(* Title: HOL/ex/unsolved
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
Problems that currently defeat the MESON procedure as well as best_tac
*)
(*from Vladimir Lifschitz, What Is the Inverse Method?, JAR 5 1989. 1--23*)
(*27 clauses; 81 Horn clauses*)
goal HOL.thy "? x x'. ! y. ? z z'. (~P y y | P x x | ~S z x) & \
\ (S x y | ~S y z | Q z' z') & \
\ (Q x' y | ~Q y z' | S x' x')";
writeln"Problem 55";
(*Original, equational version by Len Schubert [via Pelletier] *)
goal HOL.thy
"(? x. lives x & killed x agatha) & \
\ lives agatha & lives butler & lives charles & \
\ (! x. lives x --> x=agatha | x=butler | x=charles) & \
\ (! x y. killed x y --> hates x y) & \
\ (! x y. killed x y --> ~richer x y) & \
\ (! x. hates agatha x --> ~hates charles x) & \
\ (! x. ~ x=butler --> hates agatha x) & \
\ (! x. ~richer x agatha --> hates butler x) & \
\ (! x. hates agatha x --> hates butler x) & \
\ (! x. ? y. ~hates x y) & \
\ ~ agatha=butler --> \
\ killed agatha agatha";
(*Halting problem: Formulation of Li Dafa (AAR Newsletter 27, Oct 1994.)
author U. Egly; 46 clauses; 264 Horn clauses*)
goal HOL.thy
"((EX X. (a X) & (ALL Y. (c Y) --> (ALL Z. (d X Y Z)))) --> \
\ (EX W. (c W) & (ALL Y. (c Y) --> (ALL Z. (d W Y Z))))) \
\ & \
\ (ALL W. (c W) & (ALL U. (c U) --> (ALL V. (d W U V))) --> \
\ (ALL Y Z. \
\ ((c Y) & (h2 Y Z) --> (h3 W Y Z) & (oo W g)) & \
\ ((c Y) & ~(h2 Y Z) --> (h3 W Y Z) & (oo W b)))) \
\ & \
\ (ALL W. (c W) & \
\ (ALL Y Z. \
\ ((c Y) & (h2 Y Z) --> (h3 W Y Z) & (oo W g)) & \
\ ((c Y) & ~(h2 Y Z) --> (h3 W Y Z) & (oo W b))) --> \
\ (EX V. (c V) & \
\ (ALL Y. (((c Y) & (h3 W Y Y)) & (oo W g) --> ~(h2 V Y)) & \
\ (((c Y) & (h3 W Y Y)) & (oo W b) --> (h2 V Y) & (oo V b))))) \
\ --> \
\ ~ (EX X. (a X) & (ALL Y. (c Y) --> (ALL Z. (d X Y Z))))";