%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : PUZ024-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:11:24 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   9 unt;   0 def)
%            Number of atoms       :   34 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   28 (  10   ~;  18   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   15 (   1 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(all_truthtellers,plain,
    ! [A,B,C] :
      ( a_truth(all_are_liars)
      | ~ people(A,B,C)
      | a_truth(truthteller(A))
      | a_truth(truthteller(B))
      | a_truth(truthteller(C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),
    [] ).

cnf(163969216,plain,
    ( a_truth(all_are_liars)
    | ~ people(A,B,C)
    | a_truth(truthteller(A))
    | a_truth(truthteller(B))
    | a_truth(truthteller(C)) ),
    inference(rewrite,[status(thm)],[all_truthtellers]),
    [] ).

fof(prove_there_is_a_truthteller,plain,
    ! [A] : ~ a_truth(truthteller(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),
    [] ).

cnf(163997304,plain,
    ~ a_truth(truthteller(A)),
    inference(rewrite,[status(thm)],[prove_there_is_a_truthteller]),
    [] ).

fof(truths_are_told_by_truthtellers,plain,
    ! [A,B] :
      ( ~ a_truth(A)
      | ~ a_truth(says(B,A))
      | a_truth(truthteller(B)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),
    [] ).

cnf(163882312,plain,
    ( ~ a_truth(A)
    | ~ a_truth(says(B,A))
    | a_truth(truthteller(B)) ),
    inference(rewrite,[status(thm)],[truths_are_told_by_truthtellers]),
    [] ).

fof(a_says_all_are_liars,plain,
    a_truth(says(a,all_are_liars)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),
    [] ).

cnf(163846368,plain,
    a_truth(says(a,all_are_liars)),
    inference(rewrite,[status(thm)],[a_says_all_are_liars]),
    [] ).

cnf(172047776,plain,
    ~ a_truth(all_are_liars),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[163997304,163882312,163846368]),
    [] ).

cnf(172179592,plain,
    ( ~ people(A,B,C)
    | a_truth(truthteller(A))
    | a_truth(truthteller(B))
    | a_truth(truthteller(C)) ),
    inference(resolution,[status(thm)],[163969216,172047776]),
    [] ).

fof(b_c_a_people,plain,
    people(b,c,a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),
    [] ).

cnf(163973800,plain,
    people(b,c,a),
    inference(rewrite,[status(thm)],[b_c_a_people]),
    [] ).

cnf(172189032,plain,
    ( a_truth(truthteller(b))
    | a_truth(truthteller(c))
    | a_truth(truthteller(a)) ),
    inference(resolution,[status(thm)],[172179592,163973800]),
    [] ).

cnf(172319560,plain,
    ( a_truth(truthteller(c))
    | a_truth(truthteller(a)) ),
    inference(resolution,[status(thm)],[172189032,163997304]),
    [] ).

cnf(172329872,plain,
    a_truth(truthteller(a)),
    inference(resolution,[status(thm)],[172319560,163997304]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[172329872,163997304]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(all_truthtellers,plain,(a_truth(all_are_liars)|~people(A,B,C)|a_truth(truthteller(A))|a_truth(truthteller(B))|a_truth(truthteller(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),[]).
% 
% cnf(163969216,plain,(a_truth(all_are_liars)|~people(A,B,C)|a_truth(truthteller(A))|a_truth(truthteller(B))|a_truth(truthteller(C))),inference(rewrite,[status(thm)],[all_truthtellers]),[]).
% 
% fof(prove_there_is_a_truthteller,plain,(~a_truth(truthteller(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),[]).
% 
% cnf(163997304,plain,(~a_truth(truthteller(A))),inference(rewrite,[status(thm)],[prove_there_is_a_truthteller]),[]).
% 
% fof(truths_are_told_by_truthtellers,plain,(~a_truth(A)|~a_truth(says(B,A))|a_truth(truthteller(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),[]).
% 
% cnf(163882312,plain,(~a_truth(A)|~a_truth(says(B,A))|a_truth(truthteller(B))),inference(rewrite,[status(thm)],[truths_are_told_by_truthtellers]),[]).
% 
% fof(a_says_all_are_liars,plain,(a_truth(says(a,all_are_liars))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),[]).
% 
% cnf(163846368,plain,(a_truth(says(a,all_are_liars))),inference(rewrite,[status(thm)],[a_says_all_are_liars]),[]).
% 
% cnf(172047776,plain,(~a_truth(all_are_liars)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163997304,163882312,163846368]),[]).
% 
% cnf(172179592,plain,(~people(A,B,C)|a_truth(truthteller(A))|a_truth(truthteller(B))|a_truth(truthteller(C))),inference(resolution,[status(thm)],[163969216,172047776]),[]).
% 
% fof(b_c_a_people,plain,(people(b,c,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/PUZ/PUZ024-1.tptp',unknown),[]).
% 
% cnf(163973800,plain,(people(b,c,a)),inference(rewrite,[status(thm)],[b_c_a_people]),[]).
% 
% cnf(172189032,plain,(a_truth(truthteller(b))|a_truth(truthteller(c))|a_truth(truthteller(a))),inference(resolution,[status(thm)],[172179592,163973800]),[]).
% 
% cnf(172319560,plain,(a_truth(truthteller(c))|a_truth(truthteller(a))),inference(resolution,[status(thm)],[172189032,163997304]),[]).
% 
% cnf(172329872,plain,(a_truth(truthteller(a))),inference(resolution,[status(thm)],[172319560,163997304]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[172329872,163997304]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------