))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(k3\_tarski~X1 \in X0)){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(k3\_xboole\_0~X0~(k1\_zfmisc\_1~\\
X1) \in X0)){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k1\_zf\_lang~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_zf\_lang~X0))))){\unicdbdjdcd}\\
(((r1\_xboole\_0~(k1\_enumset1~(k2\_zf\_lang~k6\_numbers)~(k2\_zf\_lang~\\
np\_\_1)~(k2\_zf\_lang~np\_\_2))~(k2\_zf\_model~X1)){\unicdcdcdhd}(r1\_zf\_model~X0~\\
X2~(k8\_zf\_lang~(k2\_zf\_lang~np\_\_3)~(k13\_zf\_lang~(k2\_zf\_lang~k6\_numbers)~\\
(k8\_zf\_lang~(k2\_zf\_lang~np\_\_4)~(k12\_zf\_lang~X1~(k4\_zf\_lang~(k2\_zf\_lang~\\
np\_\_4)~(k2\_zf\_lang~k6\_numbers)))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X0){\unicdbdjdcd}(k7\_relset\_1~X0~X0~(k1\_zfmodel1~X1~X0~X2)~X3 \in X0))))))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
(\preoh (r2\_xboole\_0~X2~X3){\unicdcdcdhd}(X3 \in X1))))))){\unicdcdcdid}(v1\_zf\_model~X0)))\end{array}$$
\end{theorem}
\end{document}
