## TPTP Problem File: PUZ018-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : PUZ018-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% Domain   : Puzzles
% Problem  : The Interns
% Version  : Especial.
% English  : Three interns are residents of the same hospital. On only one
%            day of the week are all three interns on call. No intern
%            is on call on three consecutiveutive days. No two interns are
%            off on the same day more than once a week. The first intern
%            is off on Sunday, Tuesday, and Thursday. The second intern
%            is off on Thursday and Saturday. The third intern is off
%            on Sunday.  Which day of the week are all three interns
%            on call?

% Refs     : [Rap95] Raptis (1995), Email to G. Sutcliffe
% Source   : [ANL]
% Names    : interns.ver1.in [ANL]

% Status   : Unsatisfiable
% Rating   : 0.00 v6.2.0, 0.12 v6.1.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.25 v2.4.0, 0.00 v2.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :   48 (  40 unt;   2 nHn;  45 RR)
%            Number of literals    :   72 (   0 equ;  45 neg)
%            Maximal clause size   :    7 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   5 usr;   0 prp; 1-2 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :   17 (   1 sgn)
% SPC      : CNF_UNS_EPR_NEQ_NHN

% Comments : Dimitris Raptis pointed out [Rap95] that this was trivially
%            unsatisfiable, by resolving prove_all_on_one_day
%            [--all_on(Day)] with all_on_one_day.
% Bugfixes : v1.2.0 - Theorem clause prove_all_on_one_day grounded.
%--------------------------------------------------------------------------
cnf(all_on_a_on,axiom,
( ~ all_on(X)
| on(a,X) ) ).

cnf(all_on_b_on,axiom,
( ~ all_on(X)
| on(b,X) ) ).

cnf(all_on_c_on,axiom,
( ~ all_on(X)
| on(c,X) ) ).

cnf(all_on,axiom,
( all_on(X)
| ~ on(a,X)
| ~ on(b,X)
| ~ on(c,X) ) ).

cnf(all_on_well_defined,axiom,
( ~ all_on(X)
| ~ all_on(Y)
| same_day(X,Y) ) ).

cnf(monday_follows_sunday,axiom,
consecutive(sunday,monday) ).

cnf(tuesday_follows_monday,axiom,
consecutive(monday,tuesday) ).

cnf(wednesday_follows_tuesday,axiom,
consecutive(tuesday,wednesday) ).

cnf(thursday_follows_wednesday,axiom,
consecutive(wednesday,thursday) ).

cnf(friday_follows_thursday,axiom,
consecutive(thursday,friday) ).

cnf(staurday_follows_friday,axiom,
consecutive(friday,saturday) ).

cnf(sunday_follows_saturday,axiom,
consecutive(saturday,sunday) ).

cnf(reflexivity_for_same_person,axiom,
same_person(X,X) ).

cnf(a_not_b,axiom,
~ same_person(a,b) ).

cnf(a_not_c,axiom,
~ same_person(a,c) ).

cnf(b_not_c,axiom,
~ same_person(b,c) ).

cnf(reflexivity_for_same_day,axiom,
same_day(X,X) ).

cnf(sunday_not_monday,axiom,
~ same_day(sunday,monday) ).

cnf(sunday_not_tuesday,axiom,
~ same_day(sunday,tuesday) ).

cnf(sunday_not_wednesday,axiom,
~ same_day(sunday,wednesday) ).

cnf(sunday_not_thursday,axiom,
~ same_day(sunday,thursday) ).

cnf(sunday_not_friday,axiom,
~ same_day(sunday,friday) ).

cnf(sunday_not_saturday,axiom,
~ same_day(sunday,saturday) ).

cnf(monday_not_tuesday,axiom,
~ same_day(monday,tuesday) ).

cnf(monday_not_wednesday,axiom,
~ same_day(monday,wednesday) ).

cnf(monday_not_thursday,axiom,
~ same_day(monday,thursday) ).

cnf(monday_not_friday,axiom,
~ same_day(monday,friday) ).

cnf(monday_not_saturday,axiom,
~ same_day(monday,saturday) ).

cnf(tuesday_not_wednesday,axiom,
~ same_day(tuesday,wednesday) ).

cnf(tuesday_not_thursday,axiom,
~ same_day(tuesday,thursday) ).

cnf(tuesday_not_friday,axiom,
~ same_day(tuesday,friday) ).

cnf(tuesday_not_saturday,axiom,
~ same_day(tuesday,saturday) ).

cnf(wednesday_not_thursday,axiom,
~ same_day(wednesday,thursday) ).

cnf(wednesday_not_friday,axiom,
~ same_day(wednesday,friday) ).

cnf(wednesday_not_saturday,axiom,
~ same_day(wednesday,saturday) ).

cnf(thursday_not_friday,axiom,
~ same_day(thursday,friday) ).

cnf(thursday_not_saturday,axiom,
~ same_day(thursday,saturday) ).

cnf(friday_not_saturday,axiom,
~ same_day(friday,saturday) ).

cnf(all_on_one_day,hypothesis,
( all_on(sunday)
| all_on(monday)
| all_on(tuesday)
| all_on(wednesday)
| all_on(thursday)
| all_on(friday)
| all_on(saturday) ) ).

cnf(not_on_for_3_days,hypothesis,
( ~ consecutive(X,Y)
| ~ consecutive(Y,Z)
| ~ consecutive(Z,W)
| ~ on(U,X)
| ~ on(U,Y)
| ~ on(U,Z) ) ).

cnf(no_two_off_twice_together,hypothesis,
( on(X,Y)
| on(X,Z)
| on(W,Y)
| on(W,Z)
| same_person(X,W)
| same_day(Y,Z) ) ).

cnf(a_off_sunday,hypothesis,
~ on(a,sunday) ).

cnf(a_off_tuesday,hypothesis,
~ on(a,tuesday) ).

cnf(a_off_thursday,hypothesis,
~ on(a,thursday) ).

cnf(b_off_thursday,hypothesis,
~ on(b,thursday) ).

cnf(b_off_saturday,hypothesis,
~ on(b,saturday) ).

cnf(c_off_sunday,hypothesis,
~ on(c,sunday) ).

cnf(prove_all_on_friday,negated_conjecture,
~ all_on(friday) ).

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