%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB024+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:39 AM UTC 2025
% Result : Theorem 0.55s 0.76s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWB024+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 07:53:20 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.55/0.76 % SZS status Theorem
% 0.55/0.76 % SZS output start Proof
% 0.55/0.76 tff(iext_type, type, (
% 0.55/0.76 iext: ( $i * $i * $i ) > $o)).
% 0.55/0.76 tff(tptp_fun_Y_12_type, type, (
% 0.55/0.76 tptp_fun_Y_12: ( $i * $i ) > $i)).
% 0.55/0.76 tff(uri_ex_hasAncestor_type, type, (
% 0.55/0.76 uri_ex_hasAncestor: $i)).
% 0.55/0.76 tff(uri_ex_bob_type, type, (
% 0.55/0.76 uri_ex_bob: $i)).
% 0.55/0.76 tff(uri_ex_alice_type, type, (
% 0.55/0.76 uri_ex_alice: $i)).
% 0.55/0.76 tff(icext_type, type, (
% 0.55/0.76 icext: ( $i * $i ) > $o)).
% 0.55/0.76 tff(tptp_fun_BNODE_z_140_type, type, (
% 0.55/0.76 tptp_fun_BNODE_z_140: $i)).
% 0.55/0.76 tff(literal_typed_type, type, (
% 0.55/0.76 literal_typed: ( $i * $i ) > $i)).
% 0.55/0.76 tff(uri_xsd_nonNegativeInteger_type, type, (
% 0.55/0.76 uri_xsd_nonNegativeInteger: $i)).
% 0.55/0.76 tff(dat_str_1_type, type, (
% 0.55/0.76 dat_str_1: $i)).
% 0.55/0.76 tff(uri_owl_minCardinality_type, type, (
% 0.55/0.76 uri_owl_minCardinality: $i)).
% 0.55/0.76 tff(uri_ex_Person_type, type, (
% 0.55/0.76 uri_ex_Person: $i)).
% 0.55/0.76 tff(uri_rdf_type_type, type, (
% 0.55/0.76 uri_rdf_type: $i)).
% 0.55/0.76 tff(uri_owl_onProperty_type, type, (
% 0.55/0.76 uri_owl_onProperty: $i)).
% 0.55/0.76 tff(uri_owl_Restriction_type, type, (
% 0.55/0.76 uri_owl_Restriction: $i)).
% 0.55/0.76 tff(uri_rdfs_subClassOf_type, type, (
% 0.55/0.76 uri_rdfs_subClassOf: $i)).
% 0.55/0.76 tff(uri_owl_TransitiveProperty_type, type, (
% 0.55/0.76 uri_owl_TransitiveProperty: $i)).
% 0.55/0.76 tff(ic_type, type, (
% 0.55/0.76 ic: $i > $o)).
% 0.55/0.76 tff(ip_type, type, (
% 0.55/0.76 ip: $i > $o)).
% 0.55/0.76 tff(tptp_fun_Z_121_type, type, (
% 0.55/0.76 tptp_fun_Z_121: $i > $i)).
% 0.55/0.76 tff(tptp_fun_X_123_type, type, (
% 0.55/0.76 tptp_fun_X_123: $i > $i)).
% 0.55/0.76 tff(tptp_fun_Y_122_type, type, (
% 0.55/0.76 tptp_fun_Y_122: $i > $i)).
% 0.55/0.76 tff(1,plain,
% 0.55/0.76 (?[BNODE_z: $i] : (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) <=> ?[BNODE_z: $i] : (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(2,plain,
% 0.55/0.76 (^[BNODE_z: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction))), ((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) <=> ((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)))), rewrite(((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor))), ((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)))), (((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) <=> ((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), rewrite(((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))), (((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), ((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) <=> ((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)))), rewrite(((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person))), ((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)))), (((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) <=> ((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)))), rewrite(((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person))), (((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)))), ((((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) <=> ((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)))), rewrite(((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))), ((((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) <=> (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(3,plain,
% 0.55/0.76 (?[BNODE_z: $i] : (((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) <=> ?[BNODE_z: $i] : (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[2])).
% 0.55/0.76 tff(4,axiom,(?[BNODE_z: $i] : (((((((iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z)) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor)) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties')).
% 0.55/0.76 tff(5,plain,
% 0.55/0.76 (?[BNODE_z: $i] : (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.55/0.76 tff(6,plain,
% 0.55/0.76 (?[BNODE_z: $i] : (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.55/0.76 tff(7,plain,(
% 0.55/0.76 iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z!140) & iext(uri_rdf_type, BNODE_z!140, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z!140, uri_ex_hasAncestor) & iext(uri_owl_minCardinality, BNODE_z!140, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)),
% 0.55/0.76 inference(skolemize,[status(sab)],[6])).
% 0.55/0.76 tff(8,plain,
% 0.55/0.76 (iext(uri_owl_minCardinality, BNODE_z!140, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))),
% 0.55/0.76 inference(and_elim,[status(thm)],[7])).
% 0.55/0.76 tff(9,plain,
% 0.55/0.76 (iext(uri_owl_onProperty, BNODE_z!140, uri_ex_hasAncestor)),
% 0.55/0.76 inference(and_elim,[status(thm)],[7])).
% 0.55/0.76 tff(10,plain,
% 0.55/0.76 (^[Z: $i, P: $i] : refl(((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(11,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))) <=> ![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[10])).
% 0.55/0.76 tff(12,plain,
% 0.55/0.76 (^[Z: $i, P: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(13,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))) <=> ![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[12])).
% 0.55/0.76 tff(14,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))) <=> ![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))),
% 0.55/0.76 inference(transitivity,[status(thm)],[13, 11])).
% 0.55/0.76 tff(15,plain,
% 0.55/0.76 (^[Z: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))), ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))))), rewrite((~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))) <=> (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))), ((((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))) <=> (((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))), rewrite((((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))) <=> (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))), ((((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))) <=> (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))))), (![X: $i] : (((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))) <=> ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))), (((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))) <=> (((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))))), rewrite((((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))), (((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(16,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y))))) <=> ![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[15])).
% 0.55/0.76 tff(17,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y))) <=> ![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(18,plain,
% 0.55/0.76 (^[Z: $i, P: $i] : rewrite(((iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y))) <=> ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(19,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y))) <=> ![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y)))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[18])).
% 0.55/0.76 tff(20,axiom,(![Z: $i, P: $i] : ((iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_restrict_mincard_001')).
% 0.55/0.76 tff(21,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.55/0.76 tff(22,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : iext(P, X, Y)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.55/0.76 tff(23,plain,(
% 0.55/0.76 ![Z: $i, P: $i] : ((~(iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P))) & (icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))),
% 0.55/0.76 inference(skolemize,[status(sab)],[22])).
% 0.55/0.76 tff(24,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.55/0.76 tff(25,plain,
% 0.55/0.76 (![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.55/0.76 tff(26,plain,
% 0.55/0.76 (((~![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_ex_hasAncestor)) | (~iext(uri_owl_minCardinality, BNODE_z!140, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | iext(uri_ex_hasAncestor, X, tptp_fun_Y_12(X, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : (~iext(uri_ex_hasAncestor, X, Y)))))))) <=> ((~![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))) | (~iext(uri_owl_onProperty, BNODE_z!140, uri_ex_hasAncestor)) | (~iext(uri_owl_minCardinality, BNODE_z!140, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | iext(uri_ex_hasAncestor, X, tptp_fun_Y_12(X, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : (~iext(uri_ex_hasAncestor, X, Y)))))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(27,plain,
% 0.60/0.77 ((~![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_ex_hasAncestor)) | (~iext(uri_owl_minCardinality, BNODE_z!140, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | iext(uri_ex_hasAncestor, X, tptp_fun_Y_12(X, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : (~iext(uri_ex_hasAncestor, X, Y)))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(28,plain,
% 0.60/0.77 ((~![Z: $i, P: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_minCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | iext(P, X, tptp_fun_Y_12(X, P)))) | (~(icext(Z, X) | ![Y: $i] : (~iext(P, X, Y)))))))) | (~iext(uri_owl_onProperty, BNODE_z!140, uri_ex_hasAncestor)) | (~iext(uri_owl_minCardinality, BNODE_z!140, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | iext(uri_ex_hasAncestor, X, tptp_fun_Y_12(X, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : (~iext(uri_ex_hasAncestor, X, Y))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.60/0.77 tff(29,plain,
% 0.60/0.77 (![X: $i] : (~((~((~icext(BNODE_z!140, X)) | iext(uri_ex_hasAncestor, X, tptp_fun_Y_12(X, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : (~iext(uri_ex_hasAncestor, X, Y))))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[28, 25, 9, 8])).
% 0.60/0.77 tff(30,plain,
% 0.60/0.77 ((~![X: $i] : (~((~((~icext(BNODE_z!140, X)) | iext(uri_ex_hasAncestor, X, tptp_fun_Y_12(X, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : (~iext(uri_ex_hasAncestor, X, Y))))))) | (~((~((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, uri_ex_bob) | ![Y: $i] : (~iext(uri_ex_hasAncestor, uri_ex_bob, Y))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(31,plain,
% 0.60/0.77 (~((~((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, uri_ex_bob) | ![Y: $i] : (~iext(uri_ex_hasAncestor, uri_ex_bob, Y)))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.60/0.77 tff(32,plain,
% 0.60/0.77 (((~((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) | (~(icext(BNODE_z!140, uri_ex_bob) | ![Y: $i] : (~iext(uri_ex_hasAncestor, uri_ex_bob, Y))))) | ((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(33,plain,
% 0.60/0.77 ((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.60/0.77 tff(34,plain,
% 0.60/0.77 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(35,plain,
% 0.60/0.77 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[34])).
% 0.60/0.77 tff(36,plain,
% 0.60/0.77 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(37,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.60/0.77 tff(38,plain,
% 0.60/0.77 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.60/0.77 tff(39,plain,(
% 0.60/0.77 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.60/0.77 inference(skolemize,[status(sab)],[38])).
% 0.60/0.77 tff(40,plain,
% 0.60/0.77 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.60/0.77 tff(41,plain,
% 0.60/0.77 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) <=> icext(uri_ex_Person, uri_ex_bob))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(42,plain,
% 0.60/0.77 (iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) <=> icext(uri_ex_Person, uri_ex_bob)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.60/0.77 tff(43,plain,
% 0.60/0.77 (iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)),
% 0.60/0.77 inference(and_elim,[status(thm)],[7])).
% 0.60/0.77 tff(44,plain,
% 0.60/0.77 ((~(iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) <=> icext(uri_ex_Person, uri_ex_bob))) | (~iext(uri_rdf_type, uri_ex_bob, uri_ex_Person)) | icext(uri_ex_Person, uri_ex_bob)),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(45,plain,
% 0.60/0.77 ((~(iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) <=> icext(uri_ex_Person, uri_ex_bob))) | icext(uri_ex_Person, uri_ex_bob)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.60/0.77 tff(46,plain,
% 0.60/0.77 (icext(uri_ex_Person, uri_ex_bob)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[45, 42])).
% 0.60/0.77 tff(47,plain,
% 0.60/0.77 (iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z!140)),
% 0.60/0.77 inference(and_elim,[status(thm)],[7])).
% 0.60/0.77 tff(48,plain,
% 0.60/0.77 (^[C: $i, D: $i] : refl(((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(49,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[48])).
% 0.60/0.77 tff(50,plain,
% 0.60/0.77 (^[C: $i, D: $i] : rewrite(((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(51,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[50])).
% 0.60/0.77 tff(52,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[51, 49])).
% 0.60/0.77 tff(53,plain,
% 0.60/0.77 (^[C: $i, D: $i] : rewrite(((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(54,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[53])).
% 0.60/0.77 tff(55,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(56,plain,
% 0.60/0.77 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((icext(C, X) => icext(D, X)) <=> ((~icext(C, X)) | icext(D, X)))), (![X: $i] : (icext(C, X) => icext(D, X)) <=> ![X: $i] : ((~icext(C, X)) | icext(D, X)))), (((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))) <=> ((ic(C) & ic(D)) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), rewrite(((ic(C) & ic(D)) & ![X: $i] : ((~icext(C, X)) | icext(D, X))) <=> (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))), (((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))) <=> (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), ((iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> (iext(uri_rdfs_subClassOf, C, D) => (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))))), rewrite((iext(uri_rdfs_subClassOf, C, D) => (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), ((iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(57,plain,
% 0.60/0.77 (![C: $i, D: $i] : (iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[56])).
% 0.60/0.77 tff(58,axiom,(![C: $i, D: $i] : (iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_subclassof_main')).
% 0.60/0.77 tff(59,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.60/0.77 tff(60,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.60/0.77 tff(61,plain,(
% 0.60/0.77 ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.60/0.77 inference(skolemize,[status(sab)],[60])).
% 0.60/0.77 tff(62,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.60/0.77 tff(63,plain,
% 0.60/0.77 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.60/0.77 tff(64,plain,
% 0.60/0.77 (((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_Person)) | (~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))))))) <=> ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_Person)) | (~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(65,plain,
% 0.60/0.77 ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_Person)) | (~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(66,plain,
% 0.60/0.77 ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_Person)) | (~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X)))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.60/0.77 tff(67,plain,
% 0.60/0.77 (~((~ic(BNODE_z!140)) | (~ic(uri_ex_Person)) | (~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[66, 63, 47])).
% 0.60/0.77 tff(68,plain,
% 0.60/0.77 (((~ic(BNODE_z!140)) | (~ic(uri_ex_Person)) | (~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X)))) | ![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(69,plain,
% 0.60/0.77 (![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.60/0.77 tff(70,plain,
% 0.60/0.77 (((~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))) | ((~icext(uri_ex_Person, uri_ex_bob)) | icext(BNODE_z!140, uri_ex_bob))) <=> ((~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))) | (~icext(uri_ex_Person, uri_ex_bob)) | icext(BNODE_z!140, uri_ex_bob))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(71,plain,
% 0.60/0.77 ((~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))) | ((~icext(uri_ex_Person, uri_ex_bob)) | icext(BNODE_z!140, uri_ex_bob))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(72,plain,
% 0.60/0.77 ((~![X: $i] : ((~icext(uri_ex_Person, X)) | icext(BNODE_z!140, X))) | (~icext(uri_ex_Person, uri_ex_bob)) | icext(BNODE_z!140, uri_ex_bob)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.60/0.77 tff(73,plain,
% 0.60/0.77 (icext(BNODE_z!140, uri_ex_bob)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[72, 69, 46])).
% 0.60/0.77 tff(74,plain,
% 0.60/0.77 ((~((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) | (~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(75,plain,
% 0.60/0.77 ((~((~icext(BNODE_z!140, uri_ex_bob)) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) | iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.60/0.77 tff(76,plain,
% 0.60/0.77 (iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[75, 33])).
% 0.60/0.77 tff(77,plain,
% 0.60/0.77 (^[BNODE_x: $i] : refl(((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))) <=> ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(78,plain,
% 0.60/0.77 (![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))) <=> ![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[77])).
% 0.60/0.77 tff(79,plain,
% 0.60/0.77 (^[BNODE_x: $i] : trans(monotonicity(rewrite((iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)) <=> (~((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))))), ((~(iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))) <=> (~(~((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))))))), rewrite((~(~((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))))) <=> ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))), ((~(iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))) <=> ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(80,plain,
% 0.60/0.77 (![BNODE_x: $i] : (~(iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))) <=> ![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[79])).
% 0.60/0.77 tff(81,plain,
% 0.60/0.77 ((~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))) <=> (~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(82,axiom,(~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties')).
% 0.60/0.77 tff(83,plain,
% 0.60/0.77 (~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.60/0.77 tff(84,plain,
% 0.60/0.77 (~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[83, 81])).
% 0.60/0.77 tff(85,plain,
% 0.60/0.77 (~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.60/0.77 tff(86,plain,
% 0.60/0.77 (~?[BNODE_x: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.60/0.77 tff(87,plain,
% 0.60/0.77 (^[BNODE_x: $i] : refl($oeq((~(iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))), (~(iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(88,plain,(
% 0.60/0.77 ![BNODE_x: $i] : (~(iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))),
% 0.60/0.77 inference(nnf-neg,[status(sab)],[86, 87])).
% 0.60/0.77 tff(89,plain,
% 0.60/0.77 (![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[88, 80])).
% 0.60/0.77 tff(90,plain,
% 0.60/0.77 (![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[89, 78])).
% 0.60/0.77 tff(91,plain,
% 0.60/0.77 (((~![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))) | ((~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))) <=> ((~![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(92,plain,
% 0.60/0.77 ((~![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))) | ((~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(93,plain,
% 0.60/0.77 ((~![BNODE_x: $i] : ((~iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x)))) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.60/0.77 tff(94,plain,
% 0.60/0.77 (~iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[93, 90, 76])).
% 0.60/0.77 tff(95,plain,
% 0.60/0.77 (^[P: $i] : rewrite((~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(96,plain,
% 0.60/0.77 (![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[95])).
% 0.60/0.77 tff(97,plain,
% 0.60/0.77 (^[P: $i] : refl((~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(98,plain,
% 0.60/0.77 (![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[97])).
% 0.60/0.77 tff(99,plain,
% 0.60/0.77 (^[P: $i] : rewrite((~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(100,plain,
% 0.60/0.77 (![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[99])).
% 0.60/0.77 tff(101,plain,
% 0.60/0.77 (![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[100, 98])).
% 0.60/0.77 tff(102,plain,
% 0.60/0.77 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) <=> ((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)))) <=> (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))), ((icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P))))) <=> (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))), rewrite((icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))) <=> (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))), ((icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P))))) <=> (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))), ((((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)))))) <=> (((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))))), rewrite((((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) <=> (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))), ((((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)))))) <=> (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(103,plain,
% 0.60/0.77 (![P: $i] : (((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[102])).
% 0.60/0.77 tff(104,plain,
% 0.60/0.77 (^[P: $i] : rewrite((((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P))))))) <=> (((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(105,plain,
% 0.60/0.77 (![P: $i] : (((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P))))))) <=> ![P: $i] : (((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P))))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[104])).
% 0.60/0.78 tff(106,plain,
% 0.60/0.78 (![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) <=> ![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(107,plain,
% 0.60/0.78 (^[P: $i] : rewrite((icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((iext(P, X, Y) & iext(P, Y, Z)) => iext(P, X, Z)))) <=> (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(108,plain,
% 0.60/0.78 (![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((iext(P, X, Y) & iext(P, Y, Z)) => iext(P, X, Z)))) <=> ![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z))))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[107])).
% 0.60/0.78 tff(109,axiom,(![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((iext(P, X, Y) & iext(P, Y, Z)) => iext(P, X, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_char_transitive')).
% 0.60/0.78 tff(110,plain,
% 0.60/0.78 (![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.60/0.78 tff(111,plain,
% 0.60/0.78 (![P: $i] : (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.60/0.78 tff(112,plain,(
% 0.60/0.78 ![P: $i] : (((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)))))))),
% 0.60/0.78 inference(skolemize,[status(sab)],[111])).
% 0.60/0.78 tff(113,plain,
% 0.60/0.78 (![P: $i] : (((~icext(uri_owl_TransitiveProperty, P)) | (ip(P) & ![X: $i, Y: $i, Z: $i] : ((~(iext(P, X, Y) & iext(P, Y, Z))) | iext(P, X, Z)))) & (icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P)) & iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))) | iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.60/0.78 tff(114,plain,
% 0.60/0.78 (![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.60/0.78 tff(115,plain,
% 0.60/0.78 (![P: $i] : (~((~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y)))))))) | (~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P)))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[114, 101])).
% 0.60/0.78 tff(116,plain,
% 0.60/0.78 (![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[115, 96])).
% 0.60/0.78 tff(117,plain,
% 0.60/0.78 (((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(118,plain,
% 0.60/0.78 ((~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~(iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, Y, Z)) | (~iext(uri_ex_hasAncestor, X, Y)))))))))) <=> (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(119,plain,
% 0.60/0.78 (((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~(iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, Y, Z)) | (~iext(uri_ex_hasAncestor, X, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[118])).
% 0.60/0.78 tff(120,plain,
% 0.60/0.78 (((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~(iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, Y, Z)) | (~iext(uri_ex_hasAncestor, X, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[119, 117])).
% 0.60/0.78 tff(121,plain,
% 0.60/0.78 ((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~(iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, Y, Z)) | (~iext(uri_ex_hasAncestor, X, Y))))))))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(122,plain,
% 0.60/0.78 ((~![P: $i] : (~((~(icext(uri_owl_TransitiveProperty, P) | (~ip(P)) | (~(iext(P, tptp_fun_X_123(P), tptp_fun_Z_121(P)) | (~iext(P, tptp_fun_X_123(P), tptp_fun_Y_122(P))) | (~iext(P, tptp_fun_Y_122(P), tptp_fun_Z_121(P))))))) | (~((~icext(uri_owl_TransitiveProperty, P)) | (~((~ip(P)) | (~![X: $i, Y: $i, Z: $i] : (iext(P, X, Z) | (~iext(P, Y, Z)) | (~iext(P, X, Y))))))))))) | (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.60/0.78 tff(123,plain,
% 0.60/0.78 (~((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[122, 116])).
% 0.60/0.78 tff(124,plain,
% 0.60/0.78 (((~(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) | (~ip(uri_ex_hasAncestor)) | (~((~iext(uri_ex_hasAncestor, tptp_fun_Y_122(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor))) | (~iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Y_122(uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, tptp_fun_X_123(uri_ex_hasAncestor), tptp_fun_Z_121(uri_ex_hasAncestor)))))) | (~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))))) | ((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(125,plain,
% 0.60/0.78 ((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.60/0.78 tff(126,plain,
% 0.60/0.78 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) <=> icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(127,plain,
% 0.60/0.78 (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) <=> icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[126, 40])).
% 0.60/0.78 tff(128,plain,
% 0.60/0.78 (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty)),
% 0.60/0.78 inference(and_elim,[status(thm)],[7])).
% 0.60/0.78 tff(129,plain,
% 0.60/0.78 ((~(iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) <=> icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor))) | (~iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty)) | icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(130,plain,
% 0.60/0.78 ((~(iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) <=> icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor))) | icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.60/0.78 tff(131,plain,
% 0.60/0.78 (icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.60/0.78 tff(132,plain,
% 0.60/0.78 ((~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))) | (~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(133,plain,
% 0.60/0.78 ((~((~icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor)) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))))) | (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.60/0.78 tff(134,plain,
% 0.60/0.78 (~((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[133, 125])).
% 0.60/0.78 tff(135,plain,
% 0.60/0.78 (((~ip(uri_ex_hasAncestor)) | (~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z))))) | ![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))),
% 0.60/0.78 inference(tautology,[status(thm)],[])).
% 0.60/0.78 tff(136,plain,
% 0.60/0.78 (![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.60/0.78 tff(137,plain,
% 0.60/0.78 (iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)),
% 0.60/0.78 inference(and_elim,[status(thm)],[7])).
% 0.60/0.78 tff(138,plain,
% 0.60/0.78 (((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | ((~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) <=> ((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(139,plain,
% 0.60/0.78 ((iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))) <=> ((~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(140,plain,
% 0.60/0.80 (((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | (iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))) <=> ((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | ((~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[139])).
% 0.60/0.80 tff(141,plain,
% 0.60/0.80 (((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | (iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))) <=> ((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[140, 138])).
% 0.60/0.80 tff(142,plain,
% 0.60/0.80 ((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | (iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor)) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(143,plain,
% 0.60/0.80 ((~![X: $i, Y: $i, Z: $i] : (iext(uri_ex_hasAncestor, X, Z) | (~iext(uri_ex_hasAncestor, X, Y)) | (~iext(uri_ex_hasAncestor, Y, Z)))) | (~iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasAncestor, uri_ex_bob, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))) | iext(uri_ex_hasAncestor, uri_ex_alice, tptp_fun_Y_12(uri_ex_bob, uri_ex_hasAncestor))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.60/0.80 tff(144,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[143, 137, 136, 76, 94])).
% 0.60/0.80 % SZS output end Proof
% 0.60/0.81 % E exiting
%------------------------------------------------------------------------------