%--------------------------------------------------------------------------
% File     : PUZ005-1 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Puzzles
% Problem  : The Lion and the Unicorn
% Version  : Especial.
% English  : Lion lies on Monday, Tuesday and Wednesday. Unicorn lies
%            on Thursday, Friday and Saturday. Both tell truth on other
%            days. Both say yesterday was one of their lying days. Prove
%            that today is Thursday.

% Refs     : [Smu78] Smullyan (1978), What is the Name of This Book? The Ri
%          : [OS85]  Ohlbach & Schmidt-Schauss M. (1985), The Lion and the
% Source   : [OS85]
% Names    : Lion and the Unicorn [OS85]

% Status   : Unsatisfiable
% Rating   : 0.00 v2.5.0, 0.20 v2.4.0, 0.00 v2.2.1, 0.25 v2.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :   51 (   3 unt;   6 nHn;  48 RR)
%            Number of literals    :  112 (   0 equ;  71 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   9 usr;   0 prp; 1-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   56 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_NHN

% Comments :
%--------------------------------------------------------------------------
cnf(it_is_a_day,axiom,
    ( monday(X)
    | tuesday(X)
    | wednesday(X)
    | thursday(X)
    | friday(X)
    | saturday(X)
    | sunday(X) ) ).

cnf(monday_not_tuesday,axiom,
    ( ~ monday(X)
    | ~ tuesday(X) ) ).

cnf(monday_not_wednesday,axiom,
    ( ~ monday(X)
    | ~ wednesday(X) ) ).

cnf(monday_not_thursday,axiom,
    ( ~ monday(X)
    | ~ thursday(X) ) ).

cnf(monday_not_friday,axiom,
    ( ~ monday(X)
    | ~ friday(X) ) ).

cnf(monday_not_saturday,axiom,
    ( ~ monday(X)
    | ~ saturday(X) ) ).

cnf(monday_not_sunday,axiom,
    ( ~ monday(X)
    | ~ sunday(X) ) ).

cnf(tuesday_not_wednesday,axiom,
    ( ~ tuesday(X)
    | ~ wednesday(X) ) ).

cnf(tuesday_not_thursday,axiom,
    ( ~ tuesday(X)
    | ~ thursday(X) ) ).

cnf(tuesday_not_friday,axiom,
    ( ~ tuesday(X)
    | ~ friday(X) ) ).

cnf(tuesday_not_saturday,axiom,
    ( ~ tuesday(X)
    | ~ saturday(X) ) ).

cnf(tuesday_not_sunday,axiom,
    ( ~ tuesday(X)
    | ~ sunday(X) ) ).

cnf(wednesday_not_thursday,axiom,
    ( ~ wednesday(X)
    | ~ thursday(X) ) ).

cnf(wednesday_not_friday,axiom,
    ( ~ wednesday(X)
    | ~ friday(X) ) ).

cnf(wednesday_not_saturday,axiom,
    ( ~ wednesday(X)
    | ~ saturday(X) ) ).

cnf(wednesday_not_sunday,axiom,
    ( ~ wednesday(X)
    | ~ sunday(X) ) ).

cnf(thursday_not_friday,axiom,
    ( ~ thursday(X)
    | ~ friday(X) ) ).

cnf(thursday_not_saturday,axiom,
    ( ~ thursday(X)
    | ~ saturday(X) ) ).

cnf(thursday_not_sunday,axiom,
    ( ~ thursday(X)
    | ~ sunday(X) ) ).

cnf(friday_not_saturday,axiom,
    ( ~ friday(X)
    | ~ saturday(X) ) ).

cnf(friday_not_sunday,axiom,
    ( ~ friday(X)
    | ~ sunday(X) ) ).

cnf(saturday_not_sunday,axiom,
    ( ~ saturday(X)
    | ~ sunday(X) ) ).

cnf(monday_yesterday,axiom,
    ( ~ monday(yesterday(X))
    | tuesday(X) ) ).

cnf(tuesday_yesterday,axiom,
    ( ~ tuesday(yesterday(X))
    | wednesday(X) ) ).

cnf(wednesday_yesterday,axiom,
    ( ~ wednesday(yesterday(X))
    | thursday(X) ) ).

cnf(thursday_yesterday,axiom,
    ( ~ thursday(yesterday(X))
    | friday(X) ) ).

cnf(friday_yesterday,axiom,
    ( ~ friday(yesterday(X))
    | saturday(X) ) ).

cnf(saturday_yesterday,axiom,
    ( ~ saturday(yesterday(X))
    | sunday(X) ) ).

cnf(sunday_yesterday,axiom,
    ( ~ sunday(yesterday(X))
    | monday(X) ) ).

cnf(yesterday_monday,axiom,
    ( monday(yesterday(X))
    | ~ tuesday(X) ) ).

cnf(yesterday_tuesday,axiom,
    ( tuesday(yesterday(X))
    | ~ wednesday(X) ) ).

cnf(yesterday_wednesday,axiom,
    ( wednesday(yesterday(X))
    | ~ thursday(X) ) ).

cnf(yesterday_thursday,axiom,
    ( thursday(yesterday(X))
    | ~ friday(X) ) ).

cnf(yesterday_friday,axiom,
    ( friday(yesterday(X))
    | ~ saturday(X) ) ).

cnf(yesterday_saturday,axiom,
    ( saturday(yesterday(X))
    | ~ sunday(X) ) ).

cnf(yesterday_sunday,axiom,
    ( sunday(yesterday(X))
    | ~ monday(X) ) ).

cnf(lions_lying_days,axiom,
    ( ~ member(X,lying_days(lion))
    | monday(X)
    | tuesday(X)
    | wednesday(X) ) ).

cnf(unicorns_lying_days,axiom,
    ( ~ member(X,lying_days(unicorn))
    | thursday(X)
    | friday(X)
    | saturday(X) ) ).

cnf(lion_lies_on_monday,axiom,
    ( ~ monday(X)
    | member(X,lying_days(lion)) ) ).

cnf(lion_lies_on_tuesday,axiom,
    ( ~ tuesday(X)
    | member(X,lying_days(lion)) ) ).

cnf(lion_lies_on_wednesday,axiom,
    ( ~ wednesday(X)
    | member(X,lying_days(lion)) ) ).

cnf(unicorn_lies_on_thursday,axiom,
    ( ~ thursday(X)
    | member(X,lying_days(unicorn)) ) ).

cnf(unicorn_lies_on_friday,axiom,
    ( ~ friday(X)
    | member(X,lying_days(unicorn)) ) ).

cnf(unicorn_lies_on_saturday,axiom,
    ( ~ saturday(X)
    | member(X,lying_days(unicorn)) ) ).

cnf(admissions1,axiom,
    ( member(X,lying_days(T))
    | ~ admits(T,X,Y)
    | member(Y,lying_days(T)) ) ).

cnf(admissions2,axiom,
    ( member(X,lying_days(T))
    | admits(T,X,Y)
    | ~ member(Y,lying_days(T)) ) ).

cnf(admissions3,axiom,
    ( ~ member(X,lying_days(T))
    | ~ admits(T,X,Y)
    | ~ member(Y,lying_days(T)) ) ).

cnf(admissions4,axiom,
    ( ~ member(X,lying_days(T))
    | admits(T,X,Y)
    | member(Y,lying_days(T)) ) ).

cnf(admissions5,axiom,
    admits(lion,today,yesterday(today)) ).

cnf(admissions6,axiom,
    admits(unicorn,today,yesterday(today)) ).

cnf(prove_today_is_thursday,negated_conjecture,
    ~ thursday(today) ).

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