%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL054-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.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 11:32:49 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    9 (   7 unt;   0 def)
%            Number of atoms       :   11 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   6   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_birds_are_compatible,plain,
    ! [A,B] :
      ( ~ $equal(response(a,A),B)
      | ~ $equal(response(b,B),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL054-1.tptp',unknown),
    [] ).

cnf(146963960,plain,
    ( ~ $equal(response(a,A),B)
    | ~ $equal(response(b,B),A) ),
    inference(rewrite,[status(thm)],[prove_birds_are_compatible]),
    [] ).

fof(composer_exists,plain,
    ! [A,B,C] : $equal(response(A,response(B,C)),response(compose(A,B),C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL054-1.tptp',unknown),
    [] ).

cnf(146942784,plain,
    $equal(response(A,response(B,C)),response(compose(A,B),C)),
    inference(rewrite,[status(thm)],[composer_exists]),
    [] ).

cnf(154781072,plain,
    ~ $equal(response(b,response(compose(a,A),B)),response(A,B)),
    inference(resolution,[status(thm)],[146963960,146942784]),
    [] ).

fof(mocking_bird_exists,plain,
    ! [A] : $equal(response(mocking_bird,A),response(A,A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL054-1.tptp',unknown),
    [] ).

cnf(146938712,plain,
    $equal(response(mocking_bird,A),response(A,A)),
    inference(rewrite,[status(thm)],[mocking_bird_exists]),
    [] ).

cnf(155150584,plain,
    ~ $equal(response(b,response(compose(a,mocking_bird),A)),response(A,A)),
    inference(paramodulation,[status(thm)],[154781072,146938712,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[155150584,146942784]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_birds_are_compatible,plain,(~$equal(response(a,A),B)|~$equal(response(b,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL054-1.tptp',unknown),[]).
% 
% cnf(146963960,plain,(~$equal(response(a,A),B)|~$equal(response(b,B),A)),inference(rewrite,[status(thm)],[prove_birds_are_compatible]),[]).
% 
% fof(composer_exists,plain,($equal(response(A,response(B,C)),response(compose(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL054-1.tptp',unknown),[]).
% 
% cnf(146942784,plain,($equal(response(A,response(B,C)),response(compose(A,B),C))),inference(rewrite,[status(thm)],[composer_exists]),[]).
% 
% cnf(154781072,plain,(~$equal(response(b,response(compose(a,A),B)),response(A,B))),inference(resolution,[status(thm)],[146963960,146942784]),[]).
% 
% fof(mocking_bird_exists,plain,($equal(response(mocking_bird,A),response(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL054-1.tptp',unknown),[]).
% 
% cnf(146938712,plain,($equal(response(mocking_bird,A),response(A,A))),inference(rewrite,[status(thm)],[mocking_bird_exists]),[]).
% 
% cnf(155150584,plain,(~$equal(response(b,response(compose(a,mocking_bird),A)),response(A,A))),inference(paramodulation,[status(thm)],[154781072,146938712,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[155150584,146942784]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------