TSTP Solution File: CAT017-4 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT017-4 : 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 11:29:59 EDT 2009
% Result : Unsatisfiable 0.4s
% Output : Refutation 0.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(domain_has_elements,plain,
! [A] :
( ~ there_exists(domain(A))
| there_exists(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),
[] ).
cnf(163964584,plain,
( ~ there_exists(domain(A))
| there_exists(A) ),
inference(rewrite,[status(thm)],[domain_has_elements]),
[] ).
fof(prove_codomain_of_a_exists,plain,
~ there_exists(codomain(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),
[] ).
cnf(164028552,plain,
~ there_exists(codomain(a)),
inference(rewrite,[status(thm)],[prove_codomain_of_a_exists]),
[] ).
cnf(171918376,plain,
~ there_exists(domain(codomain(a))),
inference(resolution,[status(thm)],[163964584,164028552]),
[] ).
fof(assume_a_exists,plain,
there_exists(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),
[] ).
cnf(164024584,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/CAT017-4.tptp',unknown),
[] ).
cnf(163959040,plain,
( ~ there_exists(A)
| ~ $equal(B,A)
| equivalent(A,B) ),
inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),
[] ).
cnf(171820560,plain,
( ~ $equal(A,a)
| equivalent(a,A) ),
inference(resolution,[status(thm)],[163959040,164024584]),
[] ).
fof(compose_codomain,plain,
! [A] : $equal(compose(codomain(A),A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),
[] ).
cnf(164020208,plain,
$equal(compose(codomain(A),A),A),
inference(rewrite,[status(thm)],[compose_codomain]),
[] ).
cnf(175189048,plain,
equivalent(a,compose(codomain(a),a)),
inference(resolution,[status(thm)],[171820560,164020208]),
[] ).
fof(equivalence_implies_existence2,plain,
! [A,B] :
( ~ equivalent(A,B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),
[] ).
cnf(163946744,plain,
( ~ equivalent(A,B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[equivalence_implies_existence2]),
[] ).
cnf(177447848,plain,
$equal(compose(codomain(a),a),a),
inference(resolution,[status(thm)],[175189048,163946744]),
[] ).
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/CAT017-4.tptp',unknown),
[] ).
cnf(163979912,plain,
( ~ there_exists(compose(A,B))
| there_exists(domain(A)) ),
inference(rewrite,[status(thm)],[composition_implies_domain]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171918376,164024584,177447848,163979912,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(domain_has_elements,plain,(~there_exists(domain(A))|there_exists(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(163964584,plain,(~there_exists(domain(A))|there_exists(A)),inference(rewrite,[status(thm)],[domain_has_elements]),[]).
%
% fof(prove_codomain_of_a_exists,plain,(~there_exists(codomain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(164028552,plain,(~there_exists(codomain(a))),inference(rewrite,[status(thm)],[prove_codomain_of_a_exists]),[]).
%
% cnf(171918376,plain,(~there_exists(domain(codomain(a)))),inference(resolution,[status(thm)],[163964584,164028552]),[]).
%
% fof(assume_a_exists,plain,(there_exists(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(164024584,plain,(there_exists(a)),inference(rewrite,[status(thm)],[assume_a_exists]),[]).
%
% fof(existence_and_equality_implies_equivalence1,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(163959040,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),[]).
%
% cnf(171820560,plain,(~$equal(A,a)|equivalent(a,A)),inference(resolution,[status(thm)],[163959040,164024584]),[]).
%
% fof(compose_codomain,plain,($equal(compose(codomain(A),A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(164020208,plain,($equal(compose(codomain(A),A),A)),inference(rewrite,[status(thm)],[compose_codomain]),[]).
%
% cnf(175189048,plain,(equivalent(a,compose(codomain(a),a))),inference(resolution,[status(thm)],[171820560,164020208]),[]).
%
% fof(equivalence_implies_existence2,plain,(~equivalent(A,B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(163946744,plain,(~equivalent(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[equivalence_implies_existence2]),[]).
%
% cnf(177447848,plain,($equal(compose(codomain(a),a),a)),inference(resolution,[status(thm)],[175189048,163946744]),[]).
%
% fof(composition_implies_domain,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT017-4.tptp',unknown),[]).
%
% cnf(163979912,plain,(~there_exists(compose(A,B))|there_exists(domain(A))),inference(rewrite,[status(thm)],[composition_implies_domain]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[171918376,164024584,177447848,163979912,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------