\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{t35\_modelc\_3 (TMQ8gvHFMYQEiaHGyPsmHwQ1jhAENxKPCJL)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r5\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k10\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ g1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}\\
((r5\_modelc\_3~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~\\
np\_\_1~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((\\
v1\_modelc\_3~X3~X0){\unicdcdcdhd}(l1\_modelc\_3~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_modelc\_3~\\
X4~X0){\unicdcdcdhd}(l1\_modelc\_3~X4~X0)){\unicdbdjdcd}(\preoh (X3=k1\_funct\_1~X1~X2){\unicdcdcdhd}((X4=k1\_funct\_1~\\
X1~(k1\_nat\_1~X2~np\_\_1)){\unicdcdcdhd}(r4\_modelc\_3~X0~X3~X4))))))))))\end{array}
\label{hyp:egbdjdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
((((v1\_modelc\_3~X0~X1){\unicdcdcdhd}(l1\_modelc\_3~X0~X1)){\unicdbdjdcd}(k10\_modelc\_3~X0~\\
X1=X0)){\unicdcdcdhd}((\preoh (v1\_modelc\_3~X0~X1){\unicdcdcdhd}(l1\_modelc\_3~X0~X1)){\unicdbdjdcd}(k10\_modelc\_3~\\
X0~X1=g1\_modelc\_3~X1~(k7\_modelc\_3~X1)~(k7\_modelc\_3~X1)~(k7\_modelc\_3~\\
X1))))\end{array}
\label{hyp:egbdgdpfngpgegfgmgdgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_modelc\_2~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(((r5\_modelc\_3~X2~X1){\unicdcdcdhd}(r1\_xxreal\_0~\\
np\_\_1~X0)){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X1)~X0){\unicdcdcdid}(r4\_modelc\_3~X2~\\
(k10\_modelc\_3~(k1\_funct\_1~X1~X0)~X2)~(k10\_modelc\_3~(k1\_funct\_1~\\
X1~(k1\_nat\_1~X0~np\_\_1))~X2))))))\end{array}$$
\end{theorem}
\end{document}
