## TPTP Problem File: PUZ001-1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : PUZ001-1 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Puzzles
% Version  : Especial.
%            Theorem formulation : Made unsatisfiable.
% English  : Someone who lives in Dreadbury Mansion killed Aunt Agatha.
%            Agatha, the butler, and Charles live in Dreadbury Mansion,
%            and are the only people who live therein. A killer always
%            hates his victim, and is never richer than his victim.
%            Charles hates no one that Aunt Agatha hates. Agatha hates
%            everyone except the butler. The butler hates everyone not
%            richer than Aunt Agatha. The butler hates everyone Aunt
%            Agatha hates. No one hates everyone. Agatha is not the
%            butler. Therefore : Agatha killed herself.

% Refs     : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
%          : [MB88]  Manthey & Bry (1988), SATCHMO: A Theorem Prover Implem
% Source   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.00 v2.0.0
% Syntax   : Number of clauses     :   12 (   5 unt;   2 nHn;  12 RR)
%            Number of literals    :   21 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 1-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    8 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_NHN

% Comments : Modified from the [MB88] version to be unsatisfiable, by Geoff
%            Sutcliffe.
%          : Also known as "Who killed Aunt Agatha"
%------------------------------------------------------------------------------
cnf(agatha,hypothesis,
lives(agatha) ).

cnf(butler,hypothesis,
lives(butler) ).

cnf(charles,hypothesis,
lives(charles) ).

cnf(poorer_killer,hypothesis,
( ~ killed(X,Y)
| ~ richer(X,Y) ) ).

cnf(different_hates,hypothesis,
( ~ hates(agatha,X)
| ~ hates(charles,X) ) ).

cnf(no_one_hates_everyone,hypothesis,
( ~ hates(X,agatha)
| ~ hates(X,butler)
| ~ hates(X,charles) ) ).

cnf(agatha_hates_agatha,hypothesis,
hates(agatha,agatha) ).

cnf(agatha_hates_charles,hypothesis,
hates(agatha,charles) ).

cnf(killer_hates_victim,hypothesis,
( ~ killed(X,Y)
| hates(X,Y) ) ).

cnf(same_hates,hypothesis,
( ~ hates(agatha,X)
| hates(butler,X) ) ).

cnf(butler_hates_poor,hypothesis,
( ~ lives(X)
| richer(X,agatha)
| hates(butler,X) ) ).

%----Literal dropped from here to make it unsatisfiable
cnf(prove_neither_charles_nor_butler_did_it,negated_conjecture,
( killed(butler,agatha)
| killed(charles,agatha) ) ).

%------------------------------------------------------------------------------
```