%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT016-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 11:29:53 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% 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 : 22 ( 13 ~; 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 : 18 ( 5 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/CAT016-3.tptp',unknown),
[] ).
cnf(156657992,plain,
( ~ there_exists(A)
| ~ $equal(B,A)
| equivalent(A,B) ),
inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),
[] ).
fof(assume_a_exists,plain,
there_exists(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),
[] ).
cnf(156760608,plain,
there_exists(a),
inference(rewrite,[status(thm)],[assume_a_exists]),
[] ).
cnf(164557544,plain,
( ~ $equal(A,a)
| equivalent(a,A) ),
inference(resolution,[status(thm)],[156657992,156760608]),
[] ).
fof(compose_domain,plain,
! [A] : $equal(compose(A,domain(A)),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),
[] ).
cnf(156719736,plain,
$equal(compose(A,domain(A)),A),
inference(rewrite,[status(thm)],[compose_domain]),
[] ).
cnf(164608160,plain,
equivalent(a,compose(a,domain(a))),
inference(resolution,[status(thm)],[164557544,156719736]),
[] ).
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/CAT016-3.tptp',unknown),
[] ).
cnf(156683048,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/CAT016-3.tptp',unknown),
[] ).
cnf(156633296,plain,
~ there_exists(domain(a)),
inference(rewrite,[status(thm)],[prove_domain_of_a_exists]),
[] ).
cnf(165305896,plain,
~ there_exists(compose(a,A)),
inference(resolution,[status(thm)],[156683048,156633296]),
[] ).
fof(equivalence_implies_existence3,plain,
! [A,B] :
( ~ equivalent(A,B)
| there_exists(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),
[] ).
cnf(156727296,plain,
( ~ equivalent(A,B)
| there_exists(B) ),
inference(rewrite,[status(thm)],[equivalence_implies_existence3]),
[] ).
cnf(165531760,plain,
~ equivalent(B,compose(a,A)),
inference(resolution,[status(thm)],[165305896,156727296]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[164608160,165531760]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(existence_and_equality_implies_equivalence1,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),[]).
%
% cnf(156657992,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),[]).
%
% fof(assume_a_exists,plain,(there_exists(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),[]).
%
% cnf(156760608,plain,(there_exists(a)),inference(rewrite,[status(thm)],[assume_a_exists]),[]).
%
% cnf(164557544,plain,(~$equal(A,a)|equivalent(a,A)),inference(resolution,[status(thm)],[156657992,156760608]),[]).
%
% fof(compose_domain,plain,($equal(compose(A,domain(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),[]).
%
% cnf(156719736,plain,($equal(compose(A,domain(A)),A)),inference(rewrite,[status(thm)],[compose_domain]),[]).
%
% cnf(164608160,plain,(equivalent(a,compose(a,domain(a)))),inference(resolution,[status(thm)],[164557544,156719736]),[]).
%
% fof(composition_implies_domain,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),[]).
%
% cnf(156683048,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/CAT016-3.tptp',unknown),[]).
%
% cnf(156633296,plain,(~there_exists(domain(a))),inference(rewrite,[status(thm)],[prove_domain_of_a_exists]),[]).
%
% cnf(165305896,plain,(~there_exists(compose(a,A))),inference(resolution,[status(thm)],[156683048,156633296]),[]).
%
% fof(equivalence_implies_existence3,plain,(~equivalent(A,B)|there_exists(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT016-3.tptp',unknown),[]).
%
% cnf(156727296,plain,(~equivalent(A,B)|there_exists(B)),inference(rewrite,[status(thm)],[equivalence_implies_existence3]),[]).
%
% cnf(165531760,plain,(~equivalent(B,compose(a,A))),inference(resolution,[status(thm)],[165305896,156727296]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[164608160,165531760]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------