TPTP Axioms File: PUZ003-0.ax


%--------------------------------------------------------------------------
% File     : PUZ003-0 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Puzzles (Truthtellers and Liars)
% Axioms   : Truthtellers and Liars axioms for three types of people
% Version  : [ANL] axioms.
% English  : Axioms for three types of people; truthtellers, liars and
%            normal people.

% Refs     : [Smu78] Smullyan (1978), What is the name of this book?-The ri
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    8 (   3 non-Horn;   0 unit;   7 RR)
%            Number of atoms      :   23 (   0 equality)
%            Maximal clause size  :    4 (   3 average)
%            Number of predicates :    1 (   0 propositional; 1-1 arity)
%            Number of functors   :    4 (   0 constant; 1-2 arity)
%            Number of variables  :   12 (   0 singleton)
%            Maximal term depth   :    2 (   2 average)
% SPC      : 

% Comments :
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%-----The next 4 clauses says that a person is one thing
cnf(person_is_one_type,axiom,
    ( a_truth(truthteller(X))
    | a_truth(liar(X))
    | a_truth(normal(X)) )).

cnf(not_truthteller_and_normal,axiom,
    ( ~ a_truth(truthteller(X))
    | ~ a_truth(normal(X)) )).

cnf(not_truthteller_and_liar,axiom,
    ( ~ a_truth(truthteller(X))
    | ~ a_truth(liar(X)) )).

cnf(not_liar_and_normal,axiom,
    ( ~ a_truth(liar(X))
    | ~ a_truth(normal(X)) )).

cnf(truthtellers_tell_truth,axiom,
    ( ~ a_truth(truthteller(X))
    | ~ a_truth(says(X,Y))
    | a_truth(Y) )).

cnf(liars_lie,axiom,
    ( ~ a_truth(liar(X))
    | ~ a_truth(says(X,Y))
    | ~ a_truth(Y) )).

cnf(truthtellers_and_normal_tell_truth,axiom,
    ( ~ a_truth(X)
    | ~ a_truth(says(Y,X))
    | a_truth(truthteller(Y))
    | a_truth(normal(Y)) )).

cnf(liars_and_normal_lie,axiom,
    ( a_truth(X)
    | ~ a_truth(says(Y,X))
    | a_truth(liar(Y))
    | a_truth(normal(Y)) )).

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