TSTP Solution File: CAT012-4 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : CAT012-4 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 11:29:38 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 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 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(equivalence_implies_existence2,plain,
! [A,B] :
( ~ equivalent(A,B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),
[] ).
cnf(172628776,plain,
( ~ equivalent(A,B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[equivalence_implies_existence2]),
[] ).
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/CAT012-4.tptp',unknown),
[] ).
cnf(172641072,plain,
( ~ there_exists(A)
| ~ $equal(B,A)
| equivalent(A,B) ),
inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),
[] ).
fof(domain_has_elements,plain,
! [A] :
( ~ there_exists(domain(A))
| there_exists(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),
[] ).
cnf(172646616,plain,
( ~ there_exists(domain(A))
| there_exists(A) ),
inference(rewrite,[status(thm)],[domain_has_elements]),
[] ).
fof(assume_domain_exists,plain,
there_exists(domain(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),
[] ).
cnf(172706624,plain,
there_exists(domain(a)),
inference(rewrite,[status(thm)],[assume_domain_exists]),
[] ).
cnf(180479936,plain,
there_exists(a),
inference(resolution,[status(thm)],[172646616,172706624]),
[] ).
cnf(180559216,plain,
( ~ $equal(A,a)
| equivalent(a,A) ),
inference(resolution,[status(thm)],[172641072,180479936]),
[] ).
fof(compose_domain,plain,
! [A] : $equal(compose(A,domain(A)),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),
[] ).
cnf(172698504,plain,
$equal(compose(A,domain(A)),A),
inference(rewrite,[status(thm)],[compose_domain]),
[] ).
cnf(180576704,plain,
equivalent(a,compose(a,domain(a))),
inference(resolution,[status(thm)],[180559216,172698504]),
[] ).
cnf(180611352,plain,
$equal(compose(a,domain(a)),a),
inference(resolution,[status(thm)],[172628776,180576704]),
[] ).
cnf(181926712,plain,
there_exists(compose(a,domain(a))),
inference(paramodulation,[status(thm)],[180611352,180479936,theory(equality)]),
[] ).
fof(domain_codomain_composition1,plain,
! [A,B] :
( ~ there_exists(compose(A,B))
| $equal(codomain(B),domain(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),
[] ).
cnf(172674736,plain,
( ~ there_exists(compose(A,B))
| $equal(codomain(B),domain(A)) ),
inference(rewrite,[status(thm)],[domain_codomain_composition1]),
[] ).
fof(prove_codomain_of_domain_is_domain,plain,
~ $equal(codomain(domain(a)),domain(a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),
[] ).
cnf(172711392,plain,
~ $equal(codomain(domain(a)),domain(a)),
inference(rewrite,[status(thm)],[prove_codomain_of_domain_is_domain]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[181926712,172674736,172711392]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(equivalence_implies_existence2,plain,(~equivalent(A,B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172628776,plain,(~equivalent(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[equivalence_implies_existence2]),[]).
%
% fof(existence_and_equality_implies_equivalence1,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172641072,plain,(~there_exists(A)|~$equal(B,A)|equivalent(A,B)),inference(rewrite,[status(thm)],[existence_and_equality_implies_equivalence1]),[]).
%
% fof(domain_has_elements,plain,(~there_exists(domain(A))|there_exists(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172646616,plain,(~there_exists(domain(A))|there_exists(A)),inference(rewrite,[status(thm)],[domain_has_elements]),[]).
%
% fof(assume_domain_exists,plain,(there_exists(domain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172706624,plain,(there_exists(domain(a))),inference(rewrite,[status(thm)],[assume_domain_exists]),[]).
%
% cnf(180479936,plain,(there_exists(a)),inference(resolution,[status(thm)],[172646616,172706624]),[]).
%
% cnf(180559216,plain,(~$equal(A,a)|equivalent(a,A)),inference(resolution,[status(thm)],[172641072,180479936]),[]).
%
% fof(compose_domain,plain,($equal(compose(A,domain(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172698504,plain,($equal(compose(A,domain(A)),A)),inference(rewrite,[status(thm)],[compose_domain]),[]).
%
% cnf(180576704,plain,(equivalent(a,compose(a,domain(a)))),inference(resolution,[status(thm)],[180559216,172698504]),[]).
%
% cnf(180611352,plain,($equal(compose(a,domain(a)),a)),inference(resolution,[status(thm)],[172628776,180576704]),[]).
%
% cnf(181926712,plain,(there_exists(compose(a,domain(a)))),inference(paramodulation,[status(thm)],[180611352,180479936,theory(equality)]),[]).
%
% fof(domain_codomain_composition1,plain,(~there_exists(compose(A,B))|$equal(codomain(B),domain(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172674736,plain,(~there_exists(compose(A,B))|$equal(codomain(B),domain(A))),inference(rewrite,[status(thm)],[domain_codomain_composition1]),[]).
%
% fof(prove_codomain_of_domain_is_domain,plain,(~$equal(codomain(domain(a)),domain(a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/CAT/CAT012-4.tptp',unknown),[]).
%
% cnf(172711392,plain,(~$equal(codomain(domain(a)),domain(a))),inference(rewrite,[status(thm)],[prove_codomain_of_domain_is_domain]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[181926712,172674736,172711392]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------