%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB012+3 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:29:33 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWB012+3 : TPTP v9.0.0. Released v5.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:47:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(icext_type, type, (
% 0.19/0.44 icext: ( $i * $i ) > $o)).
% 0.19/0.44 tff(uri_ex_alice_type, type, (
% 0.19/0.44 uri_ex_alice: $i)).
% 0.19/0.44 tff(uri_foaf_Person_type, type, (
% 0.19/0.44 uri_foaf_Person: $i)).
% 0.19/0.44 tff(iext_type, type, (
% 0.19/0.44 iext: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(uri_rdf_type_type, type, (
% 0.19/0.44 uri_rdf_type: $i)).
% 0.19/0.44 tff(uri_owl_FunctionalProperty_type, type, (
% 0.19/0.44 uri_owl_FunctionalProperty: $i)).
% 0.19/0.44 tff(uri_ex_name_type, type, (
% 0.19/0.44 uri_ex_name: $i)).
% 0.19/0.44 tff(tptp_fun_BNODE_r_17_type, type, (
% 0.19/0.44 tptp_fun_BNODE_r_17: $i)).
% 0.19/0.44 tff(uri_owl_DatatypeProperty_type, type, (
% 0.19/0.44 uri_owl_DatatypeProperty: $i)).
% 0.19/0.44 tff(uri_ex_PersonAttribute_type, type, (
% 0.19/0.44 uri_ex_PersonAttribute: $i)).
% 0.19/0.44 tff(ic_type, type, (
% 0.19/0.44 ic: $i > $o)).
% 0.19/0.44 tff(tptp_fun_BNODE_l1_20_type, type, (
% 0.19/0.44 tptp_fun_BNODE_l1_20: $i)).
% 0.19/0.44 tff(uri_owl_intersectionOf_type, type, (
% 0.19/0.44 uri_owl_intersectionOf: $i)).
% 0.19/0.44 tff(tptp_fun_X_3_type, type, (
% 0.19/0.44 tptp_fun_X_3: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.44 tff(uri_rdf_nil_type, type, (
% 0.19/0.44 uri_rdf_nil: $i)).
% 0.19/0.44 tff(tptp_fun_BNODE_l3_18_type, type, (
% 0.19/0.44 tptp_fun_BNODE_l3_18: $i)).
% 0.19/0.44 tff(uri_rdf_rest_type, type, (
% 0.19/0.44 uri_rdf_rest: $i)).
% 0.19/0.44 tff(literal_plain_type, type, (
% 0.19/0.44 literal_plain: $i > $i)).
% 0.19/0.44 tff(dat_str_alice_type, type, (
% 0.19/0.44 dat_str_alice: $i)).
% 0.19/0.44 tff(uri_owl_hasValue_type, type, (
% 0.19/0.44 uri_owl_hasValue: $i)).
% 0.19/0.44 tff(uri_rdfs_domain_type, type, (
% 0.19/0.44 uri_rdfs_domain: $i)).
% 0.19/0.44 tff(uri_owl_onProperty_type, type, (
% 0.19/0.44 uri_owl_onProperty: $i)).
% 0.19/0.44 tff(uri_owl_Restriction_type, type, (
% 0.19/0.44 uri_owl_Restriction: $i)).
% 0.19/0.44 tff(uri_rdf_first_type, type, (
% 0.19/0.44 uri_rdf_first: $i)).
% 0.19/0.44 tff(tptp_fun_BNODE_l2_19_type, type, (
% 0.19/0.44 tptp_fun_BNODE_l2_19: $i)).
% 0.19/0.44 tff(uri_owl_Class_type, type, (
% 0.19/0.44 uri_owl_Class: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![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))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.45 (![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))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(4,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','rdfs_cext_def')).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.45 tff(6,plain,(
% 0.19/0.45 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.45 inference(skolemize,[status(sab)],[5])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (^[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty))), ((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), ((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), (((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty))), (((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)))), ((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3))), ((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)))), (((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r))), (((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r)))), ((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil))), ((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)))), (((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction))), (((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)))), ((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain))), ((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)))), (((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person))), (((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)))), ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute))), ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)))), (((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))), (((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.46 tff(15,axiom,(?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_012_Template_Class')).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.46 tff(18,plain,(
% 0.19/0.46 iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) & iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19) & iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18) & iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17) & iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r!17, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))),
% 0.19/0.46 inference(skolemize,[status(sab)],[17])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))), (((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))))), rewrite(((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))), (((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : refl(((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : rewrite(((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))))), rewrite((~(~((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))), trans(monotonicity(rewrite(((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) <=> ((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))), ((icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))))), rewrite((icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))) <=> (~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))), ((icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))), rewrite((~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))), ((icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))), ((~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))) <=> (~(~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))), rewrite((~(~(((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))), ((~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))))) <=> (((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))), rewrite((((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> (((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))))), rewrite((((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)))), ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))), ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite((iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X))))) <=> (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))), (((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))), (((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.47 tff(39,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','owl_bool_intersectionof_class_003')).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.47 tff(42,plain,(
% 0.19/0.47 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[41])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_3(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[45, 26])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(49,plain,
% 0.19/0.48 ((~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (((~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (~![X: $i] : (~(((~icext(BNODE_r!17, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(uri_owl_DatatypeProperty, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))) <=> (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (((~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (~![X: $i] : (~(((~icext(BNODE_r!17, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(uri_owl_DatatypeProperty, X))) <=> icext(uri_ex_PersonAttribute, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (((~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (~![X: $i] : (~(((~icext(BNODE_r!17, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(uri_owl_DatatypeProperty, X))) <=> icext(uri_ex_PersonAttribute, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (((~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (~![X: $i] : (~(((~icext(BNODE_r!17, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(uri_owl_DatatypeProperty, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (((~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (~![X: $i] : (~(((~icext(BNODE_r!17, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(uri_owl_DatatypeProperty, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[52, 47])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (((~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(BNODE_r!17)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_ex_PersonAttribute)) | (~![X: $i] : (~(((~icext(BNODE_r!17, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(uri_owl_DatatypeProperty, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_3(C3, C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C3, C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C3, X)) | (~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!20, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!20, BNODE_l2!19)) | (~iext(uri_rdf_first, BNODE_l2!19, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!18, BNODE_r!17)) | (~iext(uri_rdf_rest, BNODE_l3!18, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!19, BNODE_l3!18)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[55, 46, 24, 23, 22, 21, 20, 19])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (((~icext(BNODE_r!17, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_DatatypeProperty, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))) <=> icext(uri_ex_PersonAttribute, tptp_fun_X_3(BNODE_r!17, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))))) | ((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 ((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)),
% 0.19/0.49 inference(and_elim,[status(thm)],[18])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 ((~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))) | (~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 ((~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!20)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))))) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.19/0.49 tff(63,plain,
% 0.19/0.49 (((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!17)) | (~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X))))) | ![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 (![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 ((~![X: $i] : (~(((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!17, X))) <=> icext(uri_ex_PersonAttribute, X)))) | (~(((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))) <=> icext(uri_ex_PersonAttribute, uri_ex_name)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(66,plain,
% 0.19/0.49 (~(((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))) <=> icext(uri_ex_PersonAttribute, uri_ex_name))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.49 tff(67,plain,
% 0.19/0.49 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[67, 7])).
% 0.19/0.49 tff(69,plain,
% 0.19/0.49 (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)),
% 0.19/0.49 inference(and_elim,[status(thm)],[18])).
% 0.19/0.49 tff(70,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name))) | (~iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) | icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name))) | icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 (icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 ((((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))) <=> icext(uri_ex_PersonAttribute, uri_ex_name)) | (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name)))) | (~icext(uri_ex_PersonAttribute, uri_ex_name))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 ((((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))) <=> icext(uri_ex_PersonAttribute, uri_ex_name)) | (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[74, 66])).
% 0.19/0.49 tff(76,plain,
% 0.19/0.49 (((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))) | icext(uri_owl_FunctionalProperty, uri_ex_name)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(77,plain,
% 0.19/0.49 (icext(uri_owl_FunctionalProperty, uri_ex_name)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.49 tff(78,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name))) | iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) | (~icext(uri_owl_FunctionalProperty, uri_ex_name))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(79,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name))) | iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.49 tff(80,plain,
% 0.19/0.49 (iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[79, 11])).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 ((~(~((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))))) <=> ((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(82,plain,
% 0.19/0.49 ((iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) <=> (~((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))) <=> (~(~((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))) <=> ((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))) <=> (~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(86,axiom,(~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_012_Template_Class')).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 (~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 ((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[88, 80])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice))) | iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) | (~icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 ((~(iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice))) | (~icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (~icext(uri_foaf_Person, uri_ex_alice)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[91, 9])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 (iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)),
% 0.19/0.49 inference(and_elim,[status(thm)],[18])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 (iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)),
% 0.19/0.49 inference(and_elim,[status(thm)],[18])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 (^[Z: $i, P: $i, A: $i] : rewrite((![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 (^[Z: $i, P: $i, A: $i] : refl((![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (^[Z: $i, P: $i, A: $i] : rewrite((![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (^[Z: $i, P: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))), ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))))), rewrite((~(~((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))) <=> ((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P)))), ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))), (((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> (((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))))), rewrite((((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))), (((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (^[Z: $i, P: $i, A: $i] : rewrite(((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : ((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.49 tff(107,axiom,(![Z: $i, P: $i, A: $i] : ((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','owl_restrict_hasvalue')).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.49 tff(110,plain,(
% 0.19/0.49 ![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[109])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[112, 96])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)))) <=> ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | (~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person))) <=> ((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)))) <=> ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)))) <=> ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | (~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | (~iext(uri_owl_onProperty, BNODE_r!17, uri_rdfs_domain)) | ![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)) | (~iext(uri_owl_hasValue, BNODE_r!17, uri_foaf_Person))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 (![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[119, 113, 94, 93])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 ((~![X: $i] : (icext(BNODE_r!17, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person))) | (icext(BNODE_r!17, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (icext(BNODE_r!17, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 (((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!17, uri_ex_name))) | icext(BNODE_r!17, uri_ex_name)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 (icext(BNODE_r!17, uri_ex_name)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[123, 75])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 ((~(icext(BNODE_r!17, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))) | (~icext(BNODE_r!17, uri_ex_name)) | iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 ((~(icext(BNODE_r!17, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))) | iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 (iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))),
% 0.19/0.49 inference(and_elim,[status(thm)],[18])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (^[P: $i, C: $i, X: $i, Y: $i] : refl((icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C))) <=> (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C))) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (^[P: $i, C: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) <=> (~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> (~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))))), rewrite((~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 (^[P: $i, C: $i, X: $i, Y: $i] : rewrite(((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.50 tff(136,axiom,(![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','rdfs_domain_main')).
% 0.19/0.50 tff(137,plain,
% 0.19/0.50 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.19/0.50 tff(139,plain,(
% 0.19/0.50 ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[138])).
% 0.19/0.50 tff(140,plain,
% 0.19/0.50 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | ((~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(143,plain,
% 0.19/0.50 ((icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))) <=> ((~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | ((~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[143])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.50 inference(transitivity,[status(thm)],[144, 142])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[147, 141, 128, 127, 92])).
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------