\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{t27\_substut1 (TMTjQhFXVMpQDfiChdyuXQzpZ5Dxa7GaS21)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}((v4\_substut1~X1~X0){\unicdbdjdcd}((k1\_xtuple\_0~(k1\_funct\_1~(k11\_qc\_lang1~\\
X0~(k18\_substut1~X0~X1))~np\_\_1){\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k1\_xtuple\_0~(k1\_funct\_1~\\
(k11\_qc\_lang1~X0~(k18\_substut1~X0~X1))~np\_\_1){\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k1\_xtuple\_0~\\
(k1\_funct\_1~(k11\_qc\_lang1~X0~(k18\_substut1~X0~X1))~np\_\_1){\unicdcdgdad}np\_\_2){\unicdcdcdhd}\\
(k1\_xtuple\_0~(k1\_funct\_1~(k11\_qc\_lang1~X0~(k18\_substut1~X0~X1))~\\
np\_\_1){\unicdcdgdad}np\_\_3))))))\end{array}
\label{hyp:ehcdgdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}(((v2\_substut1~X1~X0){\unicdbdjdcd}(k1\_xtuple\_0~(k1\_funct\_1~(k11\_qc\_lang1~\\
X0~(k18\_substut1~X0~X1))~np\_\_1)=k6\_numbers)){\unicdcdcdhd}((\preoh (v4\_substut1~\\
X1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}(\preoh m2\_subset\_1~\\
(k1\_funct\_1~(k11\_qc\_lang1~X0~(k18\_substut1~X0~X1))~np\_\_1)~(k6\_qc\_lang1~\\
X0)~(k8\_qc\_lang1~X0~X2)))){\unicdcdcdhd}(((v5\_substut1~X1~X0){\unicdbdjdcd}(k1\_xtuple\_0~\\
(k1\_funct\_1~(k11\_qc\_lang1~X0~(k18\_substut1~X0~X1))~np\_\_1)=np\_\_1)){\unicdcdcdhd}\\
(((v6\_substut1~X1~X0){\unicdbdjdcd}(k1\_xtuple\_0~(k1\_funct\_1~(k11\_qc\_lang1~\\
X0~(k18\_substut1~X0~X1))~np\_\_1)=np\_\_2)){\unicdcdcdhd}((v7\_substut1~X1~X0){\unicdbdjdcd}\\
(k1\_xtuple\_0~(k1\_funct\_1~(k11\_qc\_lang1~X0~(k18\_substut1~X0~X1))~\\
np\_\_1)=np\_\_3)))))))\end{array}
\label{hyp:ehcdfdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_3}}}}\label{hyp:dhahdgddpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_2}}}}\label{hyp:dhahdgcdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfdhfhcgdhehfhehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}((\preoh (v4\_substut1~X1~X0){\unicdcdcdhd}(v5\_substut1~X1~X0)){\unicdcdcdhd}((\preoh (v4\_substut1~\\
X1~X0){\unicdcdcdhd}(v6\_substut1~X1~X0)){\unicdcdcdhd}((\preoh (v4\_substut1~X1~X0){\unicdcdcdhd}(v7\_substut1~\\
X1~X0)){\unicdcdcdhd}((\preoh (v5\_substut1~X1~X0){\unicdcdcdhd}(v6\_substut1~X1~X0)){\unicdcdcdhd}((\preoh (v5\_substut1~\\
X1~X0){\unicdcdcdhd}(v7\_substut1~X1~X0)){\unicdcdcdhd}((\preoh (v6\_substut1~X1~X0){\unicdcdcdhd}(v7\_substut1~\\
X1~X0)){\unicdcdcdhd}((\preoh (v2\_substut1~X1~X0){\unicdcdcdhd}(v4\_substut1~X1~X0)){\unicdcdcdhd}((\preoh (v2\_substut1~\\
X1~X0){\unicdcdcdhd}(v5\_substut1~X1~X0)){\unicdcdcdhd}((\preoh (v2\_substut1~X1~X0){\unicdcdcdhd}(v6\_substut1~\\
X1~X0)){\unicdcdcdhd}(\preoh (v2\_substut1~X1~X0){\unicdcdcdhd}(v7\_substut1~X1~X0))))))))))))\end{array}$$
\end{theorem}
\end{document}
