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Satisfaction of some intuitionistic formulas for various Kripke frames
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\documentclass[10pt,a4paper]{article} % -*- coding: utf-8 -*- | |
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\usepackage[a4paper,margin=1.5cm]{geometry} | |
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\usepackage{amsmath} | |
\usepackage{amsfonts} | |
\usepackage{amssymb} | |
\usepackage{pifont} | |
\usepackage{supertabular} | |
%\usepackage{adjustbox} | |
\usepackage{graphicx} | |
\usepackage[usenames,svgnames]{xcolor} | |
\newcommand{\sideways}[1]{\rotatebox{90}{#1}}% | |
\newcommand{\cmark}{\ding{51}}% | |
\newcommand{\xmark}{\ding{55}}% | |
\begin{document} | |
\setlength{\parindent}{0pt} | |
\textbf{Satisfaction of some intuitionistic formulas for various Kripke frames:} | |
\par | |
\begin{supertabular}{l|ccccccccccccccc} | |
&\sideways{\texttt{basic-1}} | |
&\sideways{\texttt{basic-2}} | |
&\sideways{\texttt{basic-3}} | |
&\sideways{\texttt{basic-4}} | |
&\sideways{\texttt{basic-5}} | |
&\sideways{\texttt{skvortsov-1}} | |
&\sideways{\texttt{skvortsov-2}} | |
&\sideways{\texttt{skvortsov-3}} | |
&\sideways{\texttt{skvortsov-4}} | |
&\sideways{\texttt{skvortsov-5}} | |
&\sideways{\texttt{skvortsov-6}} | |
&\sideways{\texttt{skvortsov-7}} | |
&\sideways{\texttt{skvortsov-8}} | |
&\sideways{\texttt{skvortsov-9}} | |
&\sideways{\texttt{skvortsov-10}} | |
\\\hline | |
\texttt{lem} | |
&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{smetanich} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{bd2} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{goedel-dummett} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{wlem} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{bc3} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{scott} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark} | |
\\ | |
\texttt{jankov-r} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark} | |
\\ | |
\texttt{bw2} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{kreisel-putnam} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{two-of-three} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{skvortsov} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{ceitin-star} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{bb2} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{ceitin} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{plisko-p3} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{jankov-i3} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark} | |
\\ | |
\texttt{jankov-k3} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark} | |
\\ | |
\texttt{anti-scott} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{rose} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark} | |
\\ | |
\texttt{plisko-p} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark} | |
\\ | |
\texttt{plisko-l} | |
&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{Green}{\cmark}&\textcolor{DarkRed}{\xmark}&\textcolor{Green}{\cmark} | |
\\ | |
\end{supertabular} | |
\vskip 15pt plus 1fil\relax | |
\textbf{Formulas:} | |
\par\nobreak | |
\begin{supertabular}{lp{0.8\textwidth}} | |
\texttt{lem} | |
&$p \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax \neg p$ | |
\\[1.5pt] | |
\texttt{smetanich} | |
&$(\neg q\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (((p\Rightarrow\penalty900\relax q)\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p)\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p)$ | |
\\[1.5pt] | |
\texttt{bd2} | |
&$p_{2} \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax (p_{2} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{1}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg p_{1})$ | |
\\[1.5pt] | |
\texttt{goedel-dummett} | |
&$(p_{0} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{1}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax (p_{1} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{0})$ | |
\\[1.5pt] | |
\texttt{wlem} | |
&$\neg p \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax \neg \neg p$ | |
\\[1.5pt] | |
\texttt{bc3} | |
&$p_{0} \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax (p_{0} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{1}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax (p_{0}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{1} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{2}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax \neg (p_{0}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{1}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{2})$ | |
\\[1.5pt] | |
\texttt{scott} | |
&$((\neg \neg p\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p) \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (\neg p\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax \neg \neg p)) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg p\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg \neg p)$ | |
\\[1.5pt] | |
\texttt{jankov-r} | |
&$(\neg (p\land\penalty600\relax q) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax \neg (\neg p\land\penalty600\relax \neg q) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg \neg p\Rightarrow\penalty900\relax p)\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (p\lor\penalty900\relax \neg p)) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg \neg q\Rightarrow\penalty900\relax q)\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (q\lor\penalty900\relax \neg q))) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg p\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg q)$ | |
\\[1.5pt] | |
\texttt{bw2} | |
&$(p_{0} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{1}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{2}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax (p_{1} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{0}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{2}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax (p_{2} \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax p_{0}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{1})$ | |
\\[1.5pt] | |
\texttt{kreisel-putnam} | |
&$(\neg p\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax q\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax r) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax ((\neg p\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax r))$ | |
\\[1.5pt] | |
\texttt{two-of-three} | |
&$\neg (p_{1}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{2}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{3}) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax \neg (p_{2}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{3}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax \neg (p_{1}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{3}) \mskip4mu plus 4mu\relax\relax\lor\penalty0\relax\mskip4mu plus 4mu\relax\relax \neg (p_{1}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{2})$ | |
\\[1.5pt] | |
\texttt{skvortsov} | |
&$(\neg (p_{1}\land\penalty600\relax p_{2}) \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax \neg (\neg p_{1}\land\penalty600\relax p_{2})\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg (p_{1}\land\penalty600\relax \neg p_{2})) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg (\neg p_{1}\land\penalty600\relax p_{2})\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg (p_{1}\land\penalty600\relax \neg p_{2}))$ | |
\\[1.5pt] | |
\texttt{ceitin-star} | |
&$(\neg (p_{1}\land\penalty600\relax p_{2}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (q_{1}\lor\penalty900\relax r)) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (q_{2}\lor\penalty900\relax r))) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax ((\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{1}) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax r) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{2}) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax r))$ | |
\\[1.5pt] | |
\texttt{bb2} | |
&$((p_{0}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (p_{1}\lor\penalty900\relax p_{2}))\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{2})) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax ((p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (p_{0}\lor\penalty900\relax p_{2}))\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (p_{0}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{2})) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax ((p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (p_{0}\lor\penalty900\relax p_{1}))\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (p_{0}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{1})) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (p_{0}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{1}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{2})$ | |
\\[1.5pt] | |
\texttt{ceitin} | |
&$(\neg (p_{1}\land\penalty600\relax p_{2}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (q_{1}\lor\penalty900\relax q_{2})) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (q_{1}\lor\penalty900\relax q_{2}))) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax ((\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{1}) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{2}) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{1}) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{2}))$ | |
\\[1.5pt] | |
\texttt{plisko-p3} | |
&$(\neg \neg (p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{2}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax q) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg \neg (p_{1}\lor\penalty900\relax q)\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax q) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg \neg (p_{2}\lor\penalty900\relax q)\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p_{2}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax q)) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg \neg (p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{2})\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax q)$ | |
\\[1.5pt] | |
\texttt{jankov-i3} | |
&$(\neg (p_{2}\land\penalty600\relax p_{3}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax \neg (p_{1}\land\penalty600\relax p_{3}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax \neg (p_{1}\land\penalty600\relax p_{2}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p_{2}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{3}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{3})) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (p_{3}\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg p_{3})$ | |
\\[1.5pt] | |
\texttt{jankov-k3} | |
&$\neg (p_{2}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{3}) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax \neg (p_{1}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{3}) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax \neg (p_{1}\mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax p_{2}) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax (\neg p_{1}\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (p_{2}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{3})) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax (\neg p_{2}\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{3})) \mskip3mu plus 4mu\relax\relax\land\penalty0\relax\mskip3mu plus 4mu\relax\relax (\neg p_{3}\mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (p_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax p_{2})) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (p_{1} \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{2} \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax p_{3})$ | |
\\[1.5pt] | |
\texttt{anti-scott} | |
&$(((\neg \neg p\Rightarrow\penalty900\relax p) \mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p\lor\penalty900\relax \neg \neg p)) \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (\neg p\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax \neg \neg p)) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg \neg p \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (\neg \neg p\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax p))$ | |
\\[1.5pt] | |
\texttt{rose} | |
&$((\neg \neg (\neg q_{1}\lor\penalty900\relax \neg q_{2})\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg q_{1}\lor\penalty900\relax \neg q_{2})) \mskip3mu plus 2mu\relax\relax\Rightarrow\penalty300\relax\mskip3mu plus 2mu\relax\relax (\neg (\neg q_{1}\lor\penalty900\relax \neg q_{2})\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax \neg \neg (\neg q_{1}\lor\penalty900\relax \neg q_{2}))) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg (\neg q_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax \neg q_{2})\mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg \neg (\neg q_{1}\mskip0mu\relax\lor\penalty600\relax\mskip0mu\relax \neg q_{2}))$ | |
\\[1.5pt] | |
\texttt{plisko-p} | |
&$(\neg (p_{1}\land\penalty600\relax p_{2}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax \neg (\neg q_{1}\land\penalty600\relax \neg q_{2}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (((p_{1}\Rightarrow\penalty1200\relax q_{1}) \lor\penalty900\relax (p_{1}\Rightarrow\penalty1200\relax q_{2})) \mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax ((p_{2}\Rightarrow\penalty1200\relax q_{1}) \lor\penalty900\relax (p_{2}\Rightarrow\penalty1200\relax q_{2})))) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax ((p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{1}) \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax (p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax q_{2}))$ | |
\\[1.5pt] | |
\texttt{plisko-l} | |
&$((\neg \neg p_{1}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p_{2}\land\penalty900\relax \neg p_{3})) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg \neg p_{2}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p_{3}\land\penalty900\relax \neg p_{1})) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax (\neg \neg p_{3}\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p_{1}\land\penalty900\relax \neg p_{2})) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg p_{2}\land\penalty900\relax \neg p_{3})\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax \neg \neg p_{1}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg p_{3}\land\penalty900\relax \neg p_{1})\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax \neg \neg p_{2}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg p_{1}\land\penalty900\relax \neg p_{2})\mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax \neg \neg p_{3}) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg p_{1}\Rightarrow\penalty900\relax (\neg p_{2}\lor\penalty1200\relax \neg p_{3})) \mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p_{2}\lor\penalty900\relax \neg p_{3})) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg p_{2}\Rightarrow\penalty900\relax (\neg p_{3}\lor\penalty1200\relax \neg p_{1})) \mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p_{3}\lor\penalty900\relax \neg p_{1})) \mskip1mu plus 2mu\relax\relax\land\penalty300\relax\mskip1mu plus 2mu\relax\relax ((\neg p_{3}\Rightarrow\penalty900\relax (\neg p_{1}\lor\penalty1200\relax \neg p_{2})) \mskip1mu\relax\Rightarrow\penalty600\relax\mskip1mu\relax (\neg p_{1}\lor\penalty900\relax \neg p_{2}))) \mskip5mu plus 4mu\relax\relax\Rightarrow\penalty0\relax\mskip5mu plus 4mu\relax\relax (\neg p_{1} \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg p_{2} \mskip2mu plus 2mu\relax\relax\lor\penalty300\relax\mskip2mu plus 2mu\relax\relax \neg p_{3})$ | |
\\ | |
\end{supertabular} | |
\vskip 15pt plus 1fil\relax | |
\textbf{Frames:} | |
\par\nobreak | |
{\setlength{\lineskip}{24pt plus 12pt minus 12pt} | |
\begin{tabular}[t]{ll} | |
\texttt{basic-1} | |
\\ | |
\includegraphics[scale=0.5]{testframes/basic-1} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{basic-2} | |
\\ | |
\includegraphics[scale=0.5]{testframes/basic-2} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{basic-3} | |
\\ | |
\includegraphics[scale=0.5]{testframes/basic-3} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{basic-4} | |
\\ | |
\includegraphics[scale=0.5]{testframes/basic-4} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{basic-5} | |
\\ | |
\includegraphics[scale=0.5]{testframes/basic-5} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-1} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-1} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-2} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-2} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-3} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-3} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-4} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-4} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-5} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-5} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-6} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-6} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-7} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-7} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-8} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-8} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-9} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-9} | |
\end{tabular} | |
\penalty0\hskip 2em plus 1fil\relax | |
\begin{tabular}[t]{ll} | |
\texttt{skvortsov-10} | |
\\ | |
\includegraphics[scale=0.5]{testframes/skvortsov-10} | |
\end{tabular} | |
\par} | |
\vfill | |
\end{document} |
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