\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{t19\_scpinvar (TMKC2vMsPGX2MXqC58iXGzWeJFPtZXm2asf)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_scmp\_gcd : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_scpinvar : {\iota}$ be given.
Let $ k3\_int\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_scmp\_gcd : {\iota}$ be given.
Let $ k16\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k13\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_scpinvar : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)){\unicdcdcdhd}(v5\_memstr\_0~X1~np\_\_2~k1\_scmpds\_2~k6\_numbers)))))){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~(k1\_funct\_1~X1~(k1\_scmp\_gcd~np\_\_1))~k6\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~(k1\_funct\_1~X1~(k1\_scmp\_gcd~np\_\_2))~k6\_numbers){\unicdcdcdhd}\\
(\preoh (k1\_funct\_1~(k6\_scmpds\_4~(k1\_scmpds\_4~(k3\_scmpds\_4~(k4\_scmpds\_4~\\
(k5\_scmpds\_2~k2\_scmp\_gcd~k6\_numbers)~(k16\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~\\
np\_\_3~np\_\_2))~(k4\_scpinvar~k2\_scmp\_gcd~np\_\_3~(k3\_scmpds\_4~(k3\_scmpds\_4~\\
(k3\_scmpds\_6~k2\_scmp\_gcd~np\_\_3~(k9\_compos\_1~k1\_scmpds\_2~(k13\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_1~np\_\_2))~(k9\_compos\_1~k1\_scmpds\_2~\\
(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_2~np\_\_1)))~(k16\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_3~np\_\_2))))~X1~X0)~(k1\_scmp\_gcd~np\_\_1)=k3\_int\_2~\\
(k1\_funct\_1~X1~(k1\_scmp\_gcd~np\_\_1))~(k1\_funct\_1~X1~(k1\_scmp\_gcd~\\
np\_\_2))){\unicdcdcdhd}((k1\_funct\_1~(k6\_scmpds\_4~(k1\_scmpds\_4~(k3\_scmpds\_4~\\
(k4\_scmpds\_4~(k5\_scmpds\_2~k2\_scmp\_gcd~k6\_numbers)~(k16\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_3~np\_\_2))~(k4\_scpinvar~k2\_scmp\_gcd~np\_\_3~(k3\_scmpds\_4~\\
(k3\_scmpds\_4~(k3\_scmpds\_6~k2\_scmp\_gcd~np\_\_3~(k9\_compos\_1~k1\_scmpds\_2~\\
(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_1~np\_\_2))~(k9\_compos\_1~\\
k1\_scmpds\_2~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_2~np\_\_1)))~\\
(k16\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_2))))~X1~X0)~(k1\_scmp\_gcd~np\_\_2)=\\
k3\_int\_2~(k1\_funct\_1~X1~(k1\_scmp\_gcd~np\_\_1))~(k1\_funct\_1~X1~(k1\_scmp\_gcd~\\
np\_\_2))){\unicdcdcdhd}((r1\_scmpds\_6~(k1\_scmpds\_4~(k3\_scmpds\_4~(k4\_scmpds\_4~\\
(k5\_scmpds\_2~k2\_scmp\_gcd~k6\_numbers)~(k16\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~\\
np\_\_3~np\_\_2))~(k4\_scpinvar~k2\_scmp\_gcd~np\_\_3~(k3\_scmpds\_4~(k3\_scmpds\_4~\\
(k3\_scmpds\_6~k2\_scmp\_gcd~np\_\_3~(k9\_compos\_1~k1\_scmpds\_2~(k13\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_1~np\_\_2))~(k9\_compos\_1~k1\_scmpds\_2~\\
(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_2~np\_\_1)))~(k16\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_3~np\_\_2))))~X1~X0){\unicdcdcdhd}(r2\_scmpds\_6~(k1\_scmpds\_4~\\
(k3\_scmpds\_4~(k4\_scmpds\_4~(k5\_scmpds\_2~k2\_scmp\_gcd~k6\_numbers)~\\
(k16\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_2))~(k4\_scpinvar~k2\_scmp\_gcd~\\
np\_\_3~(k3\_scmpds\_4~(k3\_scmpds\_4~(k3\_scmpds\_6~k2\_scmp\_gcd~np\_\_3~\\
(k9\_compos\_1~k1\_scmpds\_2~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~\\
np\_\_1~np\_\_2))~(k9\_compos\_1~k1\_scmpds\_2~(k13\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_2~np\_\_1)))~(k16\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~\\
np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_2))))~\\
X1~X0)))))))\end{array}
\label{hyp:mgddgdpfdhdgahjgogghbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_scpinvar=k1\_scmpds\_4~(k3\_scmpds\_4~(k4\_scmpds\_4~(k5\_scmpds\_2~\\
k2\_scmp\_gcd~k6\_numbers)~(k16\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~\\
np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_3~np\_\_2))~\\
(k4\_scpinvar~k2\_scmp\_gcd~np\_\_3~(k3\_scmpds\_4~(k3\_scmpds\_4~(k3\_scmpds\_6~\\
k2\_scmp\_gcd~np\_\_3~(k9\_compos\_1~k1\_scmpds\_2~(k13\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_1~np\_\_2))~(k9\_compos\_1~k1\_scmpds\_2~(k13\_scmpds\_2~\\
k2\_scmp\_gcd~k2\_scmp\_gcd~np\_\_2~np\_\_1)))~(k16\_scmpds\_2~k2\_scmp\_gcd~\\
k2\_scmp\_gcd~np\_\_3~np\_\_1))~(k13\_scmpds\_2~k2\_scmp\_gcd~k2\_scmp\_gcd~\\
np\_\_3~np\_\_2)))\end{array}
\label{hyp:egedpfdhdgahjgogghbgch}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfdhdgahjgogghbgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)){\unicdcdcdhd}(v5\_memstr\_0~X1~np\_\_2~k1\_scmpds\_2~k6\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(((k1\_funct\_1~\\
X1~(k1\_scmp\_gcd~np\_\_1)=X2){\unicdcdcdhd}(k1\_funct\_1~X1~(k1\_scmp\_gcd~np\_\_2)=\\
X3)){\unicdbdjdcd}((r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdid}((r1\_xxreal\_0~X3~k6\_numbers){\unicdcdcdid}\\
((k1\_funct\_1~(k6\_scmpds\_4~k5\_scpinvar~X1~X0)~(k1\_scmp\_gcd~np\_\_1)=\\
k3\_int\_2~X2~X3){\unicdcdcdhd}((k1\_funct\_1~(k6\_scmpds\_4~k5\_scpinvar~X1~X0)~(\\
k1\_scmp\_gcd~np\_\_2)=k3\_int\_2~X2~X3){\unicdcdcdhd}((r1\_scmpds\_6~k5\_scpinvar~\\
X1~X0){\unicdcdcdhd}(r2\_scmpds\_6~k5\_scpinvar~X1~X0))))))))))\end{array}$$
\end{theorem}
\end{document}
