TSTP Solution File: SWB012+2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB012+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWB012+2 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 19:20:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(icext_type, type, (
% 0.12/0.39 icext: ( $i * $i ) > $o)).
% 0.12/0.39 tff(uri_ex_alice_type, type, (
% 0.12/0.39 uri_ex_alice: $i)).
% 0.12/0.39 tff(uri_foaf_Person_type, type, (
% 0.12/0.39 uri_foaf_Person: $i)).
% 0.12/0.39 tff(iext_type, type, (
% 0.12/0.39 iext: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(uri_rdf_type_type, type, (
% 0.12/0.39 uri_rdf_type: $i)).
% 0.12/0.39 tff(uri_owl_FunctionalProperty_type, type, (
% 0.12/0.39 uri_owl_FunctionalProperty: $i)).
% 0.12/0.39 tff(uri_ex_name_type, type, (
% 0.12/0.39 uri_ex_name: $i)).
% 0.12/0.39 tff(tptp_fun_BNODE_r_1_type, type, (
% 0.12/0.39 tptp_fun_BNODE_r_1: $i)).
% 0.12/0.39 tff(uri_owl_DatatypeProperty_type, type, (
% 0.12/0.39 uri_owl_DatatypeProperty: $i)).
% 0.12/0.39 tff(uri_ex_PersonAttribute_type, type, (
% 0.12/0.39 uri_ex_PersonAttribute: $i)).
% 0.12/0.39 tff(ic_type, type, (
% 0.12/0.39 ic: $i > $o)).
% 0.12/0.39 tff(tptp_fun_BNODE_l1_4_type, type, (
% 0.12/0.39 tptp_fun_BNODE_l1_4: $i)).
% 0.12/0.39 tff(uri_owl_intersectionOf_type, type, (
% 0.12/0.39 uri_owl_intersectionOf: $i)).
% 0.12/0.39 tff(tptp_fun_X_0_type, type, (
% 0.12/0.39 tptp_fun_X_0: ( $i * $i * $i * $i ) > $i)).
% 0.12/0.39 tff(uri_rdf_nil_type, type, (
% 0.12/0.39 uri_rdf_nil: $i)).
% 0.12/0.39 tff(tptp_fun_BNODE_l3_2_type, type, (
% 0.12/0.39 tptp_fun_BNODE_l3_2: $i)).
% 0.12/0.39 tff(uri_rdf_rest_type, type, (
% 0.12/0.39 uri_rdf_rest: $i)).
% 0.12/0.39 tff(literal_plain_type, type, (
% 0.12/0.39 literal_plain: $i > $i)).
% 0.12/0.39 tff(dat_str_alice_type, type, (
% 0.12/0.39 dat_str_alice: $i)).
% 0.12/0.39 tff(uri_owl_hasValue_type, type, (
% 0.12/0.39 uri_owl_hasValue: $i)).
% 0.12/0.39 tff(uri_rdfs_domain_type, type, (
% 0.12/0.39 uri_rdfs_domain: $i)).
% 0.12/0.39 tff(uri_owl_onProperty_type, type, (
% 0.12/0.39 uri_owl_onProperty: $i)).
% 0.12/0.39 tff(uri_owl_Restriction_type, type, (
% 0.12/0.39 uri_owl_Restriction: $i)).
% 0.12/0.39 tff(uri_rdf_first_type, type, (
% 0.12/0.39 uri_rdf_first: $i)).
% 0.12/0.39 tff(tptp_fun_BNODE_l2_3_type, type, (
% 0.12/0.39 tptp_fun_BNODE_l2_3: $i)).
% 0.12/0.39 tff(uri_owl_Class_type, type, (
% 0.12/0.39 uri_owl_Class: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty))), ((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), ((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), (((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty))), (((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)))), ((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3))), ((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)))), (((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r))), (((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r)))), ((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil))), ((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)))), (((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction))), (((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)))), ((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain))), ((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)))), (((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person))), (((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)))), ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute))), ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)))), (((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> ((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))), rewrite(((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))), (((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.41 tff(15,axiom,(?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : ((((((((((((iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty)) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3)) & iext(uri_rdf_first, BNODE_l3, BNODE_r)) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil)) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain)) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person)) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_012_Template_Class')).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_l3: $i, BNODE_r: $i] : (iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & iext(uri_rdf_first, BNODE_l3, BNODE_r) & iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.41 tff(18,plain,(
% 0.19/0.41 iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) & iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty) & iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3) & iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty) & iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2) & iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1) & iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil) & iext(uri_rdf_type, BNODE_r!1, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_r!1, uri_rdfs_domain) & iext(uri_owl_hasValue, BNODE_r!1, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))),
% 0.19/0.41 inference(skolemize,[status(sab)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)),
% 0.19/0.41 inference(and_elim,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[18])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)),
% 0.19/0.41 inference(and_elim,[status(thm)],[18])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)),
% 0.19/0.41 inference(and_elim,[status(thm)],[18])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)),
% 0.19/0.41 inference(and_elim,[status(thm)],[18])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)),
% 0.19/0.41 inference(and_elim,[status(thm)],[18])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X))))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X))))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X))))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) <=> ((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))), trans(monotonicity(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))), (((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))) <=> ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))), rewrite(((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))) <=> (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))), (((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))) <=> (((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X))))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))), rewrite((((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X))))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)))), ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))), ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite((iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X))))) <=> (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))), (((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))), (((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.43 tff(39,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) & icext(C2, X)) & icext(C3, X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_bool_intersectionof_class_003')).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.43 tff(42,plain,(
% 0.19/0.43 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X) & icext(C3, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | ((~icext(Z, tptp_fun_X_0(C3, C2, C1, Z))) <=> (icext(C1, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C2, tptp_fun_X_0(C3, C2, C1, Z)) & icext(C3, tptp_fun_X_0(C3, C2, C1, Z)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[45, 26])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | (~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 ((~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))) <=> (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))) <=> ((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 ((~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))) <=> (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 ((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) <=> (~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))) <=> ((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[52, 51])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 ((~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))) <=> (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[55, 48])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | (~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[57, 47])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (icext(Z, tptp_fun_X_0(C3, C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C3, C2, C1, Z))) | (~icext(C3, tptp_fun_X_0(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C1, X)) | (~icext(C2, X)) | (~icext(C3, X)))))))))))))) | (~iext(uri_rdf_first, BNODE_l1!4, uri_owl_DatatypeProperty)) | (~iext(uri_rdf_rest, BNODE_l1!4, BNODE_l2!3)) | (~iext(uri_rdf_rest, BNODE_l2!3, BNODE_l3!2)) | (~iext(uri_rdf_first, BNODE_l2!3, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_first, BNODE_l3!2, BNODE_r!1)) | (~iext(uri_rdf_rest, BNODE_l3!2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (~((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[60, 46, 24, 23, 22, 21, 20, 19])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (((~(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4) | (~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (icext(uri_ex_PersonAttribute, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute)) <=> ((~icext(uri_owl_DatatypeProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))) | (~icext(BNODE_r!1, tptp_fun_X_0(BNODE_r!1, uri_owl_FunctionalProperty, uri_owl_DatatypeProperty, uri_ex_PersonAttribute))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))))) | ((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 ((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 ((~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))) | (~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 ((~((~iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1!4)) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))))) | (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (~((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (((~ic(uri_ex_PersonAttribute)) | (~ic(uri_owl_DatatypeProperty)) | (~ic(uri_owl_FunctionalProperty)) | (~ic(BNODE_r!1)) | (~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X))))))) | ![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 ((~![X: $i] : (icext(uri_ex_PersonAttribute, X) <=> (~((~icext(uri_owl_DatatypeProperty, X)) | (~icext(uri_owl_FunctionalProperty, X)) | (~icext(BNODE_r!1, X)))))) | (icext(uri_ex_PersonAttribute, uri_ex_name) <=> (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (icext(uri_ex_PersonAttribute, uri_ex_name) <=> (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[72, 7])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name))) | (~iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)) | icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) <=> icext(uri_ex_PersonAttribute, uri_ex_name))) | icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (icext(uri_ex_PersonAttribute, uri_ex_name)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 ((~(icext(uri_ex_PersonAttribute, uri_ex_name) <=> (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name)))))) | (~icext(uri_ex_PersonAttribute, uri_ex_name)) | (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 ((~(icext(uri_ex_PersonAttribute, uri_ex_name) <=> (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name)))))) | (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (~((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[79, 71])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name))) | icext(uri_owl_FunctionalProperty, uri_ex_name)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (icext(uri_owl_FunctionalProperty, uri_ex_name)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name))) | iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) | (~icext(uri_owl_FunctionalProperty, uri_ex_name))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_name))) | iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 (iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[84, 11])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 ((~(~((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))))) <=> ((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 ((iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) <=> (~((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))) <=> (~(~((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))) <=> ((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))) <=> (~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,axiom,(~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_012_Template_Class')).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (~(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 ((~iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) | (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (~iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[93, 85])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice))) | iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) | (~icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 ((~(iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) <=> icext(uri_foaf_Person, uri_ex_alice))) | (~icext(uri_foaf_Person, uri_ex_alice))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (~icext(uri_foaf_Person, uri_ex_alice)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[96, 9])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (iext(uri_owl_hasValue, BNODE_r!1, uri_foaf_Person)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (iext(uri_owl_onProperty, BNODE_r!1, uri_rdfs_domain)),
% 0.19/0.46 inference(and_elim,[status(thm)],[18])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (^[Z: $i, P: $i, A: $i] : rewrite((![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (^[Z: $i, P: $i, A: $i] : refl((![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (^[Z: $i, P: $i, A: $i] : rewrite((![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (^[Z: $i, P: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))), ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))))), rewrite((~(~((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))) <=> ((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P)))), ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))))), (((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> (((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))))), rewrite((((~iext(uri_owl_hasValue, Z, A)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))), (((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (^[Z: $i, P: $i, A: $i] : rewrite(((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : ((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, A))) <=> ![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.47 tff(112,axiom,(![Z: $i, P: $i, A: $i] : ((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_restrict_hasvalue')).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.19/0.47 tff(115,plain,(
% 0.19/0.47 ![Z: $i, P: $i, A: $i] : ((~(iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[114])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, A)) | (~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 (![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[117, 101])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!1, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!1, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!1, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)))) <=> ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | (~iext(uri_owl_onProperty, BNODE_r!1, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!1, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!1, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | ((~iext(uri_owl_onProperty, BNODE_r!1, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!1, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!1, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 ((~![Z: $i, P: $i, A: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_hasValue, Z, A)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, A)))) | (~iext(uri_owl_onProperty, BNODE_r!1, uri_rdfs_domain)) | (~iext(uri_owl_hasValue, BNODE_r!1, uri_foaf_Person)) | ![X: $i] : (icext(BNODE_r!1, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (![X: $i] : (icext(BNODE_r!1, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[121, 118, 99, 98])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 ((~![X: $i] : (icext(BNODE_r!1, X) <=> iext(uri_rdfs_domain, X, uri_foaf_Person))) | (icext(BNODE_r!1, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (icext(BNODE_r!1, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (((~icext(uri_owl_DatatypeProperty, uri_ex_name)) | (~icext(uri_owl_FunctionalProperty, uri_ex_name)) | (~icext(BNODE_r!1, uri_ex_name))) | icext(BNODE_r!1, uri_ex_name)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (icext(BNODE_r!1, uri_ex_name)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[125, 80])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 ((~(icext(BNODE_r!1, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))) | (~icext(BNODE_r!1, uri_ex_name)) | iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 ((~(icext(BNODE_r!1, uri_ex_name) <=> iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person))) | iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[128, 124])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))),
% 0.19/0.47 inference(and_elim,[status(thm)],[18])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (^[P: $i, C: $i, X: $i, Y: $i] : refl((icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) <=> (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (^[P: $i, C: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) <=> (~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> (~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))))), rewrite((~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (^[P: $i, C: $i, X: $i, Y: $i] : rewrite(((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.47 tff(138,axiom,(![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rdfs_domain_main')).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.19/0.47 tff(141,plain,(
% 0.19/0.47 ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.47 inference(skolemize,[status(sab)],[140])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 ((icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))) <=> ((~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)) | icext(uri_foaf_Person, uri_ex_alice) | (~iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[149, 143, 130, 129, 97])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------