%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL056-1 : 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 11:32:53 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (  11 unt;   0 def)
%            Number of atoms       :   11 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   4 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_there_exists_a_happy_bird,plain,
    ! [A,B] : ~ $equal(response(A,B),B),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),
    [] ).

cnf(145935480,plain,
    ~ $equal(response(A,B),B),
    inference(rewrite,[status(thm)],[prove_there_exists_a_happy_bird]),
    [] ).

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/COL056-1.tptp',unknown),
    [] ).

cnf(145923040,plain,
    $equal(response(A,response(B,C)),response(compose(A,B),C)),
    inference(rewrite,[status(thm)],[composer_exists]),
    [] ).

cnf(153757808,plain,
    ~ $equal(response(B,response(C,A)),A),
    inference(paramodulation,[status(thm)],[145935480,145923040,theory(equality)]),
    [] ).

fof(a_to_b_responds_c,plain,
    $equal(response(a,b),c),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),
    [] ).

cnf(145927080,plain,
    $equal(response(a,b),c),
    inference(rewrite,[status(thm)],[a_to_b_responds_c]),
    [] ).

cnf(153841944,plain,
    ~ $equal(response(A,c),b),
    inference(paramodulation,[status(thm)],[153757808,145927080,theory(equality)]),
    [] ).

fof(a_to_c_responds_b,plain,
    $equal(response(a,c),b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),
    [] ).

cnf(145931112,plain,
    $equal(response(a,c),b),
    inference(rewrite,[status(thm)],[a_to_c_responds_b]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[153841944,145931112]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_there_exists_a_happy_bird,plain,(~$equal(response(A,B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),[]).
% 
% cnf(145935480,plain,(~$equal(response(A,B),B)),inference(rewrite,[status(thm)],[prove_there_exists_a_happy_bird]),[]).
% 
% fof(composer_exists,plain,($equal(response(A,response(B,C)),response(compose(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),[]).
% 
% cnf(145923040,plain,($equal(response(A,response(B,C)),response(compose(A,B),C))),inference(rewrite,[status(thm)],[composer_exists]),[]).
% 
% cnf(153757808,plain,(~$equal(response(B,response(C,A)),A)),inference(paramodulation,[status(thm)],[145935480,145923040,theory(equality)]),[]).
% 
% fof(a_to_b_responds_c,plain,($equal(response(a,b),c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),[]).
% 
% cnf(145927080,plain,($equal(response(a,b),c)),inference(rewrite,[status(thm)],[a_to_b_responds_c]),[]).
% 
% cnf(153841944,plain,(~$equal(response(A,c),b)),inference(paramodulation,[status(thm)],[153757808,145927080,theory(equality)]),[]).
% 
% fof(a_to_c_responds_b,plain,($equal(response(a,c),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL056-1.tptp',unknown),[]).
% 
% cnf(145931112,plain,($equal(response(a,c),b)),inference(rewrite,[status(thm)],[a_to_c_responds_b]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[153841944,145931112]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------