## TPTP Problem File: PUZ028-6.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : PUZ028-6 : TPTP v8.1.0. Released v2.0.0.
% Domain   : Puzzles
% Problem  : People at a party
% Version  : [SETHEO] axioms : Especial.
% English  : We can always choose 3 persons who are either familiar with
%            each other or not familiar with each other, from 6 persons
%            who meet at a party.

% Refs     :
% Source   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.00 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.00 v2.4.0, 0.50 v2.3.0, 0.00 v2.2.0, 0.67 v2.1.0
% Syntax   : Number of clauses     :   41 (  36 unt;   1 nHn;  41 RR)
%            Number of literals    :   51 (   0 equ;  11 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 1-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   12 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_NHN

% Comments : This version is unsatisfiable because familiarity is symmetric.
%--------------------------------------------------------------------------
cnf(person_1,axiom,
person(n1) ).

cnf(person_2,axiom,
person(n2) ).

cnf(person_3,axiom,
person(n3) ).

cnf(person_4,axiom,
person(n4) ).

cnf(person_5,axiom,
person(n5) ).

cnf(person_6,axiom,
person(n6) ).

cnf(not_equal_1_2,axiom,
not_equal(n1,n2) ).

cnf(not_equal_1_3,axiom,
not_equal(n1,n3) ).

cnf(not_equal_1_4,axiom,
not_equal(n1,n4) ).

cnf(not_equal_1_5,axiom,
not_equal(n1,n5) ).

cnf(not_equal_1_6,axiom,
not_equal(n1,n6) ).

cnf(not_equal_2_1,axiom,
not_equal(n2,n1) ).

cnf(not_equal_2_3,axiom,
not_equal(n2,n3) ).

cnf(not_equal_2_4,axiom,
not_equal(n2,n4) ).

cnf(not_equal_2_5,axiom,
not_equal(n2,n5) ).

cnf(not_equal_2_6,axiom,
not_equal(n2,n6) ).

cnf(not_equal_3_1,axiom,
not_equal(n3,n1) ).

cnf(not_equal_3_2,axiom,
not_equal(n3,n2) ).

cnf(not_equal_3_4,axiom,
not_equal(n3,n4) ).

cnf(not_equal_3_5,axiom,
not_equal(n3,n5) ).

cnf(not_equal_3_6,axiom,
not_equal(n3,n6) ).

cnf(not_equal_4_1,axiom,
not_equal(n4,n1) ).

cnf(not_equal_4_2,axiom,
not_equal(n4,n2) ).

cnf(not_equal_4_3,axiom,
not_equal(n4,n3) ).

cnf(not_equal_4_5,axiom,
not_equal(n4,n5) ).

cnf(not_equal_4_6,axiom,
not_equal(n4,n6) ).

cnf(not_equal_5_1,axiom,
not_equal(n5,n1) ).

cnf(not_equal_5_2,axiom,
not_equal(n5,n2) ).

cnf(not_equal_5_3,axiom,
not_equal(n5,n3) ).

cnf(not_equal_5_4,axiom,
not_equal(n5,n4) ).

cnf(not_equal_5_6,axiom,
not_equal(n5,n6) ).

cnf(not_equal_6_1,axiom,
not_equal(n6,n1) ).

cnf(not_equal_6_2,axiom,
not_equal(n6,n2) ).

cnf(not_equal_6_3,axiom,
not_equal(n6,n3) ).

cnf(not_equal_6_4,axiom,
not_equal(n6,n4) ).

cnf(not_equal_6_5,axiom,
not_equal(n6,n5) ).

cnf(familiar_or_not,axiom,
( familiar(X,Y)
| not_familiar(X,Y)
| ~ person(X)
| ~ person(Y)
| ~ not_equal(X,Y) ) ).

cnf(symmetry_of_familiar,axiom,
( ~ familiar(X1,X2)
| familiar(X2,X1) ) ).

cnf(symmetry_of_not_familiar,axiom,
( ~ not_familiar(X1,X2)
| not_familiar(X2,X1) ) ).

cnf(three_familiar,negated_conjecture,
( ~ familiar(X1,X2)
| ~ familiar(X2,X3)
| ~ familiar(X3,X1) ) ).

cnf(three_not_familiar,negated_conjecture,
( ~ not_familiar(X1,X2)
| ~ not_familiar(X2,X3)
| ~ not_familiar(X3,X1) ) ).

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