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| 1 | +%------------------------------------------------------------------------------ |
| 2 | +% File : PUZ001+1 : TPTP v6.4.0. Released v2.0.0. |
| 3 | +% Domain : Puzzles |
| 4 | +% Problem : Dreadbury Mansion |
| 5 | +% Version : Especial. |
| 6 | +% Theorem formulation : Reduced > Complete. |
| 7 | +% English : Someone who lives in Dreadbury Mansion killed Aunt Agatha. |
| 8 | +% Agatha, the butler, and Charles live in Dreadbury Mansion, |
| 9 | +% and are the only people who live therein. A killer always |
| 10 | +% hates his victim, and is never richer than his victim. |
| 11 | +% Charles hates no one that Aunt Agatha hates. Agatha hates |
| 12 | +% everyone except the butler. The butler hates everyone not |
| 13 | +% richer than Aunt Agatha. The butler hates everyone Aunt |
| 14 | +% Agatha hates. No one hates everyone. Agatha is not the |
| 15 | +% butler. Therefore : Agatha killed herself. |
| 16 | + |
| 17 | +% Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au |
| 18 | +% : [Hah94] Haehnle (1994), Email to G. Sutcliffe |
| 19 | +% Source : [Hah94] |
| 20 | +% Names : Pelletier 55 [Pel86] |
| 21 | + |
| 22 | +% Status : Theorem |
| 23 | +% Rating : 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.26 v5.5.0, 0.07 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.14 v3.5.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.11 v3.2.0, 0.22 v3.1.0, 0.17 v2.7.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1, 0.00 v2.1.0 |
| 24 | +% Syntax : Number of formulae : 14 ( 6 unit) |
| 25 | +% Number of atoms : 24 ( 5 equality) |
| 26 | +% Maximal formula depth : 5 ( 3 average) |
| 27 | +% Number of connectives : 16 ( 6 ~; 2 |; 1 &) |
| 28 | +% ( 0 <=>; 7 =>; 0 <=; 0 <~>) |
| 29 | +% ( 0 ~|; 0 ~&) |
| 30 | +% Number of predicates : 5 ( 0 propositional; 1-2 arity) |
| 31 | +% Number of functors : 3 ( 3 constant; 0-0 arity) |
| 32 | +% Number of variables : 12 ( 0 sgn; 10 !; 2 ?) |
| 33 | +% Maximal term depth : 1 ( 1 average) |
| 34 | +% SPC : FOF_THM_RFO_SEQ |
| 35 | + |
| 36 | +% Comments : Modified by Geoff Sutcliffe. |
| 37 | +% : Also known as "Who killed Aunt Agatha" |
| 38 | +%------------------------------------------------------------------------------ |
| 39 | +%----Problem axioms |
| 40 | +fof(pel55_1,axiom, |
| 41 | + ( ? [X] : |
| 42 | + ( lives(X) |
| 43 | + & killed(X,agatha) ) )). |
| 44 | + |
| 45 | +fof(pel55_2_1,axiom, |
| 46 | + ( lives(agatha) )). |
| 47 | + |
| 48 | +fof(pel55_2_2,axiom, |
| 49 | + ( lives(butler) )). |
| 50 | + |
| 51 | +fof(pel55_2_3,axiom, |
| 52 | + ( lives(charles) )). |
| 53 | + |
| 54 | +fof(pel55_3,axiom, |
| 55 | + ( ! [X] : |
| 56 | + ( lives(X) |
| 57 | + => ( X = agatha |
| 58 | + | X = butler |
| 59 | + | X = charles ) ) )). |
| 60 | + |
| 61 | +fof(pel55_4,axiom, |
| 62 | + ( ! [X,Y] : |
| 63 | + ( killed(X,Y) |
| 64 | + => hates(X,Y) ) )). |
| 65 | + |
| 66 | +fof(pel55_5,axiom, |
| 67 | + ( ! [X,Y] : |
| 68 | + ( killed(X,Y) |
| 69 | + => ~ richer(X,Y) ) )). |
| 70 | + |
| 71 | +fof(pel55_6,axiom, |
| 72 | + ( ! [X] : |
| 73 | + ( hates(agatha,X) |
| 74 | + => ~ hates(charles,X) ) )). |
| 75 | + |
| 76 | +fof(pel55_7,axiom, |
| 77 | + ( ! [X] : |
| 78 | + ( X != butler |
| 79 | + => hates(agatha,X) ) )). |
| 80 | + |
| 81 | +fof(pel55_8,axiom, |
| 82 | + ( ! [X] : |
| 83 | + ( ~ richer(X,agatha) |
| 84 | + => hates(butler,X) ) )). |
| 85 | + |
| 86 | +fof(pel55_9,axiom, |
| 87 | + ( ! [X] : |
| 88 | + ( hates(agatha,X) |
| 89 | + => hates(butler,X) ) )). |
| 90 | + |
| 91 | +fof(pel55_10,axiom, |
| 92 | + ( ! [X] : |
| 93 | + ? [Y] : ~ hates(X,Y) )). |
| 94 | + |
| 95 | +fof(pel55_11,axiom, |
| 96 | + ( agatha != butler )). |
| 97 | + |
| 98 | +fof(pel55,conjecture, |
| 99 | + ( killed(agatha,agatha) )). |
| 100 | + |
| 101 | +%------------------------------------------------------------------------------ |
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