%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : FLD006-3 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:47:14 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   6 unt;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   6   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :    8 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(existence_of_inverse_addition,plain,
    ! [A] :
      ( sum(additive_inverse(A),A,additive_identity)
      | ~ defined(A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),
    [] ).

cnf(160011760,plain,
    ( sum(additive_inverse(A),A,additive_identity)
    | ~ defined(A) ),
    inference(rewrite,[status(thm)],[existence_of_inverse_addition]),
    [] ).

fof(well_definedness_of_additive_identity,plain,
    defined(additive_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),
    [] ).

cnf(160089408,plain,
    defined(additive_identity),
    inference(rewrite,[status(thm)],[well_definedness_of_additive_identity]),
    [] ).

cnf(168026560,plain,
    sum(additive_inverse(additive_identity),additive_identity,additive_identity),
    inference(resolution,[status(thm)],[160011760,160089408]),
    [] ).

fof(commutativity_addition,plain,
    ! [A,B,C] :
      ( sum(A,B,C)
      | ~ sum(B,A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),
    [] ).

cnf(160015704,plain,
    ( sum(A,B,C)
    | ~ sum(B,A,C) ),
    inference(rewrite,[status(thm)],[commutativity_addition]),
    [] ).

fof(not_sum_1,plain,
    ~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),
    [] ).

cnf(160193048,plain,
    ~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
    inference(rewrite,[status(thm)],[not_sum_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[168026560,160015704,160193048]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(existence_of_inverse_addition,plain,(sum(additive_inverse(A),A,additive_identity)|~defined(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),[]).
% 
% cnf(160011760,plain,(sum(additive_inverse(A),A,additive_identity)|~defined(A)),inference(rewrite,[status(thm)],[existence_of_inverse_addition]),[]).
% 
% fof(well_definedness_of_additive_identity,plain,(defined(additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),[]).
% 
% cnf(160089408,plain,(defined(additive_identity)),inference(rewrite,[status(thm)],[well_definedness_of_additive_identity]),[]).
% 
% cnf(168026560,plain,(sum(additive_inverse(additive_identity),additive_identity,additive_identity)),inference(resolution,[status(thm)],[160011760,160089408]),[]).
% 
% fof(commutativity_addition,plain,(sum(A,B,C)|~sum(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),[]).
% 
% cnf(160015704,plain,(sum(A,B,C)|~sum(B,A,C)),inference(rewrite,[status(thm)],[commutativity_addition]),[]).
% 
% fof(not_sum_1,plain,(~sum(additive_identity,additive_inverse(additive_identity),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/FLD/FLD006-3.tptp',unknown),[]).
% 
% cnf(160193048,plain,(~sum(additive_identity,additive_inverse(additive_identity),additive_identity)),inference(rewrite,[status(thm)],[not_sum_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[168026560,160015704,160193048]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------