\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\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{t26\_group\_7 (TMMYmizS4mZfVBqZqGz6cCh77E7asN7wKPh)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}(l3\_algstr\_0~\\
X2))){\unicdbdjdcd}((v1\_relat\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k11\_finseq\_1~\\
X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_funct\_1~(k11\_finseq\_1~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~\\
np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_group\_7~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}(v3\_group\_7~\\
(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)))))))))\end{array}
\label{hyp:ehcdedpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_group\_1~X2){\unicdcdcdhd}(l3\_algstr\_0~\\
X2))){\unicdbdjdcd}((v1\_relat\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k11\_finseq\_1~\\
X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_funct\_1~(k11\_finseq\_1~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~\\
np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_group\_7~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}(v2\_group\_7~\\
(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)))))))))\end{array}
\label{hyp:ehcdddpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l3\_algstr\_0~X2)){\unicdbdjdcd}((v1\_relat\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_relat\_1~(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k11\_finseq\_1~\\
X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}(v1\_group\_7~(k11\_finseq\_1~\\
X0~X1~X2))))))))\end{array}
\label{hyp:ehcdcdpfhgchpgfhahpfhd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfhgchpgfhahpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_group\_1~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}(l3\_algstr\_0~X2)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k11\_finseq\_1~\\
X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_funct\_1~(k11\_finseq\_1~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~\\
np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_group\_7~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v2\_group\_7~\\
(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}(v3\_group\_7~\\
(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3))))))))))\end{array}$$
\end{theorem}
\end{document}
