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tptp.tex
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\documentclass[12pt]{article}
\usepackage[scaled=0.9]{beramono}
\usepackage{xcolor}
\usepackage[T1]{fontenc}
\usepackage{mathpazo}
\linespread{1.05}
\usepackage[T1,small,euler-digits]{eulervm}
\usepackage[utf8x]{inputenc}
\usepackage{hyperref}
\hypersetup{linktocpage}
\hypersetup{
colorlinks,
citecolor=amethyst,
filecolor=black,
linkcolor=blue(munsell),
urlcolor=blue(munsell)
}
\usepackage[T1]{fontenc}
\usepackage[]{amsmath,amssymb}
\definecolor{amethyst}{rgb}{0.6, 0.4, 0.8}
\definecolor{antiquefuchsia}{rgb}{0.57, 0.36, 0.51}
\definecolor{ballblue}{rgb}{0.13, 0.67, 0.8}
\definecolor{blue(munsell)}{rgb}{0.0, 0.5, 0.69}
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\definecolor{amber}{rgb}{1.0, 0.75, 0.0}
\definecolor{aliceblue}{rgb}{0.94, 0.97, 1.0}
\usepackage{listings,chngcntr}
\lstset{
aboveskip=10pt
, backgroundcolor=\color{aliceblue}
, basicstyle=\ttfamily
, belowskip=10pt
, frame=trbl
, keywords=[2]{axiom, conjecture,inference, negated_conjecture, plain}
, keywords=[3]{fof, cnf}
, keywords=[4]{canonicalize, resolve, conjunct,
strip, simplify, negate, clausify}
, keywordstyle=[2]\color{cadet}%\underbar,%\bfseries
, keywordstyle=[3]\color{bondiblue}\bfseries
, keywordstyle=[4]\bfseries
, showstringspaces=false
, emptylines = 0
}
\usepackage[]{graphicx}
\usepackage{array}
\usepackage[margin=1in]{geometry}
\usepackage{url}
\usepackage{float}
\usepackage{syntax}
% \setlength{\grammarparsep}{20pt plus 1pt minus 1pt} % increase separation between rules
\setlength{\grammarindent}{4em} % increase separation between LHS/RHS
\setlength\parindent{0pt} % Removes all indentation from paragraphs
\newcommand{\textdf}[1]{\textbf{\textsf{#1}}\index{#1}}
\newcommand{\tptp}[0]{\texorpdfstring{\texttt{TPTP}}\ \ }
\newcommand{\miss}[0]{{\colorbox{amber}{\textdf{?}}}}
\newcommand{\ttext}[1]{\texttt{\color{black} #1}}
\newcommand{\shell}[1]{\texttt{\color{black} #1}}
\newcommand{\problemtptp}[3][c]{\lstinputlisting[caption=#2, firstline=#3, label=custom#1]{#2}}
\newcommand{\solutiontstp}[2][c]{\lstinputlisting[caption=#2, firstline=5, label=custom#1]{#2}}
\setlength{\topmargin}{-.35 in}
\setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in}
\setlength{\textheight}{9.in}
\setlength{\textwidth}{6.7in}
\begin{document}
\counterwithin{lstlisting}{section}
\hrulefill\ \ Version: \today\\
\vspace{3mm}
\begin{center}
{\Large Prop-Pack Repository\footnote{
\href{https://github.com/jonaprieto/prop-pack}{{\color{blue(munsell)}
\texttt{https://github.com/jonaprieto/prop-pack}}}}
}\\
\textbf{Jonathan Prieto-Cubides}\\ %You should put your name here
\href{mailto:jprieto9@eafit.edu.co}{{\color{blue(munsell)}\texttt{jprieto9@eafit.edu.co}}}
\end{center}
\vspace{0.1 cm}
\tableofcontents
\section{\tptp Format}
The \tptp format is a precise and accurate language to describe without
ambiguities problems written in a logic. It attempts to be a standard for
all Automatic Theorems Provers (ATP). The syntax of the TPTP format is based
on the Prolog language and endeavors to be processed with a similar parser for
such a language
\footnote{\tptp v6.4.0~\url{http://www.cs.miami.edu/~tptp/TPTP/SyntaxBNF.html}}.
The following is an example taken from the \tptp
Problems repository\footnote{\url{http://www.cs.miami.edu/~tptp/cgi-bin/SeeTPTP?Category=Problems}}.
\begin{lstlisting}
fof(a1, axiom, a).
cnf(an_2, axiom, (is_a_theorem(or(not(or(X,Y)) , or(Y,X))) )).
\end{lstlisting}
We present a subset of \tptp that use for first-order logic the keyword
\ttext{fof} and the keyword \ttext{cnf} to use the clause normal form.
Their grammars are as follows.
\label{syntax:fof}
\begin{grammar}
<cnf_annotated> ::= \textbf{cnf}(<name>,<formula_role>,<cnf_formula>,<annotations>).
<fof_annotated> ::= \textbf{fof}(<name>,<formula_role>,<fof_formula>,<annotations>).
\end{grammar}
The last parameter \ttext{annotations} is optional and the others parameters like
\ttext{name}, \ttext{formula_role}, \ttext{fof_formula}, \ttext{cnf_formula} have
the following definition.
\begin{grammar}
<name> ::= <atomic_word> | <integer>
<formula_role> ::= {\bf axiom} | hypothesis | definition | assumption
\alt lemma | theorem | corollary | {\bf conjecture}
\alt {\bf negated_conjecture} | {\bf plain }| type | unknown
\end{grammar}
% For the clausal normal form, we have the following excerpt.
\begin{figure}[!ht]
\centering
\label{syntax:cnfformula}
\begin{grammar}
<cnf_formula> ::= (<disjunction>) | <disjunction>
<disjunction> ::= <literal> | <disjunction> <vline> <literal>
<literal> ::= <atomic_formula> | ~ <atomic_formula> | <fol_infix_unary>
\end{grammar}
\caption{Grammar for CNF formulas}
\end{figure}
Some of the ATP systems can process problems formatted
in TPTP syntax for their input and output. In addition, there is an extension
version of TPTP to present solutions\footnote{\url{http://www.cs.miami.edu/~tptp/TSTP/}},
the TSTP syntax. Also, the TSTP (Thousands of Solutions from Theorem Provers) is
for a library of solutions to test problems for automated theorem proving (ATP)
systems. It has solutions to problems from the TPTP Problem Library.\par
\section{TPTP Problems}
\subsection{Basic}
\problemtptp[basic-01.tptp]{problems/basic/basic-01.tptp}{1}
\problemtptp[basic-02.tptp]{problems/basic/basic-02.tptp}{1}
\problemtptp[basic-03.tptp]{problems/basic/basic-03.tptp}{1}
\problemtptp[basic-04.tptp]{problems/basic/basic-04.tptp}{1}
\subsection{Conjunction}
\problemtptp[conj-01.tptp]{problems/conjunction/conj-01.tptp}{1}
\problemtptp[conj-02.tptp]{problems/conjunction/conj-02.tptp}{1}
\problemtptp[conj-03.tptp]{problems/conjunction/conj-03.tptp}{1}
\problemtptp[conj-04.tptp]{problems/conjunction/conj-04.tptp}{1}
\problemtptp[conj-05.tptp]{problems/conjunction/conj-05.tptp}{1}
\problemtptp[conj-06.tptp]{problems/conjunction/conj-06.tptp}{1}
\subsection{Implication}
\problemtptp[impl-01.tptp]{problems/implication/impl-01.tptp}{1}
\problemtptp[impl-02.tptp]{problems/implication/impl-02.tptp}{1}
\problemtptp[impl-03.tptp]{problems/implication/impl-03.tptp}{1}
\problemtptp[impl-04.tptp]{problems/implication/impl-04.tptp}{1}
\problemtptp[impl-05.tptp]{problems/implication/impl-05.tptp}{1}
\problemtptp[impl-06.tptp]{problems/implication/impl-06.tptp}{1}
\problemtptp[impl-07.tptp]{problems/implication/impl-07.tptp}{1}
\problemtptp[impl-08.tptp]{problems/implication/impl-08.tptp}{1}
\problemtptp[impl-09.tptp]{problems/implication/impl-09.tptp}{1}
\problemtptp[impl-10.tptp]{problems/implication/impl-10.tptp}{1}
\problemtptp[impl-11.tptp]{problems/implication/impl-11.tptp}{1}
\problemtptp[impl-12.tptp]{problems/implication/impl-12.tptp}{1}
\problemtptp[impl-13.tptp]{problems/implication/impl-13.tptp}{1}
\problemtptp[impl-14.tptp]{problems/implication/impl-14.tptp}{1}
\problemtptp[impl-15.tptp]{problems/implication/impl-15.tptp}{1}
\problemtptp[impl-16.tptp]{problems/implication/impl-16.tptp}{1}
\problemtptp[impl-17.tptp]{problems/implication/impl-17.tptp}{1}
\problemtptp[impl-18.tptp]{problems/implication/impl-18.tptp}{1}
\subsection{Disjunction}
%
\problemtptp[disj-01.tptp]{problems/disjunction/disj-01.tptp}{1}
\problemtptp[disj-02.tptp]{problems/disjunction/disj-02.tptp}{1}
\problemtptp[disj-03.tptp]{problems/disjunction/disj-03.tptp}{1}
\problemtptp[disj-04.tptp]{problems/disjunction/disj-04.tptp}{1}
\problemtptp[disj-05.tptp]{problems/disjunction/disj-05.tptp}{1}
\problemtptp[disj-06.tptp]{problems/disjunction/disj-06.tptp}{1}
\problemtptp[disj-07.tptp]{problems/disjunction/disj-07.tptp}{1}
\problemtptp[disj-08.tptp]{problems/disjunction/disj-08.tptp}{1}
\problemtptp[disj-09.tptp]{problems/disjunction/disj-09.tptp}{1}
\problemtptp[disj-10.tptp]{problems/disjunction/disj-10.tptp}{1}
\problemtptp[disj-11.tptp]{problems/disjunction/disj-11.tptp}{1}
\problemtptp[disj-12.tptp]{problems/disjunction/disj-12.tptp}{1}
\problemtptp[disj-13.tptp]{problems/disjunction/disj-13.tptp}{1}
\problemtptp[disj-14.tptp]{problems/disjunction/disj-14.tptp}{1}
\problemtptp[disj-15.tptp]{problems/disjunction/disj-15.tptp}{1}
%
\subsection{Biimplication}
\problemtptp[bicond-01.tptp]{problems/biconditional/bicond-01.tptp}{1}
\problemtptp[bicond-02.tptp]{problems/biconditional/bicond-02.tptp}{1}
\problemtptp[bicond-03.tptp]{problems/biconditional/bicond-03.tptp}{1}
\problemtptp[bicond-04.tptp]{problems/biconditional/bicond-04.tptp}{1}
\problemtptp[bicond-05.tptp]{problems/biconditional/bicond-05.tptp}{1}
\problemtptp[bicond-06.tptp]{problems/biconditional/bicond-06.tptp}{1}
\problemtptp[bicond-07.tptp]{problems/biconditional/bicond-07.tptp}{1}
\problemtptp[bicond-08.tptp]{problems/biconditional/bicond-08.tptp}{1}
\problemtptp[bicond-09.tptp]{problems/biconditional/bicond-09.tptp}{1}
\problemtptp[bicond-10.tptp]{problems/biconditional/bicond-10.tptp}{1}
\problemtptp[bicond-11.tptp]{problems/biconditional/bicond-11.tptp}{1}
\problemtptp[bicond-12.tptp]{problems/biconditional/bicond-12.tptp}{1}
\problemtptp[bicond-13.tptp]{problems/biconditional/bicond-13.tptp}{1}
\subsection{Negation}
\problemtptp[neg-01.tptp]{problems/negation/neg-01.tptp}{1}
\problemtptp[neg-02.tptp]{problems/negation/neg-02.tptp}{1}
\problemtptp[neg-03.tptp]{problems/negation/neg-03.tptp}{1}
\problemtptp[neg-04.tptp]{problems/negation/neg-04.tptp}{1}
\problemtptp[neg-05.tptp]{problems/negation/neg-05.tptp}{1}
\problemtptp[neg-06.tptp]{problems/negation/neg-06.tptp}{1}
\problemtptp[neg-07.tptp]{problems/negation/neg-07.tptp}{1}
\problemtptp[neg-08.tptp]{problems/negation/neg-08.tptp}{1}
\problemtptp[neg-09.tptp]{problems/negation/neg-09.tptp}{1}
\problemtptp[neg-10.tptp]{problems/negation/neg-10.tptp}{1}
\problemtptp[neg-11.tptp]{problems/negation/neg-11.tptp}{1}
\problemtptp[neg-12.tptp]{problems/negation/neg-12.tptp}{1}
\problemtptp[neg-13.tptp]{problems/negation/neg-13.tptp}{1}
\problemtptp[neg-14.tptp]{problems/negation/neg-14.tptp}{1}
\problemtptp[neg-15.tptp]{problems/negation/neg-15.tptp}{1}
\problemtptp[neg-16.tptp]{problems/negation/neg-16.tptp}{1}
\problemtptp[neg-17.tptp]{problems/negation/neg-17.tptp}{1}
\problemtptp[neg-18.tptp]{problems/negation/neg-18.tptp}{1}
\problemtptp[neg-19.tptp]{problems/negation/neg-19.tptp}{1}
\problemtptp[neg-20.tptp]{problems/negation/neg-20.tptp}{1}
\problemtptp[neg-21.tptp]{problems/negation/neg-21.tptp}{1}
\problemtptp[neg-22.tptp]{problems/negation/neg-22.tptp}{1}
\problemtptp[neg-23.tptp]{problems/negation/neg-23.tptp}{1}
\problemtptp[neg-24.tptp]{problems/negation/neg-24.tptp}{1}
\problemtptp[neg-25.tptp]{problems/negation/neg-25.tptp}{1}
\problemtptp[neg-26.tptp]{problems/negation/neg-26.tptp}{1}
\problemtptp[neg-27.tptp]{problems/negation/neg-27.tptp}{1}
\problemtptp[neg-28.tptp]{problems/negation/neg-28.tptp}{1}
\problemtptp[neg-29.tptp]{problems/negation/neg-29.tptp}{1}
\problemtptp[neg-30.tptp]{problems/negation/neg-30.tptp}{1}
\problemtptp[neg-31.tptp]{problems/negation/neg-31.tptp}{1}
\problemtptp[neg-32.tptp]{problems/negation/neg-32.tptp}{1}
\subsection{Additional Propositional Problems}
\problemtptp[prop-01.tptp]{problems/prop-metis/prop-01.tptp}{1}
\problemtptp[prop-02.tptp]{problems/prop-metis/prop-02.tptp}{1}
\problemtptp[prop-03.tptp]{problems/prop-metis/prop-03.tptp}{1}
\problemtptp[prop-04.tptp]{problems/prop-metis/prop-04.tptp}{1}
\problemtptp[prop-05.tptp]{problems/prop-metis/prop-05.tptp}{1}
\problemtptp[prop-06.tptp]{problems/prop-metis/prop-06.tptp}{1}
\problemtptp[prop-07.tptp]{problems/prop-metis/prop-07.tptp}{1}
\problemtptp[prop-08.tptp]{problems/prop-metis/prop-08.tptp}{1}
\problemtptp[prop-09.tptp]{problems/prop-metis/prop-09.tptp}{1}
\problemtptp[prop-10.tptp]{problems/prop-metis/prop-10.tptp}{1}
\problemtptp[prop-11.tptp]{problems/prop-metis/prop-11.tptp}{1}
\problemtptp[prop-12.tptp]{problems/prop-metis/prop-12.tptp}{1}
\problemtptp[prop-13.tptp]{problems/prop-metis/prop-13.tptp}{1}
\problemtptp[prop-14.tptp]{problems/prop-metis/prop-14.tptp}{1}
\problemtptp[prop-15.tptp]{problems/prop-metis/prop-15.tptp}{1}
\problemtptp[prop-16.tptp]{problems/prop-metis/prop-16.tptp}{1}
\problemtptp[prop-17.tptp]{problems/prop-metis/prop-17.tptp}{1}
\problemtptp[prop-18.tptp]{problems/prop-metis/prop-18.tptp}{1}
\problemtptp[prop-19.tptp]{problems/prop-metis/prop-19.tptp}{1}
\problemtptp[prop-20.tptp]{problems/prop-metis/prop-20.tptp}{1}
\problemtptp[prop-21.tptp]{problems/prop-metis/prop-21.tptp}{1}
\problemtptp[prop-22.tptp]{problems/prop-metis/prop-22.tptp}{1}
\problemtptp[prop-23.tptp]{problems/prop-metis/prop-23.tptp}{1}
\section{References}
\begin{thebibliography}{9}
\bibitem{alastair2017}
Car Alastair (2017). \textit{The Natural Deduction Pack}.
Revisited edition, Feb. 2017.
\end{thebibliography}
\end{document}