%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL051-1 : 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 11:32:40 EDT 2009

% Result   : Unsatisfiable 0.0s
% Output   : Refutation 0.0s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   10 (  10 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_the_bird_exists,plain,
    ! [A] : ~ $equal(response(A,A),A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL051-1.tptp',unknown),
    [] ).

cnf(158470744,plain,
    ~ $equal(response(A,A),A),
    inference(rewrite,[status(thm)],[prove_the_bird_exists]),
    [] ).

fof(mocking_bird_exists,plain,
    ! [A] : $equal(response(mocking_bird,A),response(A,A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL051-1.tptp',unknown),
    [] ).

cnf(158462064,plain,
    $equal(response(mocking_bird,A),response(A,A)),
    inference(rewrite,[status(thm)],[mocking_bird_exists]),
    [] ).

cnf(166238784,plain,
    ~ $equal(response(mocking_bird,A),A),
    inference(paramodulation,[status(thm)],[158470744,158462064,theory(equality)]),
    [] ).

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/COL051-1.tptp',unknown),
    [] ).

cnf(158466072,plain,
    $equal(response(A,response(B,C)),response(compose(A,B),C)),
    inference(rewrite,[status(thm)],[composer_exists]),
    [] ).

cnf(166317288,plain,
    ~ $equal(response(compose(mocking_bird,A),B),response(A,B)),
    inference(paramodulation,[status(thm)],[166238784,158466072,theory(equality)]),
    [] ).

cnf(166348920,plain,
    ~ $equal(response(compose(mocking_bird,mocking_bird),A),response(A,A)),
    inference(paramodulation,[status(thm)],[166317288,158462064,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(equality_resolution,[status(thm)],[166348920]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_the_bird_exists,plain,(~$equal(response(A,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL051-1.tptp',unknown),[]).
% 
% cnf(158470744,plain,(~$equal(response(A,A),A)),inference(rewrite,[status(thm)],[prove_the_bird_exists]),[]).
% 
% fof(mocking_bird_exists,plain,($equal(response(mocking_bird,A),response(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL051-1.tptp',unknown),[]).
% 
% cnf(158462064,plain,($equal(response(mocking_bird,A),response(A,A))),inference(rewrite,[status(thm)],[mocking_bird_exists]),[]).
% 
% cnf(166238784,plain,(~$equal(response(mocking_bird,A),A)),inference(paramodulation,[status(thm)],[158470744,158462064,theory(equality)]),[]).
% 
% fof(composer_exists,plain,($equal(response(A,response(B,C)),response(compose(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL051-1.tptp',unknown),[]).
% 
% cnf(158466072,plain,($equal(response(A,response(B,C)),response(compose(A,B),C))),inference(rewrite,[status(thm)],[composer_exists]),[]).
% 
% cnf(166317288,plain,(~$equal(response(compose(mocking_bird,A),B),response(A,B))),inference(paramodulation,[status(thm)],[166238784,158466072,theory(equality)]),[]).
% 
% cnf(166348920,plain,(~$equal(response(compose(mocking_bird,mocking_bird),A),response(A,A))),inference(paramodulation,[status(thm)],[166317288,158462064,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[166348920]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------