TSTP Solution File: SWB013+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB013+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Tue Sep 20 08:31:43 EDT 2022
% Result : Theorem 0.86s 0.84s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWB013+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 19:28:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.86/0.84 % SZS status Theorem
% 0.86/0.84 % SZS output start Proof
% 0.86/0.84 tff(iext_type, type, (
% 0.86/0.84 iext: ( $i * $i * $i ) > $o)).
% 0.86/0.84 tff(uri_ex_JoesGang_type, type, (
% 0.86/0.84 uri_ex_JoesGang: $i)).
% 0.86/0.84 tff(uri_ex_sameCliqueAs_type, type, (
% 0.86/0.84 uri_ex_sameCliqueAs: $i)).
% 0.86/0.84 tff(tptp_fun_Y_42_type, type, (
% 0.86/0.84 tptp_fun_Y_42: ( $i * $i * $i ) > $i)).
% 0.86/0.84 tff(uri_ex_Clique_type, type, (
% 0.86/0.84 uri_ex_Clique: $i)).
% 0.86/0.84 tff(uri_owl_sameAs_type, type, (
% 0.86/0.84 uri_owl_sameAs: $i)).
% 0.86/0.84 tff(icext_type, type, (
% 0.86/0.84 icext: ( $i * $i ) > $o)).
% 0.86/0.84 tff(tptp_fun_BNODE_r_144_type, type, (
% 0.86/0.84 tptp_fun_BNODE_r_144: $i)).
% 0.86/0.84 tff(uri_owl_someValuesFrom_type, type, (
% 0.86/0.84 uri_owl_someValuesFrom: $i)).
% 0.86/0.84 tff(uri_ex_bob_type, type, (
% 0.86/0.84 uri_ex_bob: $i)).
% 0.86/0.84 tff(uri_rdf_type_type, type, (
% 0.86/0.84 uri_rdf_type: $i)).
% 0.86/0.84 tff(uri_ex_alice_type, type, (
% 0.86/0.84 uri_ex_alice: $i)).
% 0.86/0.84 tff(tptp_fun_BNODE_i_143_type, type, (
% 0.86/0.84 tptp_fun_BNODE_i_143: $i)).
% 0.86/0.84 tff(uri_owl_inverseOf_type, type, (
% 0.86/0.84 uri_owl_inverseOf: $i)).
% 0.86/0.84 tff(uri_rdf_nil_type, type, (
% 0.86/0.84 uri_rdf_nil: $i)).
% 0.86/0.84 tff(tptp_fun_BNODE_l3_140_type, type, (
% 0.86/0.84 tptp_fun_BNODE_l3_140: $i)).
% 0.86/0.84 tff(uri_rdf_rest_type, type, (
% 0.86/0.84 uri_rdf_rest: $i)).
% 0.86/0.84 tff(uri_rdf_first_type, type, (
% 0.86/0.84 uri_rdf_first: $i)).
% 0.86/0.84 tff(tptp_fun_BNODE_l2_141_type, type, (
% 0.86/0.84 tptp_fun_BNODE_l2_141: $i)).
% 0.86/0.84 tff(tptp_fun_BNODE_l1_142_type, type, (
% 0.86/0.84 tptp_fun_BNODE_l1_142: $i)).
% 0.86/0.84 tff(uri_foaf_knows_type, type, (
% 0.86/0.84 uri_foaf_knows: $i)).
% 0.86/0.84 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.86/0.84 uri_owl_propertyChainAxiom: $i)).
% 0.86/0.84 tff(uri_owl_ObjectProperty_type, type, (
% 0.86/0.84 uri_owl_ObjectProperty: $i)).
% 0.86/0.84 tff(uri_owl_onProperty_type, type, (
% 0.86/0.84 uri_owl_onProperty: $i)).
% 0.86/0.84 tff(uri_owl_Restriction_type, type, (
% 0.86/0.84 uri_owl_Restriction: $i)).
% 0.86/0.84 tff(uri_rdfs_subClassOf_type, type, (
% 0.86/0.84 uri_rdfs_subClassOf: $i)).
% 0.86/0.84 tff(uri_rdfs_range_type, type, (
% 0.86/0.84 uri_rdfs_range: $i)).
% 0.86/0.84 tff(uri_rdfs_subPropertyOf_type, type, (
% 0.86/0.84 uri_rdfs_subPropertyOf: $i)).
% 0.86/0.84 tff(uri_owl_Class_type, type, (
% 0.86/0.84 uri_owl_Class: $i)).
% 0.86/0.84 tff(ic_type, type, (
% 0.86/0.84 ic: $i > $o)).
% 0.86/0.84 tff(ip_type, type, (
% 0.86/0.84 ip: $i > $o)).
% 0.86/0.84 tff(tptp_fun_X_108_type, type, (
% 0.86/0.84 tptp_fun_X_108: ( $i * $i ) > $i)).
% 0.86/0.84 tff(tptp_fun_Y_107_type, type, (
% 0.86/0.84 tptp_fun_Y_107: ( $i * $i ) > $i)).
% 0.86/0.84 tff(tptp_fun_Y3_103_type, type, (
% 0.86/0.84 tptp_fun_Y3_103: ( $i * $i * $i * $i ) > $i)).
% 0.86/0.84 tff(tptp_fun_Y2_104_type, type, (
% 0.86/0.84 tptp_fun_Y2_104: ( $i * $i * $i * $i ) > $i)).
% 0.86/0.84 tff(tptp_fun_Y1_105_type, type, (
% 0.86/0.84 tptp_fun_Y1_105: ( $i * $i * $i * $i ) > $i)).
% 0.86/0.84 tff(tptp_fun_Y0_106_type, type, (
% 0.86/0.84 tptp_fun_Y0_106: ( $i * $i * $i * $i ) > $i)).
% 0.86/0.84 tff(1,plain,
% 0.86/0.84 (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(2,plain,
% 0.86/0.84 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[1])).
% 0.86/0.84 tff(3,plain,
% 0.86/0.84 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 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')).
% 0.86/0.84 tff(5,plain,
% 0.86/0.84 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.86/0.84 tff(6,plain,(
% 0.86/0.84 ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.86/0.84 inference(skolemize,[status(sab)],[5])).
% 0.86/0.84 tff(7,plain,
% 0.86/0.84 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.86/0.84 tff(8,plain,
% 0.86/0.84 ((~![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)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(9,plain,
% 0.86/0.84 (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))),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.86/0.84 tff(10,plain,
% 0.86/0.84 (?[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))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(11,plain,
% 0.86/0.84 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(12,plain,
% 0.91/0.86 (?[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))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[11])).
% 0.91/0.86 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')).
% 0.91/0.86 tff(14,plain,
% 0.91/0.86 (?[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))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.91/0.86 tff(15,plain,
% 0.91/0.86 (?[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))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.91/0.86 tff(16,plain,(
% 0.91/0.86 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)),
% 0.91/0.86 inference(skolemize,[status(sab)],[15])).
% 0.91/0.86 tff(17,plain,
% 0.91/0.86 (iext(uri_owl_someValuesFrom, BNODE_r!144, uri_ex_Clique)),
% 0.91/0.86 inference(and_elim,[status(thm)],[16])).
% 0.91/0.86 tff(18,plain,
% 0.91/0.86 (iext(uri_owl_onProperty, BNODE_r!144, uri_ex_sameCliqueAs)),
% 0.91/0.86 inference(and_elim,[status(thm)],[16])).
% 0.91/0.86 tff(19,plain,
% 0.91/0.86 (^[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)))))))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(20,plain,
% 0.91/0.86 (![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))))))))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[19])).
% 0.91/0.86 tff(21,plain,
% 0.91/0.86 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(22,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[21])).
% 0.91/0.86 tff(23,plain,
% 0.91/0.86 (^[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))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(24,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[23])).
% 0.91/0.86 tff(25,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(transitivity,[status(thm)],[24, 22])).
% 0.91/0.86 tff(26,plain,
% 0.91/0.86 (^[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)))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(27,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[26])).
% 0.91/0.86 tff(28,plain,
% 0.91/0.86 (![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))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(29,plain,
% 0.91/0.86 (^[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)))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(30,plain,
% 0.91/0.86 (![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))))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[29])).
% 0.91/0.86 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')).
% 0.91/0.86 tff(32,plain,
% 0.91/0.86 (![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))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.91/0.86 tff(33,plain,
% 0.91/0.86 (![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))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.91/0.86 tff(34,plain,(
% 0.91/0.86 ![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))))))),
% 0.91/0.86 inference(skolemize,[status(sab)],[33])).
% 0.91/0.86 tff(35,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.91/0.86 tff(36,plain,
% 0.91/0.86 (![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)))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.91/0.86 tff(37,plain,
% 0.91/0.86 (![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))))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[36, 20])).
% 0.91/0.86 tff(38,plain,
% 0.91/0.86 (((~![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)) | (~((~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))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(39,plain,
% 0.91/0.86 ((~![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))))))))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(40,plain,
% 0.91/0.86 ((~![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)))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.91/0.86 tff(41,plain,
% 0.91/0.86 (![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)))))))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[40, 37, 18, 17])).
% 0.91/0.86 tff(42,plain,
% 0.91/0.86 ((~![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)))))))) | (~((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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))))))) | (~(icext(BNODE_r!144, uri_ex_JoesGang) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, Y)))))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(43,plain,
% 0.91/0.87 (~((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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))))))) | (~(icext(BNODE_r!144, uri_ex_JoesGang) | ![Y: $i] : ((~icext(uri_ex_Clique, Y)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, Y))))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.91/0.87 tff(44,plain,
% 0.91/0.87 (((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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))))))) | (~(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)) | (~((~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))))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(45,plain,
% 0.91/0.87 ((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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)))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.91/0.87 tff(46,plain,
% 0.91/0.87 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(47,plain,
% 0.91/0.87 (![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))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[46])).
% 0.91/0.87 tff(48,plain,
% 0.91/0.87 (![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))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(49,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')).
% 0.91/0.87 tff(50,plain,
% 0.91/0.87 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.91/0.87 tff(51,plain,(
% 0.91/0.87 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.91/0.87 inference(skolemize,[status(sab)],[50])).
% 0.91/0.87 tff(52,plain,
% 0.91/0.87 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.91/0.87 tff(53,plain,
% 0.91/0.87 ((~![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))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(54,plain,
% 0.91/0.87 (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) <=> icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.91/0.87 tff(55,plain,
% 0.91/0.87 (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique)),
% 0.91/0.87 inference(and_elim,[status(thm)],[16])).
% 0.91/0.87 tff(56,plain,
% 0.91/0.87 ((~(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)),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(57,plain,
% 0.91/0.87 ((~(iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) <=> icext(uri_ex_Clique, uri_ex_JoesGang))) | icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.91/0.87 tff(58,plain,
% 0.91/0.87 (icext(uri_ex_Clique, uri_ex_JoesGang)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.91/0.87 tff(59,plain,
% 0.91/0.87 (iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r!144)),
% 0.91/0.87 inference(and_elim,[status(thm)],[16])).
% 0.91/0.87 tff(60,plain,
% 0.91/0.87 (^[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)))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(61,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[60])).
% 0.91/0.87 tff(62,plain,
% 0.91/0.87 (^[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)))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(63,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[62])).
% 0.91/0.87 tff(64,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(transitivity,[status(thm)],[63, 61])).
% 0.91/0.87 tff(65,plain,
% 0.91/0.87 (^[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)))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(66,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[65])).
% 0.91/0.87 tff(67,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(68,plain,
% 0.91/0.87 (^[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))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(69,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[68])).
% 0.91/0.87 tff(70,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')).
% 0.91/0.87 tff(71,plain,
% 0.91/0.87 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.91/0.87 tff(72,plain,
% 0.91/0.87 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.91/0.87 tff(73,plain,(
% 0.91/0.87 ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.91/0.87 inference(skolemize,[status(sab)],[72])).
% 0.91/0.87 tff(74,plain,
% 0.91/0.87 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.91/0.87 tff(75,plain,
% 0.91/0.87 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.91/0.87 tff(76,plain,
% 0.91/0.87 (((~![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))))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(77,plain,
% 0.91/0.87 ((~![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))))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(78,plain,
% 0.91/0.87 ((~![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)))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.91/0.87 tff(79,plain,
% 0.91/0.87 (~((~ic(BNODE_r!144)) | (~ic(uri_ex_Clique)) | (~![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[78, 75, 59])).
% 0.91/0.87 tff(80,plain,
% 0.91/0.87 (((~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))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(81,plain,
% 0.91/0.87 (![X: $i] : ((~icext(uri_ex_Clique, X)) | icext(BNODE_r!144, X))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.91/0.87 tff(82,plain,
% 0.91/0.87 (((~![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))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(83,plain,
% 0.91/0.87 ((~![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))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(84,plain,
% 0.91/0.87 ((~![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)),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.91/0.87 tff(85,plain,
% 0.91/0.87 (icext(BNODE_r!144, uri_ex_JoesGang)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[84, 81, 58])).
% 0.91/0.87 tff(86,plain,
% 0.91/0.87 ((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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))))))) | (~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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)))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(87,plain,
% 0.91/0.87 ((~((~icext(BNODE_r!144, uri_ex_JoesGang)) | (~((~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))) | (~icext(uri_ex_Clique, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.91/0.87 tff(88,plain,
% 0.91/0.87 (~((~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))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[87, 45])).
% 0.91/0.87 tff(89,plain,
% 0.91/0.87 (((~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))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(90,plain,
% 0.91/0.87 (iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.91/0.87 tff(91,plain,
% 0.91/0.87 (iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs)),
% 0.91/0.87 inference(and_elim,[status(thm)],[16])).
% 0.91/0.87 tff(92,plain,
% 0.91/0.87 (^[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)))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(93,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[92])).
% 0.91/0.87 tff(94,plain,
% 0.91/0.87 (^[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)))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(95,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[94])).
% 0.91/0.87 tff(96,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(transitivity,[status(thm)],[95, 93])).
% 0.91/0.87 tff(97,plain,
% 0.91/0.87 (^[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)))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(98,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[97])).
% 0.91/0.87 tff(99,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(100,plain,
% 0.91/0.87 (^[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))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(101,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[100])).
% 0.91/0.87 tff(102,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')).
% 0.91/0.87 tff(103,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.91/0.87 tff(104,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.91/0.87 tff(105,plain,(
% 0.91/0.87 ![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))))),
% 0.91/0.87 inference(skolemize,[status(sab)],[104])).
% 0.91/0.87 tff(106,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.91/0.87 tff(107,plain,
% 0.91/0.87 (![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))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.91/0.87 tff(108,plain,
% 0.91/0.87 (((~![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))))))) | ((~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)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(109,plain,
% 0.91/0.87 ((~![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))))))) | ((~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))))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(110,plain,
% 0.91/0.87 ((~![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))))))) | (~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)))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.91/0.87 tff(111,plain,
% 0.91/0.87 (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[110, 107, 91])).
% 0.91/0.87 tff(112,plain,
% 0.91/0.87 (((~ip(uri_owl_sameAs)) | (~ip(uri_ex_sameCliqueAs)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(113,plain,
% 0.91/0.87 (![X: $i, Y: $i] : ((~iext(uri_ex_sameCliqueAs, X, Y)) | iext(uri_owl_sameAs, X, Y))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.91/0.87 tff(114,plain,
% 0.91/0.87 (((~![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)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(115,plain,
% 0.91/0.87 ((~![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)))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(116,plain,
% 0.91/0.87 ((~![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))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.91/0.87 tff(117,plain,
% 0.91/0.87 (iext(uri_owl_sameAs, uri_ex_JoesGang, tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[116, 113, 90])).
% 0.91/0.87 tff(118,plain,
% 0.91/0.87 ((~(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))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(119,plain,
% 0.91/0.87 ((~(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))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.91/0.87 tff(120,plain,
% 0.91/0.87 (uri_ex_JoesGang = tptp_fun_Y_42(uri_ex_JoesGang, uri_ex_Clique, uri_ex_sameCliqueAs)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[119, 9])).
% 0.91/0.87 tff(121,plain,
% 0.91/0.87 (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))),
% 0.91/0.87 inference(monotonicity,[status(thm)],[120])).
% 0.91/0.87 tff(122,plain,
% 0.91/0.87 (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)),
% 0.91/0.87 inference(symmetry,[status(thm)],[121])).
% 0.91/0.87 tff(123,plain,
% 0.91/0.87 (iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[90, 122])).
% 0.91/0.87 tff(124,plain,
% 0.91/0.87 (^[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))))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(125,plain,
% 0.91/0.87 (![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)))))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[124])).
% 0.91/0.87 tff(126,plain,
% 0.91/0.87 (^[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))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(127,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[126])).
% 0.91/0.87 tff(128,plain,
% 0.91/0.87 (^[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))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(129,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[128])).
% 0.91/0.87 tff(130,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(transitivity,[status(thm)],[129, 127])).
% 0.91/0.87 tff(131,plain,
% 0.91/0.87 (^[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))))))), 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(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)))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(132,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[131])).
% 0.91/0.87 tff(133,plain,
% 0.91/0.87 (^[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))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(134,plain,
% 0.91/0.87 (![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)))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[133])).
% 0.91/0.87 tff(135,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(136,plain,
% 0.91/0.87 (^[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)))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(137,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[136])).
% 0.91/0.88 tff(138,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')).
% 0.91/0.88 tff(139,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.91/0.88 tff(140,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.91/0.88 tff(141,plain,(
% 0.91/0.88 ![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)))))))),
% 0.91/0.88 inference(skolemize,[status(sab)],[140])).
% 0.91/0.88 tff(142,plain,
% 0.91/0.88 (![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)))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.91/0.88 tff(143,plain,
% 0.91/0.88 (![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)))))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.91/0.88 tff(144,plain,
% 0.91/0.88 (![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)))))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[143, 130])).
% 0.91/0.88 tff(145,plain,
% 0.91/0.88 (![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)))))))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[144, 125])).
% 0.91/0.88 tff(146,plain,
% 0.91/0.88 ((~![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)))))))))),
% 0.91/0.88 inference(quant_inst,[status(thm)],[])).
% 0.91/0.88 tff(147,plain,
% 0.91/0.88 (~((~(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))))))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.91/0.88 tff(148,plain,
% 0.91/0.88 (((~(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))))))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(149,plain,
% 0.91/0.88 ((~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)))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.91/0.88 tff(150,plain,
% 0.91/0.88 (iext(uri_owl_inverseOf, BNODE_i!143, uri_rdf_type)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(151,plain,
% 0.91/0.88 ((~((~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)))))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(152,plain,
% 0.91/0.88 ((~((~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)))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.91/0.88 tff(153,plain,
% 0.91/0.88 (~((~ip(uri_rdf_type)) | (~ip(BNODE_i!143)) | (~![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.91/0.88 tff(154,plain,
% 0.91/0.88 (((~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))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(155,plain,
% 0.91/0.88 (![X: $i, Y: $i] : (iext(BNODE_i!143, X, Y) <=> iext(uri_rdf_type, Y, X))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.91/0.88 tff(156,plain,
% 0.91/0.88 ((~![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))),
% 0.91/0.88 inference(quant_inst,[status(thm)],[])).
% 0.91/0.88 tff(157,plain,
% 0.91/0.88 (iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob) <=> iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.91/0.88 tff(158,plain,
% 0.91/0.88 (iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(159,plain,
% 0.91/0.88 ((~(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))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(160,plain,
% 0.91/0.88 ((~(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)),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.91/0.88 tff(161,plain,
% 0.91/0.88 (iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[160, 157])).
% 0.91/0.88 tff(162,plain,
% 0.91/0.88 (iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(163,plain,
% 0.91/0.88 (iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(164,plain,
% 0.91/0.88 (iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(165,plain,
% 0.91/0.88 (iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(166,plain,
% 0.91/0.88 (iext(uri_rdf_rest, BNODE_l1!142, BNODE_l2!141)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(167,plain,
% 0.91/0.88 (iext(uri_rdf_first, BNODE_l1!142, uri_rdf_type)),
% 0.91/0.88 inference(and_elim,[status(thm)],[16])).
% 0.91/0.88 tff(168,plain,
% 0.91/0.88 (^[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)))))))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(169,plain,
% 0.91/0.88 (![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)))))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[168])).
% 0.91/0.88 tff(170,plain,
% 0.91/0.88 (^[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)))))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(171,plain,
% 0.91/0.88 (![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))))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[170])).
% 0.91/0.88 tff(172,plain,
% 0.91/0.88 (^[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)))))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(173,plain,
% 0.91/0.88 (![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))))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[172])).
% 0.91/0.88 tff(174,plain,
% 0.91/0.88 (![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))))))))))),
% 0.91/0.88 inference(transitivity,[status(thm)],[173, 171])).
% 0.91/0.88 tff(175,plain,
% 0.91/0.88 (^[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))))))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(176,plain,
% 0.91/0.88 (![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))))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[175])).
% 0.91/0.88 tff(177,plain,
% 0.91/0.88 (^[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))))))))),
% 0.91/0.89 inference(bind,[status(th)],[])).
% 0.91/0.89 tff(178,plain,
% 0.91/0.89 (![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)))))))),
% 0.91/0.89 inference(quant_intro,[status(thm)],[177])).
% 0.91/0.89 tff(179,plain,
% 0.91/0.89 (![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)))))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(180,plain,
% 0.91/0.89 (^[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)))))))),
% 0.91/0.89 inference(bind,[status(th)],[])).
% 0.91/0.89 tff(181,plain,
% 0.91/0.89 (![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)))))),
% 0.91/0.89 inference(quant_intro,[status(thm)],[180])).
% 0.91/0.89 tff(182,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')).
% 0.91/0.89 tff(183,plain,
% 0.91/0.89 (![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)))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.91/0.89 tff(184,plain,
% 0.91/0.89 (![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)))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.91/0.89 tff(185,plain,(
% 0.91/0.89 ![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))))))))),
% 0.91/0.89 inference(skolemize,[status(sab)],[184])).
% 0.91/0.89 tff(186,plain,
% 0.91/0.89 (![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)))))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.91/0.89 tff(187,plain,
% 0.91/0.89 (![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))))))))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.91/0.89 tff(188,plain,
% 0.91/0.89 (![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))))))))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[187, 174])).
% 0.91/0.89 tff(189,plain,
% 0.91/0.89 (![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)))))))))))),
% 0.91/0.89 inference(modus_ponens,[status(thm)],[188, 169])).
% 0.91/0.89 tff(190,plain,
% 0.91/0.89 (((~![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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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)))))))))))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(191,plain,
% 0.91/0.89 (((~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(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(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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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)))))))))))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(192,plain,
% 0.91/0.89 ((~((~(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(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(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))))))))))),
% 0.91/0.89 inference(rewrite,[status(thm)],[])).
% 0.91/0.89 tff(193,plain,
% 0.91/0.89 (((~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(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(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)))))))))))),
% 0.91/0.89 inference(monotonicity,[status(thm)],[192])).
% 0.91/0.89 tff(194,plain,
% 0.91/0.89 (((~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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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)))))))))))),
% 0.91/0.90 inference(transitivity,[status(thm)],[193, 191])).
% 0.91/0.90 tff(195,plain,
% 0.91/0.90 (((~![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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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))))))))))))),
% 0.91/0.90 inference(monotonicity,[status(thm)],[194])).
% 0.91/0.90 tff(196,plain,
% 0.91/0.90 (((~![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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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)))))))))))),
% 0.91/0.90 inference(transitivity,[status(thm)],[195, 190])).
% 0.91/0.90 tff(197,plain,
% 0.91/0.90 ((~![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)))))))))))),
% 0.91/0.90 inference(quant_inst,[status(thm)],[])).
% 0.91/0.90 tff(198,plain,
% 0.91/0.90 ((~![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_rest, BNODE_l1!142, BNODE_l2!141)) | (~iext(uri_rdf_first, BNODE_l2!141, uri_ex_sameCliqueAs)) | (~iext(uri_rdf_first, BNODE_l3!140, BNODE_i!143)) | (~iext(uri_rdf_rest, BNODE_l2!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l3!140, uri_rdf_nil)) | (~((~(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(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(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))))))))))),
% 0.91/0.90 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.91/0.90 tff(199,plain,
% 0.91/0.90 (~((~(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(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(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)))))))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[198, 189, 167, 166, 165, 164, 163, 162])).
% 0.91/0.90 tff(200,plain,
% 0.91/0.90 (((~(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(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(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)))))))),
% 0.91/0.90 inference(tautology,[status(thm)],[])).
% 0.91/0.90 tff(201,plain,
% 0.91/0.90 ((~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))))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.91/0.90 tff(202,plain,
% 0.91/0.90 (iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1!142)),
% 0.91/0.90 inference(and_elim,[status(thm)],[16])).
% 0.91/0.90 tff(203,plain,
% 0.91/0.90 ((~((~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))))))),
% 0.91/0.90 inference(tautology,[status(thm)],[])).
% 0.91/0.90 tff(204,plain,
% 0.91/0.90 ((~((~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))))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.91/0.90 tff(205,plain,
% 0.91/0.90 (~((~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)))))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[204, 201])).
% 0.91/0.90 tff(206,plain,
% 0.91/0.90 (((~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)))),
% 0.91/0.90 inference(tautology,[status(thm)],[])).
% 0.91/0.90 tff(207,plain,
% 0.91/0.90 (![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)))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.91/0.90 tff(208,plain,
% 0.91/0.90 (iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)),
% 0.91/0.90 inference(and_elim,[status(thm)],[16])).
% 0.91/0.90 tff(209,plain,
% 0.91/0.90 ((~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)) <=> (~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob))),
% 0.91/0.90 inference(rewrite,[status(thm)],[])).
% 0.91/0.90 tff(210,axiom,(~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_013_Cliques')).
% 0.91/0.90 tff(211,plain,
% 0.91/0.90 (~iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)),
% 0.91/0.90 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.91/0.90 tff(212,plain,
% 0.91/0.90 (((~![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)))),
% 0.91/0.90 inference(rewrite,[status(thm)],[])).
% 0.91/0.90 tff(213,plain,
% 0.91/0.90 (((~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)))),
% 0.91/0.92 inference(rewrite,[status(thm)],[])).
% 0.91/0.92 tff(214,plain,
% 0.91/0.92 (((~![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))))),
% 0.91/0.92 inference(monotonicity,[status(thm)],[213])).
% 0.91/0.92 tff(215,plain,
% 0.91/0.92 (((~![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)))),
% 0.91/0.92 inference(transitivity,[status(thm)],[214, 212])).
% 0.91/0.92 tff(216,plain,
% 0.91/0.92 ((~![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)))),
% 0.91/0.92 inference(quant_inst,[status(thm)],[])).
% 0.91/0.92 tff(217,plain,
% 0.91/0.92 ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i] : ((~iext(uri_ex_sameCliqueAs, Y1, Y2)) | iext(uri_foaf_knows, Y0, Y3) | (~iext(uri_rdf_type, Y0, Y1)) | (~iext(BNODE_i!143, Y2, Y3)))) | iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) | (~iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang)) | (~iext(BNODE_i!143, uri_ex_JoesGang, uri_ex_bob)) | (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang))),
% 0.91/0.92 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.91/0.92 tff(218,plain,
% 0.91/0.92 (~iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang)),
% 0.91/0.92 inference(unit_resolution,[status(thm)],[217, 211, 208, 207, 161])).
% 0.91/0.92 tff(219,plain,
% 0.91/0.92 ($false),
% 0.91/0.92 inference(unit_resolution,[status(thm)],[218, 123])).
% 0.91/0.92 % SZS output end Proof
%------------------------------------------------------------------------------