src/HOL/ex/unsolved.ML
 author paulson Wed Nov 05 13:23:46 1997 +0100 (1997-11-05) changeset 4153 e534c4c32d54 parent 2031 03a843f0f447 permissions -rw-r--r--
Ran expandshort, especially to introduce Safe_tac
1 (*  Title:      HOL/ex/unsolved
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4     Copyright   1992  University of Cambridge
6 Problems that currently defeat the MESON procedure as well as best_tac
7 *)
9 (*from Vladimir Lifschitz, What Is the Inverse Method?, JAR 5  1989.  1--23*)
10         (*27 clauses; 81 Horn clauses*)
11 goal HOL.thy "? x x'. ! y. ? z z'. (~P y y | P x x | ~S z x) & \
12 \                                  (S x y | ~S y z | Q z' z')  & \
13 \                                  (Q x' y | ~Q y z' | S x' x')";
17 writeln"Problem 55";
19 (*Original, equational version by Len Schubert [via Pelletier] *)
20 goal HOL.thy
21   "(? x. lives x & killed x agatha) & \
22 \  lives agatha & lives butler & lives charles & \
23 \  (! x. lives x --> x=agatha | x=butler | x=charles) & \
24 \  (! x y. killed x y --> hates x y) & \
25 \  (! x y. killed x y --> ~richer x y) & \
26 \  (! x. hates agatha x --> ~hates charles x) & \
27 \  (! x. ~ x=butler --> hates agatha x) & \
28 \  (! x. ~richer x agatha --> hates butler x) & \
29 \  (! x. hates agatha x --> hates butler x) & \
30 \  (! x. ? y. ~hates x y) & \
31 \  ~ agatha=butler --> \
32 \  killed agatha agatha";
34 (*Halting problem: Formulation of Li Dafa (AAR Newsletter 27, Oct 1994.)
35         author U. Egly;  46 clauses; 264 Horn clauses*)
36 goal HOL.thy
37  "((EX X. (a X) & (ALL Y. (c Y) --> (ALL Z. (d X Y Z)))) -->  \
38 \  (EX W. (c W) & (ALL Y. (c Y) --> (ALL Z. (d W Y Z)))))     \
39 \ &                                                          \
40 \ (ALL W. (c W) & (ALL U. (c U) --> (ALL V. (d W U V))) -->       \
41 \       (ALL Y Z.                                               \
42 \           ((c Y) & (h2 Y Z) --> (h3 W Y Z) & (oo W g)) &       \
43 \           ((c Y) & ~(h2 Y Z) --> (h3 W Y Z) & (oo W b))))  \
44 \ &                    \
45 \ (ALL W. (c W) &       \
46 \   (ALL Y Z.          \
47 \       ((c Y) & (h2 Y Z) --> (h3 W Y Z) & (oo W g)) &       \
48 \       ((c Y) & ~(h2 Y Z) --> (h3 W Y Z) & (oo W b))) -->       \
49 \   (EX V. (c V) &       \
50 \         (ALL Y. (((c Y) & (h3 W Y Y)) & (oo W g) --> ~(h2 V Y)) &       \
51 \                 (((c Y) & (h3 W Y Y)) & (oo W b) --> (h2 V Y) & (oo V b))))) \
52 \  -->                  \
53 \  ~ (EX X. (a X) & (ALL Y. (c Y) --> (ALL Z. (d X Y Z))))";