%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : CAT016-4 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:29:55 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   17 (  10 unt;   0 def)
%            Number of atoms       :   26 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   21 (  12   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   16 (   2 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(assume_a_exists,plain,
    there_exists(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),
    [] ).

cnf(172564744,plain,
    there_exists(a),
    inference(rewrite,[status(thm)],[assume_a_exists]),
    [] ).

fof(existence_and_equality_implies_equivalence1,plain,
    ! [A,B] :
      ( ~ there_exists(A)
      | ~ $equal(B,A)
      | equivalent(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),
    [] ).

cnf(172499200,plain,
    ( ~ there_exists(A)
    | ~ $equal(B,A)
    | equivalent(A,B) ),
    inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),
    [] ).

cnf(180360720,plain,
    ( ~ $equal(A,a)
    | equivalent(a,A) ),
    inference(resolution,[status(thm)],[172499200,172564744]),
    [] ).

fof(compose_domain,plain,
    ! [A] : $equal(compose(A,domain(A)),A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),
    [] ).

cnf(172556632,plain,
    $equal(compose(A,domain(A)),A),
    inference(rewrite,[status(thm)],[compose_domain]),
    [] ).

cnf(184533720,plain,
    equivalent(a,compose(a,domain(a))),
    inference(resolution,[status(thm)],[180360720,172556632]),
    [] ).

fof(equivalence_implies_existence2,plain,
    ! [A,B] :
      ( ~ equivalent(A,B)
      | $equal(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),
    [] ).

cnf(172486904,plain,
    ( ~ equivalent(A,B)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[equivalence_implies_existence2]),
    [] ).

cnf(185977152,plain,
    $equal(compose(a,domain(a)),a),
    inference(resolution,[status(thm)],[184533720,172486904]),
    [] ).

fof(composition_implies_domain,plain,
    ! [A,B] :
      ( ~ there_exists(compose(A,B))
      | there_exists(domain(A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),
    [] ).

cnf(172520072,plain,
    ( ~ there_exists(compose(A,B))
    | there_exists(domain(A)) ),
    inference(rewrite,[status(thm)],[composition_implies_domain]),
    [] ).

fof(prove_domain_of_a_exists,plain,
    ~ there_exists(domain(a)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),
    [] ).

cnf(172568712,plain,
    ~ there_exists(domain(a)),
    inference(rewrite,[status(thm)],[prove_domain_of_a_exists]),
    [] ).

cnf(180431464,plain,
    ~ there_exists(compose(a,A)),
    inference(resolution,[status(thm)],[172520072,172568712]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[172564744,185977152,180431464,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(assume_a_exists,plain,(there_exists(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),[]).
% 
% cnf(172564744,plain,(there_exists(a)),inference(rewrite,[status(thm)],[assume_a_exists]),[]).
% 
% fof(existence_and_equality_implies_equivalence1,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),[]).
% 
% cnf(172499200,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),[]).
% 
% cnf(180360720,plain,(~$equal(A,a)|equivalent(a,A)),inference(resolution,[status(thm)],[172499200,172564744]),[]).
% 
% fof(compose_domain,plain,($equal(compose(A,domain(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),[]).
% 
% cnf(172556632,plain,($equal(compose(A,domain(A)),A)),inference(rewrite,[status(thm)],[compose_domain]),[]).
% 
% cnf(184533720,plain,(equivalent(a,compose(a,domain(a)))),inference(resolution,[status(thm)],[180360720,172556632]),[]).
% 
% fof(equivalence_implies_existence2,plain,(~equivalent(A,B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),[]).
% 
% cnf(172486904,plain,(~equivalent(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[equivalence_implies_existence2]),[]).
% 
% cnf(185977152,plain,($equal(compose(a,domain(a)),a)),inference(resolution,[status(thm)],[184533720,172486904]),[]).
% 
% fof(composition_implies_domain,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),[]).
% 
% cnf(172520072,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),inference(rewrite,[status(thm)],[composition_implies_domain]),[]).
% 
% fof(prove_domain_of_a_exists,plain,(~there_exists(domain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-4.tptp',unknown),[]).
% 
% cnf(172568712,plain,(~there_exists(domain(a))),inference(rewrite,[status(thm)],[prove_domain_of_a_exists]),[]).
% 
% cnf(180431464,plain,(~there_exists(compose(a,A))),inference(resolution,[status(thm)],[172520072,172568712]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[172564744,185977152,180431464,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------