clasohm@1465: (*  Title:      HOL/ex/unsolved
clasohm@969:     ID:         $Id$
clasohm@1465:     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@969:     Copyright   1992  University of Cambridge
clasohm@969: 
clasohm@969: Problems that currently defeat the MESON procedure as well as best_tac
clasohm@969: *)
clasohm@969: 
paulson@1586: (*from Vladimir Lifschitz, What Is the Inverse Method?, JAR 5  1989.  1--23*)
paulson@2031:         (*27 clauses; 81 Horn clauses*)
paulson@1586: goal HOL.thy "? x x'. ! y. ? z z'. (~P y y | P x x | ~S z x) & \
paulson@1586: \                                  (S x y | ~S y z | Q z' z')  & \
paulson@1586: \                                  (Q x' y | ~Q y z' | S x' x')";
clasohm@969: 
clasohm@969: 
clasohm@969: 
clasohm@969: writeln"Problem 55";
clasohm@969: 
paulson@1586: (*Original, equational version by Len Schubert [via Pelletier] *)
clasohm@969: goal HOL.thy
paulson@1586:   "(? x. lives x & killed x agatha) & \
paulson@1586: \  lives agatha & lives butler & lives charles & \
paulson@1586: \  (! x. lives x --> x=agatha | x=butler | x=charles) & \
paulson@1586: \  (! x y. killed x y --> hates x y) & \
paulson@1586: \  (! x y. killed x y --> ~richer x y) & \
paulson@1586: \  (! x. hates agatha x --> ~hates charles x) & \
paulson@1586: \  (! x. ~ x=butler --> hates agatha x) & \
paulson@1586: \  (! x. ~richer x agatha --> hates butler x) & \
paulson@1586: \  (! x. hates agatha x --> hates butler x) & \
paulson@1586: \  (! x. ? y. ~hates x y) & \
clasohm@969: \  ~ agatha=butler --> \
paulson@1586: \  killed agatha agatha";
clasohm@969: 
paulson@1586: (*Halting problem: Formulation of Li Dafa (AAR Newsletter 27, Oct 1994.)
paulson@2031:         author U. Egly;  46 clauses; 264 Horn clauses*)
paulson@1586: goal HOL.thy
paulson@1586:  "((EX X. (a X) & (ALL Y. (c Y) --> (ALL Z. (d X Y Z)))) -->  \
paulson@1586: \  (EX W. (c W) & (ALL Y. (c Y) --> (ALL Z. (d W Y Z)))))     \
paulson@1586: \ &                                                          \
paulson@1586: \ (ALL W. (c W) & (ALL U. (c U) --> (ALL V. (d W U V))) -->       \
paulson@1586: \       (ALL Y Z.                                               \
paulson@1586: \           ((c Y) & (h2 Y Z) --> (h3 W Y Z) & (oo W g)) &       \
paulson@1586: \           ((c Y) & ~(h2 Y Z) --> (h3 W Y Z) & (oo W b))))  \
paulson@1586: \ &                    \
paulson@1586: \ (ALL W. (c W) &       \
paulson@1586: \   (ALL Y Z.          \
paulson@1586: \       ((c Y) & (h2 Y Z) --> (h3 W Y Z) & (oo W g)) &       \
paulson@1586: \       ((c Y) & ~(h2 Y Z) --> (h3 W Y Z) & (oo W b))) -->       \
paulson@1586: \   (EX V. (c V) &       \
paulson@1586: \         (ALL Y. (((c Y) & (h3 W Y Y)) & (oo W g) --> ~(h2 V Y)) &       \
paulson@1586: \                 (((c Y) & (h3 W Y Y)) & (oo W b) --> (h2 V Y) & (oo V b))))) \
paulson@1586: \  -->                  \
paulson@1586: \  ~ (EX X. (a X) & (ALL Y. (c Y) --> (ALL Z. (d X Y Z))))";
clasohm@969: