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Z3---4.15.1.THM-Prf.s

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Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWB013+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n003.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 0.67s 0.84s
% Output   : Proof 0.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWB013+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 20 07:47:24 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 0.67/0.84  % SZS status Theorem
% 0.67/0.84  % SZS output start Proof
% 0.67/0.84  tff(iext_type, type, (
% 0.67/0.84     iext: ( $i * $i * $i ) > $o)).
% 0.67/0.84  tff(uri_ex_JoesGang_type, type, (
% 0.67/0.84     uri_ex_JoesGang: $i)).
% 0.67/0.84  tff(uri_ex_sameCliqueAs_type, type, (
% 0.67/0.84     uri_ex_sameCliqueAs: $i)).
% 0.67/0.84  tff(tptp_fun_Y_42_type, type, (
% 0.67/0.84     tptp_fun_Y_42: ( $i * $i * $i ) > $i)).
% 0.67/0.84  tff(uri_ex_Clique_type, type, (
% 0.67/0.84     uri_ex_Clique: $i)).
% 0.67/0.84  tff(uri_owl_sameAs_type, type, (
% 0.67/0.84     uri_owl_sameAs: $i)).
% 0.67/0.84  tff(icext_type, type, (
% 0.67/0.84     icext: ( $i * $i ) > $o)).
% 0.67/0.84  tff(tptp_fun_BNODE_r_144_type, type, (
% 0.67/0.84     tptp_fun_BNODE_r_144: $i)).
% 0.67/0.84  tff(uri_owl_someValuesFrom_type, type, (
% 0.67/0.84     uri_owl_someValuesFrom: $i)).
% 0.67/0.84  tff(uri_ex_bob_type, type, (
% 0.67/0.84     uri_ex_bob: $i)).
% 0.67/0.84  tff(uri_rdf_type_type, type, (
% 0.67/0.84     uri_rdf_type: $i)).
% 0.67/0.84  tff(uri_ex_alice_type, type, (
% 0.67/0.84     uri_ex_alice: $i)).
% 0.67/0.84  tff(tptp_fun_BNODE_i_143_type, type, (
% 0.67/0.84     tptp_fun_BNODE_i_143: $i)).
% 0.67/0.84  tff(uri_owl_inverseOf_type, type, (
% 0.67/0.84     uri_owl_inverseOf: $i)).
% 0.67/0.84  tff(uri_rdf_nil_type, type, (
% 0.67/0.84     uri_rdf_nil: $i)).
% 0.67/0.84  tff(tptp_fun_BNODE_l3_140_type, type, (
% 0.67/0.84     tptp_fun_BNODE_l3_140: $i)).
% 0.67/0.84  tff(uri_rdf_rest_type, type, (
% 0.67/0.84     uri_rdf_rest: $i)).
% 0.67/0.84  tff(uri_rdf_first_type, type, (
% 0.67/0.84     uri_rdf_first: $i)).
% 0.67/0.84  tff(tptp_fun_BNODE_l2_141_type, type, (
% 0.67/0.84     tptp_fun_BNODE_l2_141: $i)).
% 0.67/0.84  tff(tptp_fun_BNODE_l1_142_type, type, (
% 0.67/0.84     tptp_fun_BNODE_l1_142: $i)).
% 0.67/0.84  tff(uri_foaf_knows_type, type, (
% 0.67/0.84     uri_foaf_knows: $i)).
% 0.67/0.84  tff(uri_owl_propertyChainAxiom_type, type, (
% 0.67/0.84     uri_owl_propertyChainAxiom: $i)).
% 0.67/0.84  tff(uri_owl_ObjectProperty_type, type, (
% 0.67/0.84     uri_owl_ObjectProperty: $i)).
% 0.67/0.84  tff(uri_owl_onProperty_type, type, (
% 0.67/0.84     uri_owl_onProperty: $i)).
% 0.67/0.84  tff(uri_owl_Restriction_type, type, (
% 0.67/0.84     uri_owl_Restriction: $i)).
% 0.67/0.84  tff(uri_rdfs_subClassOf_type, type, (
% 0.67/0.84     uri_rdfs_subClassOf: $i)).
% 0.67/0.84  tff(uri_rdfs_range_type, type, (
% 0.67/0.84     uri_rdfs_range: $i)).
% 0.67/0.84  tff(uri_rdfs_subPropertyOf_type, type, (
% 0.67/0.84     uri_rdfs_subPropertyOf: $i)).
% 0.67/0.84  tff(uri_owl_Class_type, type, (
% 0.67/0.84     uri_owl_Class: $i)).
% 0.67/0.84  tff(ic_type, type, (
% 0.67/0.84     ic: $i > $o)).
% 0.67/0.84  tff(ip_type, type, (
% 0.67/0.84     ip: $i > $o)).
% 0.67/0.84  tff(tptp_fun_X_108_type, type, (
% 0.67/0.84     tptp_fun_X_108: ( $i * $i ) > $i)).
% 0.67/0.84  tff(tptp_fun_Y_107_type, type, (
% 0.67/0.84     tptp_fun_Y_107: ( $i * $i ) > $i)).
% 0.67/0.84  tff(tptp_fun_Y3_103_type, type, (
% 0.67/0.84     tptp_fun_Y3_103: ( $i * $i * $i * $i ) > $i)).
% 0.67/0.84  tff(tptp_fun_Y0_106_type, type, (
% 0.67/0.84     tptp_fun_Y0_106: ( $i * $i * $i * $i ) > $i)).
% 0.67/0.84  tff(tptp_fun_Y1_105_type, type, (
% 0.67/0.84     tptp_fun_Y1_105: ( $i * $i * $i * $i ) > $i)).
% 0.67/0.84  tff(tptp_fun_Y2_104_type, type, (
% 0.67/0.84     tptp_fun_Y2_104: ( $i * $i * $i * $i ) > $i)).
% 0.67/0.84  tff(1,plain,
% 0.67/0.84      (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.67/0.84      inference(bind,[status(th)],[])).
% 0.67/0.84  tff(2,plain,
% 0.67/0.84      (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.67/0.84      inference(quant_intro,[status(thm)],[1])).
% 0.67/0.84  tff(3,plain,
% 0.67/0.84      (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.67/0.84      inference(rewrite,[status(thm)],[])).
% 0.67/0.84  tff(4,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_sameas')).
% 0.67/0.84  tff(5,plain,
% 0.67/0.84      (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.67/0.84      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.67/0.84  tff(6,plain,(
% 0.67/0.84      ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.67/0.84      inference(skolemize,[status(sab)],[5])).
% 0.67/0.84  tff(7,plain,
% 0.67/0.84      (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.67/0.84      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.67/0.84  tff(8,plain,
% 0.67/0.84      ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)) <=> (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))),
% 0.67/0.84      inference(quant_inst,[status(thm)],[])).
% 0.67/0.84  tff(9,plain,
% 0.67/0.84      (iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)) <=> (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.84      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.67/0.85  tff(10,plain,
% 0.67/0.85      (?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)) <=> ?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))),
% 0.67/0.85      inference(rewrite,[status(thm)],[])).
% 0.67/0.85  tff(11,plain,
% 0.67/0.85      (^[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique))), ((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r))), ((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)))), (((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction))), (((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)))), ((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs))), ((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)))), (((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique))), (((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)))), ((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty))), ((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)))), (((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1))), (((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)))), ((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type))), ((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)))), (((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), (((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), ((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs))), ((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)))), (((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3))), (((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)))), ((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i))), ((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i)))), (((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil))), (((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)))), ((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type))), ((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)))), (((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique))), (((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)))), ((((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang))), ((((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)))), (((((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)) <=> ((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)))), rewrite(((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))), (((((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)) <=> (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))))),
% 0.67/0.86      inference(bind,[status(th)],[])).
% 0.67/0.86  tff(12,plain,
% 0.67/0.86      (?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : ((((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)) <=> ?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))),
% 0.67/0.86      inference(quant_intro,[status(thm)],[11])).
% 0.67/0.86  tff(13,axiom,(?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : ((((((((((((((((((iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique)) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs)) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique)) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty)) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_i)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type)) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_013_Cliques')).
% 0.67/0.86  tff(14,plain,
% 0.67/0.86      (?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))),
% 0.67/0.86      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.67/0.86  tff(15,plain,
% 0.67/0.86      (?[BNODE_r: $i, BNODE_i: $i, BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i] : (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_i) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))),
% 0.67/0.86      inference(modus_ponens,[status(thm)],[14, 10])).
% 0.67/0.86  tff(16,plain,(
% 0.67/0.86      iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144) & iext(uri_rdf_type, BNODE_r!144, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs) & iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique) & iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) & iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type) & iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141) & iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs) & iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140) & iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143) & iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type) & iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)),
% 0.67/0.87      inference(skolemize,[status(sab)],[15])).
% 0.67/0.87  tff(17,plain,
% 0.67/0.87      (iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)),
% 0.67/0.87      inference(and_elim,[status(thm)],[16])).
% 0.67/0.87  tff(18,plain,
% 0.67/0.87      (iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)),
% 0.67/0.87      inference(and_elim,[status(thm)],[16])).
% 0.67/0.87  tff(19,plain,
% 0.67/0.87      (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(20,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[19])).
% 0.67/0.87  tff(21,plain,
% 0.67/0.87      (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(22,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[21])).
% 0.67/0.87  tff(23,plain,
% 0.67/0.87      (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(24,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[23])).
% 0.67/0.87  tff(25,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.67/0.87      inference(transitivity,[status(thm)],[24, 22])).
% 0.67/0.87  tff(26,plain,
% 0.67/0.87      (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))), ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))))), rewrite((~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)))), ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) <=> ((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))), rewrite((icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))) <=> (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))), rewrite((((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), (![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))), (((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> (((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), rewrite((((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))), (((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(27,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[26])).
% 0.67/0.87  tff(28,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(29,plain,
% 0.67/0.87      (^[Z: $i, P: $i, C: $i] : rewrite(((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(30,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[29])).
% 0.67/0.87  tff(31,axiom,(![Z: $i, P: $i, C: $i] : ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_restrict_somevaluesfrom')).
% 0.67/0.87  tff(32,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[31, 30])).
% 0.67/0.87  tff(33,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[32, 28])).
% 0.67/0.87  tff(34,plain,(
% 0.67/0.87      ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))))),
% 0.67/0.87      inference(skolemize,[status(sab)],[33])).
% 0.67/0.87  tff(35,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[34, 27])).
% 0.67/0.87  tff(36,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[35, 25])).
% 0.67/0.87  tff(37,plain,
% 0.67/0.87      (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[36, 20])).
% 0.67/0.87  tff(38,plain,
% 0.67/0.87      (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))))))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(39,plain,
% 0.67/0.87      (((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~((~icext(BNODE_r!144, X)) | (~((~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))) | (~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))))))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(40,plain,
% 0.67/0.87      (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~((~icext(BNODE_r!144, X)) | (~((~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))) | (~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs)))))))))))),
% 0.67/0.87      inference(monotonicity,[status(thm)],[39])).
% 0.67/0.87  tff(41,plain,
% 0.67/0.87      (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~((~icext(BNODE_r!144, X)) | (~((~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))) | (~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))))))),
% 0.67/0.87      inference(transitivity,[status(thm)],[40, 38])).
% 0.67/0.87  tff(42,plain,
% 0.67/0.87      ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~((~icext(BNODE_r!144, X)) | (~((~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))))))) | (~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))))))),
% 0.67/0.87      inference(quant_inst,[status(thm)],[])).
% 0.67/0.87  tff(43,plain,
% 0.67/0.87      ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)) | (~iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)) | ![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs)))))))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[42, 41])).
% 0.67/0.87  tff(44,plain,
% 0.67/0.87      (![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs)))))))))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[43, 37, 18, 17])).
% 0.67/0.87  tff(45,plain,
% 0.67/0.87      ((~![X: $i] : (~((~(icext(BNODE_r!144, X) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, X, Y))))) | (~((~icext(BNODE_r!144, X)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, X, tptp_fun_Y_42(X, uri_ex_Clique, uri_ex_sameCliqueAs)))))))))) | (~((~(icext(BNODE_r!144, uri_ex_JoesGang) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, Y))))) | (~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))))))))),
% 0.67/0.87      inference(quant_inst,[status(thm)],[])).
% 0.67/0.87  tff(46,plain,
% 0.67/0.87      (~((~(icext(BNODE_r!144, uri_ex_JoesGang) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, Y))))) | (~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))))))))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[45, 44])).
% 0.67/0.87  tff(47,plain,
% 0.67/0.87      (((~(icext(BNODE_r!144, uri_ex_JoesGang) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, Y))))) | (~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))))))) | ((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))))))),
% 0.67/0.87      inference(tautology,[status(thm)],[])).
% 0.67/0.87  tff(48,plain,
% 0.67/0.87      ((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[47, 46])).
% 0.67/0.87  tff(49,plain,
% 0.67/0.87      (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(50,plain,
% 0.67/0.87      (![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))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[49])).
% 0.67/0.87  tff(51,plain,
% 0.67/0.87      (![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))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(52,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.67/0.87  tff(53,plain,
% 0.67/0.87      (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[52, 51])).
% 0.67/0.87  tff(54,plain,(
% 0.67/0.87      ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.67/0.87      inference(skolemize,[status(sab)],[53])).
% 0.67/0.87  tff(55,plain,
% 0.67/0.87      (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[54, 50])).
% 0.67/0.87  tff(56,plain,
% 0.67/0.87      ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) <=> icext(uri_ex_Clique, uri_ex_JoesGang))),
% 0.67/0.87      inference(quant_inst,[status(thm)],[])).
% 0.67/0.87  tff(57,plain,
% 0.67/0.87      (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) <=> icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[56, 55])).
% 0.67/0.87  tff(58,plain,
% 0.67/0.87      (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)),
% 0.67/0.87      inference(and_elim,[status(thm)],[16])).
% 0.67/0.87  tff(59,plain,
% 0.67/0.87      ((~(iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) <=> icext(uri_ex_Clique, uri_ex_JoesGang))) | (~iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)) | icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.67/0.87      inference(tautology,[status(thm)],[])).
% 0.67/0.87  tff(60,plain,
% 0.67/0.87      ((~(iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) <=> icext(uri_ex_Clique, uri_ex_JoesGang))) | icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[59, 58])).
% 0.67/0.87  tff(61,plain,
% 0.67/0.87      (icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[60, 57])).
% 0.67/0.87  tff(62,plain,
% 0.67/0.87      (iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144)),
% 0.67/0.87      inference(and_elim,[status(thm)],[16])).
% 0.67/0.87  tff(63,plain,
% 0.67/0.87      (^[C: $i, D: $i] : refl(((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(64,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[63])).
% 0.67/0.87  tff(65,plain,
% 0.67/0.87      (^[C: $i, D: $i] : rewrite(((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(66,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[65])).
% 0.67/0.87  tff(67,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(transitivity,[status(thm)],[66, 64])).
% 0.67/0.87  tff(68,plain,
% 0.67/0.87      (^[C: $i, D: $i] : rewrite(((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(69,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[68])).
% 0.67/0.87  tff(70,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(71,plain,
% 0.67/0.87      (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((icext(C, X) => icext(D, X)) <=> ((~icext(C, X)) | icext(D, X)))), (![X: $i] : (icext(C, X) => icext(D, X)) <=> ![X: $i] : ((~icext(C, X)) | icext(D, X)))), (((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))) <=> ((ic(C) & ic(D)) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), rewrite(((ic(C) & ic(D)) & ![X: $i] : ((~icext(C, X)) | icext(D, X))) <=> (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))), (((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))) <=> (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), ((iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> (iext(uri_rdfs_subClassOf, C, D) => (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))))), rewrite((iext(uri_rdfs_subClassOf, C, D) => (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), ((iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(72,plain,
% 0.67/0.87      (![C: $i, D: $i] : (iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[71])).
% 0.67/0.87  tff(73,axiom,(![C: $i, D: $i] : (iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_subclassof_main')).
% 0.67/0.87  tff(74,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[73, 72])).
% 0.67/0.87  tff(75,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[74, 70])).
% 0.67/0.87  tff(76,plain,(
% 0.67/0.87      ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.67/0.87      inference(skolemize,[status(sab)],[75])).
% 0.67/0.87  tff(77,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[76, 69])).
% 0.67/0.87  tff(78,plain,
% 0.67/0.87      (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[77, 67])).
% 0.67/0.87  tff(79,plain,
% 0.67/0.87      (((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144)) | (~((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))))))) <=> ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144)) | (~((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))))))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(80,plain,
% 0.67/0.87      ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144)) | (~((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))))))),
% 0.67/0.87      inference(quant_inst,[status(thm)],[])).
% 0.67/0.87  tff(81,plain,
% 0.67/0.87      ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144)) | (~((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X)))))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[80, 79])).
% 0.67/0.87  tff(82,plain,
% 0.67/0.87      (~((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[81, 78, 62])).
% 0.67/0.87  tff(83,plain,
% 0.67/0.87      (((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X)))) | ![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))),
% 0.67/0.87      inference(tautology,[status(thm)],[])).
% 0.67/0.87  tff(84,plain,
% 0.67/0.87      (![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[83, 82])).
% 0.67/0.87  tff(85,plain,
% 0.67/0.87      (((~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))) | ((~icext(uri_ex_Clique, uri_ex_JoesGang)) | icext(BNODE_r!144, uri_ex_JoesGang))) <=> ((~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))) | (~icext(uri_ex_Clique, uri_ex_JoesGang)) | icext(BNODE_r!144, uri_ex_JoesGang))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(86,plain,
% 0.67/0.87      ((~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))) | ((~icext(uri_ex_Clique, uri_ex_JoesGang)) | icext(BNODE_r!144, uri_ex_JoesGang))),
% 0.67/0.87      inference(quant_inst,[status(thm)],[])).
% 0.67/0.87  tff(87,plain,
% 0.67/0.87      ((~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))) | (~icext(uri_ex_Clique, uri_ex_JoesGang)) | icext(BNODE_r!144, uri_ex_JoesGang)),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.67/0.87  tff(88,plain,
% 0.67/0.87      (icext(BNODE_r!144, uri_ex_JoesGang)),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[87, 84, 61])).
% 0.67/0.87  tff(89,plain,
% 0.67/0.87      ((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))))))) | (~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))))),
% 0.67/0.87      inference(tautology,[status(thm)],[])).
% 0.67/0.87  tff(90,plain,
% 0.67/0.87      ((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))))))) | (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.67/0.87  tff(91,plain,
% 0.67/0.87      (~((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[90, 48])).
% 0.67/0.87  tff(92,plain,
% 0.67/0.87      (((~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))) | iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.87      inference(tautology,[status(thm)],[])).
% 0.67/0.87  tff(93,plain,
% 0.67/0.87      (iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.87      inference(unit_resolution,[status(thm)],[92, 91])).
% 0.67/0.87  tff(94,plain,
% 0.67/0.87      (iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)),
% 0.67/0.87      inference(and_elim,[status(thm)],[16])).
% 0.67/0.87  tff(95,plain,
% 0.67/0.87      (^[P: $i, Q: $i] : refl(((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(96,plain,
% 0.67/0.87      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[95])).
% 0.67/0.87  tff(97,plain,
% 0.67/0.87      (^[P: $i, Q: $i] : rewrite(((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(98,plain,
% 0.67/0.87      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[97])).
% 0.67/0.87  tff(99,plain,
% 0.67/0.87      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.87      inference(transitivity,[status(thm)],[98, 96])).
% 0.67/0.87  tff(100,plain,
% 0.67/0.87      (^[P: $i, Q: $i] : rewrite(((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(101,plain,
% 0.67/0.87      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[100])).
% 0.67/0.87  tff(102,plain,
% 0.67/0.87      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.67/0.87      inference(rewrite,[status(thm)],[])).
% 0.67/0.87  tff(103,plain,
% 0.67/0.87      (^[P: $i, Q: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i, Y: $i] : rewrite((iext(P, X, Y) => iext(Q, X, Y)) <=> ((~iext(P, X, Y)) | iext(Q, X, Y)))), (![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)) <=> ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))), (((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y))) <=> ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))), rewrite(((ip(P) & ip(Q)) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))) <=> (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))), (((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y))) <=> (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))), ((iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)))) <=> (iext(uri_rdfs_subPropertyOf, P, Q) => (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))), rewrite((iext(uri_rdfs_subPropertyOf, P, Q) => (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))), ((iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(104,plain,
% 0.67/0.87      (![P: $i, Q: $i] : (iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[103])).
% 0.67/0.88  tff(105,axiom,(![P: $i, Q: $i] : (iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_subpropertyof_main')).
% 0.67/0.88  tff(106,plain,
% 0.67/0.88      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[105, 104])).
% 0.67/0.88  tff(107,plain,
% 0.67/0.88      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[106, 102])).
% 0.67/0.88  tff(108,plain,(
% 0.67/0.88      ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.67/0.88      inference(skolemize,[status(sab)],[107])).
% 0.67/0.88  tff(109,plain,
% 0.67/0.88      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[108, 101])).
% 0.67/0.88  tff(110,plain,
% 0.67/0.88      (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[109, 99])).
% 0.67/0.88  tff(111,plain,
% 0.67/0.88      (((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs)))))) <=> ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | (~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs)))))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(112,plain,
% 0.67/0.88      (((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y)))))) <=> ((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs)))))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(113,plain,
% 0.67/0.88      (((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))))))) <=> ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs))))))),
% 0.67/0.88      inference(monotonicity,[status(thm)],[112])).
% 0.67/0.88  tff(114,plain,
% 0.67/0.88      (((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))))))) <=> ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | (~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs)))))),
% 0.67/0.88      inference(transitivity,[status(thm)],[113, 111])).
% 0.67/0.88  tff(115,plain,
% 0.67/0.88      ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))))))),
% 0.67/0.88      inference(quant_inst,[status(thm)],[])).
% 0.67/0.88  tff(116,plain,
% 0.67/0.88      ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | (~iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)) | (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[115, 114])).
% 0.67/0.88  tff(117,plain,
% 0.67/0.88      (~((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs)))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[116, 110, 94])).
% 0.67/0.88  tff(118,plain,
% 0.67/0.88      (((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_owl_sameAs))) | ![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))),
% 0.67/0.88      inference(tautology,[status(thm)],[])).
% 0.67/0.88  tff(119,plain,
% 0.67/0.88      (![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[118, 117])).
% 0.67/0.88  tff(120,plain,
% 0.67/0.88      (((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | ((~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(121,plain,
% 0.67/0.88      ((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | ((~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))),
% 0.67/0.88      inference(quant_inst,[status(thm)],[])).
% 0.67/0.88  tff(122,plain,
% 0.67/0.88      ((~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.67/0.88  tff(123,plain,
% 0.67/0.88      (iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[122, 119, 93])).
% 0.67/0.88  tff(124,plain,
% 0.67/0.88      ((~(iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)) <=> (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))) | (~iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))) | (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.88      inference(tautology,[status(thm)],[])).
% 0.67/0.88  tff(125,plain,
% 0.67/0.88      ((~(iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)) <=> (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))) | (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[124, 123])).
% 0.67/0.88  tff(126,plain,
% 0.67/0.88      (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[125, 9])).
% 0.67/0.88  tff(127,plain,
% 0.67/0.88      (iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang) <=> iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.67/0.88      inference(monotonicity,[status(thm)],[126])).
% 0.67/0.88  tff(128,plain,
% 0.67/0.88      (iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)) <=> iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)),
% 0.67/0.88      inference(symmetry,[status(thm)],[127])).
% 0.67/0.88  tff(129,plain,
% 0.67/0.88      (iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[93, 128])).
% 0.67/0.88  tff(130,plain,
% 0.67/0.88      (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(131,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[130])).
% 0.67/0.88  tff(132,plain,
% 0.67/0.88      (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(133,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[132])).
% 0.67/0.88  tff(134,plain,
% 0.67/0.88      (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(135,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[134])).
% 0.67/0.88  tff(136,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.88      inference(transitivity,[status(thm)],[135, 133])).
% 0.67/0.88  tff(137,plain,
% 0.67/0.88      (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))), trans(monotonicity(rewrite((~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))) <=> (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), rewrite((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))), rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(138,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[137])).
% 0.67/0.88  tff(139,plain,
% 0.67/0.88      (^[P1: $i, P2: $i] : rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(140,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[139])).
% 0.67/0.88  tff(141,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(142,plain,
% 0.67/0.88      (^[P1: $i, P2: $i] : rewrite((iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(143,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[142])).
% 0.67/0.88  tff(144,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_inv')).
% 0.67/0.88  tff(145,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.67/0.88  tff(146,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[145, 141])).
% 0.67/0.88  tff(147,plain,(
% 0.67/0.88      ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.67/0.88      inference(skolemize,[status(sab)],[146])).
% 0.67/0.88  tff(148,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[147, 140])).
% 0.67/0.88  tff(149,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[148, 138])).
% 0.67/0.88  tff(150,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[149, 136])).
% 0.67/0.88  tff(151,plain,
% 0.67/0.88      (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[150, 131])).
% 0.67/0.88  tff(152,plain,
% 0.67/0.88      ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type) | (~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~(iext(BNODE_i!143, tptp_fun_X_108(uri_rdf_type, BNODE_i!143), tptp_fun_Y_107(uri_rdf_type, BNODE_i!143)) <=> iext(uri_rdf_type, tptp_fun_Y_107(uri_rdf_type, BNODE_i!143), tptp_fun_X_108(uri_rdf_type, BNODE_i!143)))))) | (~((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X)))))))))),
% 0.67/0.88      inference(quant_inst,[status(thm)],[])).
% 0.67/0.88  tff(153,plain,
% 0.67/0.88      (~((~(iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type) | (~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~(iext(BNODE_i!143, tptp_fun_X_108(uri_rdf_type, BNODE_i!143), tptp_fun_Y_107(uri_rdf_type, BNODE_i!143)) <=> iext(uri_rdf_type, tptp_fun_Y_107(uri_rdf_type, BNODE_i!143), tptp_fun_X_108(uri_rdf_type, BNODE_i!143)))))) | (~((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))))))))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[152, 151])).
% 0.67/0.88  tff(154,plain,
% 0.67/0.88      (((~(iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type) | (~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~(iext(BNODE_i!143, tptp_fun_X_108(uri_rdf_type, BNODE_i!143), tptp_fun_Y_107(uri_rdf_type, BNODE_i!143)) <=> iext(uri_rdf_type, tptp_fun_Y_107(uri_rdf_type, BNODE_i!143), tptp_fun_X_108(uri_rdf_type, BNODE_i!143)))))) | (~((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X)))))))) | ((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))))))),
% 0.67/0.88      inference(tautology,[status(thm)],[])).
% 0.67/0.88  tff(155,plain,
% 0.67/0.88      ((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X)))))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[154, 153])).
% 0.67/0.88  tff(156,plain,
% 0.67/0.88      (iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(157,plain,
% 0.67/0.88      ((~((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))))))) | (~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X)))))),
% 0.67/0.88      inference(tautology,[status(thm)],[])).
% 0.67/0.88  tff(158,plain,
% 0.67/0.88      ((~((~iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))))))) | (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X)))))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[157, 156])).
% 0.67/0.88  tff(159,plain,
% 0.67/0.88      (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[158, 155])).
% 0.67/0.88  tff(160,plain,
% 0.67/0.88      (((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X)))) | ![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))),
% 0.67/0.88      inference(tautology,[status(thm)],[])).
% 0.67/0.88  tff(161,plain,
% 0.67/0.88      (![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[160, 159])).
% 0.67/0.88  tff(162,plain,
% 0.67/0.88      ((~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))) | (iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob) <=> iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))),
% 0.67/0.88      inference(quant_inst,[status(thm)],[])).
% 0.67/0.88  tff(163,plain,
% 0.67/0.88      (iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob) <=> iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[162, 161])).
% 0.67/0.88  tff(164,plain,
% 0.67/0.88      (iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(165,plain,
% 0.67/0.88      ((~(iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob) <=> iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))) | iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))),
% 0.67/0.88      inference(tautology,[status(thm)],[])).
% 0.67/0.88  tff(166,plain,
% 0.67/0.88      ((~(iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob) <=> iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang))) | iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[165, 164])).
% 0.67/0.88  tff(167,plain,
% 0.67/0.88      (iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)),
% 0.67/0.88      inference(unit_resolution,[status(thm)],[166, 163])).
% 0.67/0.88  tff(168,plain,
% 0.67/0.88      (iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(169,plain,
% 0.67/0.88      (iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(170,plain,
% 0.67/0.88      (iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(171,plain,
% 0.67/0.88      (iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(172,plain,
% 0.67/0.88      (iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(173,plain,
% 0.67/0.88      (iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)),
% 0.67/0.88      inference(and_elim,[status(thm)],[16])).
% 0.67/0.88  tff(174,plain,
% 0.67/0.88      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))), (((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))))), rewrite(((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))), (((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(175,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[174])).
% 0.67/0.88  tff(176,plain,
% 0.67/0.88      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : refl(((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(177,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[176])).
% 0.67/0.89  tff(178,plain,
% 0.67/0.89      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : rewrite(((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(179,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[178])).
% 0.67/0.89  tff(180,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))),
% 0.67/0.89      inference(transitivity,[status(thm)],[179, 177])).
% 0.67/0.89  tff(181,plain,
% 0.67/0.89      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2))))))), rewrite((~(~((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) <=> (((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))))), rewrite((((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) <=> ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(182,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[181])).
% 0.67/0.89  tff(183,plain,
% 0.67/0.89      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~ip(P3)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(184,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~ip(P3)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[183])).
% 0.67/0.89  tff(185,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))))),
% 0.67/0.89      inference(rewrite,[status(thm)],[])).
% 0.67/0.89  tff(186,plain,
% 0.67/0.89      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3)))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3)))), ((((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))), ((((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) <=> ((((ip(P) & ip(P1)) & ip(P2)) & ip(P3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) & iext(P3, Y2, Y3)) => iext(P, Y0, Y3)))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3))))), (((((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((((ip(P) & ip(P1)) & ip(P2)) & ip(P3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) & iext(P3, Y2, Y3)) => iext(P, Y0, Y3))))) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3))))))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))))), (((((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((((ip(P) & ip(P1)) & ip(P2)) & ip(P3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) & iext(P3, Y2, Y3)) => iext(P, Y0, Y3))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(187,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((((ip(P) & ip(P1)) & ip(P2)) & ip(P3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) & iext(P3, Y2, Y3)) => iext(P, Y0, Y3))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[186])).
% 0.67/0.89  tff(188,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, P3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((((ip(P) & ip(P1)) & ip(P2)) & ip(P3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) & iext(P3, Y2, Y3)) => iext(P, Y0, Y3)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_chain_003')).
% 0.67/0.89  tff(189,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[188, 187])).
% 0.67/0.89  tff(190,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[189, 185])).
% 0.67/0.89  tff(191,plain,(
% 0.67/0.89      ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~ip(P3)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))),
% 0.67/0.89      inference(skolemize,[status(sab)],[190])).
% 0.67/0.89  tff(192,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ip(P3) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) | iext(P, Y0, Y3)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P)) & iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P)) & iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))) | iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[191, 184])).
% 0.67/0.89  tff(193,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[192, 182])).
% 0.67/0.89  tff(194,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[193, 180])).
% 0.67/0.89  tff(195,plain,
% 0.67/0.89      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[194, 175])).
% 0.67/0.89  tff(196,plain,
% 0.67/0.89      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))))),
% 0.67/0.90      inference(rewrite,[status(thm)],[])).
% 0.67/0.90  tff(197,plain,
% 0.67/0.90      (((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))))),
% 0.67/0.90      inference(rewrite,[status(thm)],[])).
% 0.67/0.90  tff(198,plain,
% 0.67/0.90      ((~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~(iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(uri_foaf_knows, Y0, Y3) | (~iext(BNODE_i!143, Y2, Y3)) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(uri_ex_sameCliqueAs, Y1, Y2)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))))))),
% 0.67/0.90      inference(rewrite,[status(thm)],[])).
% 0.67/0.90  tff(199,plain,
% 0.67/0.90      (((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~(iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(uri_foaf_knows, Y0, Y3) | (~iext(BNODE_i!143, Y2, Y3)) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(uri_ex_sameCliqueAs, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))))),
% 0.67/0.90      inference(monotonicity,[status(thm)],[198])).
% 0.67/0.90  tff(200,plain,
% 0.67/0.90      (((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~(iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(uri_foaf_knows, Y0, Y3) | (~iext(BNODE_i!143, Y2, Y3)) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(uri_ex_sameCliqueAs, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))))),
% 0.67/0.90      inference(transitivity,[status(thm)],[199, 197])).
% 0.67/0.90  tff(201,plain,
% 0.67/0.90      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~(iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(uri_foaf_knows, Y0, Y3) | (~iext(BNODE_i!143, Y2, Y3)) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(uri_ex_sameCliqueAs, Y1, Y2)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))))))))),
% 0.67/0.90      inference(monotonicity,[status(thm)],[200])).
% 0.67/0.90  tff(202,plain,
% 0.67/0.90      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~(iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(uri_foaf_knows, Y0, Y3) | (~iext(BNODE_i!143, Y2, Y3)) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(uri_ex_sameCliqueAs, Y1, Y2)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))))),
% 0.67/0.90      inference(transitivity,[status(thm)],[201, 196])).
% 0.67/0.90  tff(203,plain,
% 0.67/0.90      ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~(iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(BNODE_i!143)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(uri_foaf_knows, Y0, Y3) | (~iext(BNODE_i!143, Y2, Y3)) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(uri_ex_sameCliqueAs, Y1, Y2)))))))))))),
% 0.67/0.90      inference(quant_inst,[status(thm)],[])).
% 0.67/0.90  tff(204,plain,
% 0.67/0.90      ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i, S3: $i, P3: $i] : ((~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, P3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P)) | (~iext(P1, tptp_fun_Y0_106(P3, P2, P1, P), tptp_fun_Y1_105(P3, P2, P1, P))) | (~iext(P2, tptp_fun_Y1_105(P3, P2, P1, P), tptp_fun_Y2_104(P3, P2, P1, P))) | (~iext(P3, tptp_fun_Y2_104(P3, P2, P1, P), tptp_fun_Y3_103(P3, P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P3)) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : (iext(P, Y0, Y3) | (~iext(P3, Y2, Y3)) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))))))),
% 0.67/0.90      inference(modus_ponens,[status(thm)],[203, 202])).
% 0.67/0.90  tff(205,plain,
% 0.67/0.90      (~((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[204, 195, 173, 172, 171, 170, 169, 168])).
% 0.67/0.90  tff(206,plain,
% 0.67/0.90      (((~(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142) | (~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~((~iext(BNODE_i!143, tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_ex_sameCliqueAs, tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y2_104(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | (~iext(uri_rdf_type, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y1_105(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows))) | iext(uri_foaf_knows, tptp_fun_Y0_106(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows), tptp_fun_Y3_103(BNODE_i!143, uri_ex_sameCliqueAs, uri_rdf_type, uri_foaf_knows)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))),
% 0.67/0.90      inference(tautology,[status(thm)],[])).
% 0.67/0.90  tff(207,plain,
% 0.67/0.90      ((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[206, 205])).
% 0.67/0.90  tff(208,plain,
% 0.67/0.90      (iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)),
% 0.67/0.90      inference(and_elim,[status(thm)],[16])).
% 0.67/0.90  tff(209,plain,
% 0.67/0.90      ((~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))) | (~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))),
% 0.67/0.90      inference(tautology,[status(thm)],[])).
% 0.67/0.90  tff(210,plain,
% 0.67/0.90      ((~((~iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))))) | (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))))),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[209, 208])).
% 0.67/0.91  tff(211,plain,
% 0.67/0.91      (~((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))))),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[210, 207])).
% 0.67/0.91  tff(212,plain,
% 0.67/0.91      (((~ip(uri_rdf_type)) | (~ip(uri_foaf_knows)) | (~ip(uri_ex_sameCliqueAs)) | (~ip(BNODE_i!143)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3))))) | ![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))),
% 0.67/0.91      inference(tautology,[status(thm)],[])).
% 0.67/0.91  tff(213,plain,
% 0.67/0.91      (![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[212, 211])).
% 0.67/0.91  tff(214,plain,
% 0.67/0.91      (iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)),
% 0.67/0.91      inference(and_elim,[status(thm)],[16])).
% 0.67/0.91  tff(215,plain,
% 0.67/0.91      ((~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)) <=> (~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(216,axiom,(~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_013_Cliques')).
% 0.67/0.91  tff(217,plain,
% 0.67/0.91      (~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)),
% 0.67/0.91      inference(modus_ponens,[status(thm)],[216, 215])).
% 0.67/0.91  tff(218,plain,
% 0.67/0.91      (((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | (iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(219,plain,
% 0.67/0.91      (((~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob))) <=> (iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(220,plain,
% 0.67/0.91      (((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | ((~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | (iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang))))),
% 0.67/0.92      inference(monotonicity,[status(thm)],[219])).
% 0.67/0.92  tff(221,plain,
% 0.67/0.92      (((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | ((~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)))),
% 0.67/0.92      inference(transitivity,[status(thm)],[220, 218])).
% 0.67/0.92  tff(222,plain,
% 0.67/0.92      ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | ((~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)))),
% 0.67/0.92      inference(quant_inst,[status(thm)],[])).
% 0.67/0.92  tff(223,plain,
% 0.67/0.92      ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang))),
% 0.67/0.92      inference(modus_ponens,[status(thm)],[222, 221])).
% 0.67/0.92  tff(224,plain,
% 0.67/0.92      (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)),
% 0.67/0.92      inference(unit_resolution,[status(thm)],[223, 217, 214, 213, 167])).
% 0.67/0.92  tff(225,plain,
% 0.67/0.92      ($false),
% 0.67/0.92      inference(unit_resolution,[status(thm)],[224, 129])).
% 0.67/0.92  % SZS output end Proof
% 0.77/0.93  % E exiting
%------------------------------------------------------------------------------