0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn 0.03/0.24 % Computer : n186.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:01:25 CDT 2018 0.03/0.24 % CPUTime : 54.20/54.41 % SZS status Theorem 54.20/54.41 54.20/54.42 % SZS output start Proof 54.20/54.42 Take the following subset of the input axioms: 54.20/54.44 fof(owl_bool_intersectionof_class_003, axiom, 54.20/54.44 ![Z, S1, C1, C2, S2, S3, C3]: 54.20/54.44 (((ic(C1) 54.20/54.44 & (ic(C3) 54.20/54.44 & (![X]: 54.20/54.44 ((icext(C2, X) & (icext(C3, X) & icext(C1, X))) <=> icext(Z, X)) 54.20/54.44 & (ic(C2) & ic(Z))))) 54.20/54.44 <=> iext(uri_owl_intersectionOf, Z, S1)) 54.20/54.44 <= (iext(uri_rdf_rest, S1, S2) 54.20/54.44 & (iext(uri_rdf_rest, S2, S3) 54.20/54.44 & (iext(uri_rdf_first, S3, C3) 54.20/54.44 & (iext(uri_rdf_rest, S3, uri_rdf_nil) 54.20/54.44 & (iext(uri_rdf_first, S2, C2) 54.20/54.44 & iext(uri_rdf_first, S1, C1)))))))). 54.20/54.44 fof(owl_restrict_hasvalue, axiom, 54.20/54.44 ![Z, P, A]: 54.20/54.44 ((iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)) 54.20/54.44 => ![X]: (iext(P, X, A) <=> icext(Z, X)))). 54.20/54.44 fof(rdfs_cext_def, axiom, 54.20/54.44 ![X, C]: (iext(uri_rdf_type, X, C) <=> icext(C, X))). 54.20/54.44 fof(rdfs_domain_main, axiom, 54.20/54.44 ![X, C, P, Y]: 54.20/54.44 ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X))). 54.20/54.44 fof(testcase_conclusion_fullish_012_Template_Class, conjecture, 54.20/54.44 iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) 54.20/54.44 & iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)). 54.20/54.44 fof(testcase_premise_fullish_012_Template_Class, axiom, 54.20/54.44 ?[BNODE_l1, BNODE_l2, BNODE_l3, BNODE_r]: 54.20/54.44 (iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) 54.20/54.44 & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) 54.20/54.44 & (iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) 54.20/54.44 & (iext(uri_rdf_first, BNODE_l3, BNODE_r) 54.20/54.44 & (iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) 54.20/54.44 & (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) 54.20/54.44 & (iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)) 54.20/54.44 & (iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) 54.20/54.44 & (iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) 54.20/54.44 & (iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) 54.20/54.44 & (iext(uri_rdf_rest, BNODE_l2, BNODE_l3) 54.20/54.44 & (iext(uri_rdf_first, BNODE_l1, 54.20/54.44 uri_owl_DatatypeProperty) 54.20/54.44 & iext(uri_rdf_type, 54.20/54.44 uri_foaf_Person, 54.20/54.44 uri_owl_Class)))))))))))))). 54.20/54.44 54.20/54.44 Now clausify the problem and encode Horn clauses using encoding 3 of 54.20/54.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 54.20/54.44 We repeatedly replace C & s=t => u=v by the two clauses: 54.20/54.44 $$fresh(y, y, x1...xn) = u 54.20/54.44 C => $$fresh(s, t, x1...xn) = v 54.20/54.44 where $$fresh is a fresh function symbol and x1..xn are the free 54.20/54.44 variables of u and v. 54.20/54.44 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 54.20/54.44 input problem has no model of domain size 1). 54.20/54.44 54.20/54.44 The encoding turns the above axioms into the following unit equations and goals: 54.20/54.44 54.20/54.44 Axiom 83 (owl_bool_intersectionof_class_003_10): $$fresh132(X, X, Y, Z) = $$true2. 54.20/54.44 Axiom 84 (owl_bool_intersectionof_class_003_11): $$fresh131(X, X, Y, Z) = $$true2. 54.20/54.44 Axiom 113 (owl_bool_intersectionof_class_003_6): $$fresh219(X, X, Y, Z, W, V, U, T) = sP1_owl_bool_intersectionof_class_003_equiv(Z, V, U, T). 54.20/54.44 Axiom 114 (owl_bool_intersectionof_class_003_6): $$fresh221(X, X, Y, Z, W, V) = $$true2. 54.20/54.44 Axiom 115 (owl_bool_intersectionof_class_003_6): $$fresh222(X, X, Y, Z, W, V, U, T, S) = $$fresh221(iext(uri_rdf_rest, Y, W), $$true2, Z, V, T, S). 54.20/54.44 Axiom 116 (owl_bool_intersectionof_class_003_6): $$fresh218(X, X, Y, Z, W, V, U, T, S, X2) = $$fresh222(iext(uri_rdf_rest, T, uri_rdf_nil), $$true2, Z, W, V, U, T, S, X2). 54.20/54.44 Axiom 117 (owl_bool_intersectionof_class_003_6): $$fresh220(X, X, Y, Z, W, V, U, T, S) = $$fresh219(iext(uri_rdf_rest, W, U), $$true2, Y, Z, W, V, T, S). 54.20/54.44 Axiom 118 (owl_bool_intersectionof_class_003_6): $$fresh217(X, X, Y, Z, W, V, U, T, S, X2) = $$fresh220(iext(uri_owl_intersectionOf, Y, Z), $$true2, Z, W, V, U, T, S, X2). 54.20/54.44 Axiom 119 (owl_bool_intersectionof_class_003_6): $$fresh216(X, X, Y, Z, W, V, U, T, S, X2) = $$fresh218(iext(uri_rdf_first, Z, W), $$true2, Y, Z, W, V, U, T, S, X2). 54.20/54.44 Axiom 120 (owl_bool_intersectionof_class_003_6): $$fresh215(X, X, Y, Z, W, V, U, T, S, X2) = $$fresh217(iext(uri_rdf_first, V, U), $$true2, Y, Z, W, V, U, T, S, X2). 54.20/54.44 Axiom 351 (owl_restrict_hasvalue_1): $$fresh36(X, X, Y, Z, W, V) = iext(Z, V, W). 54.20/54.44 Axiom 352 (owl_restrict_hasvalue_1): $$fresh337(X, X, Y, Z, W) = $$true2. 54.20/54.44 Axiom 353 (owl_restrict_hasvalue_1): $$fresh338(X, X, Y, Z, W, V) = $$fresh337(iext(uri_owl_onProperty, Y, Z), $$true2, Z, W, V). 54.20/54.44 Axiom 366 (rdfs_cext_def): $$fresh31(X, X, Y, Z) = $$true2. 54.20/54.44 Axiom 367 (rdfs_cext_def_1): $$fresh30(X, X, Y, Z) = $$true2. 54.20/54.44 Axiom 371 (rdfs_domain_main): $$fresh26(X, X, Y, Z, W, V) = icext(Z, W). 54.20/54.44 Axiom 372 (rdfs_domain_main): $$fresh25(X, X, Y, Z) = $$true2. 54.20/54.44 Axiom 453 (owl_restrict_hasvalue_1): $$fresh338(icext(X, Y), $$true2, X, Z, W, Y) = $$fresh36(iext(uri_owl_hasValue, X, W), $$true2, X, Z, W, Y). 54.20/54.44 Axiom 484 (rdfs_domain_main): $$fresh26(iext(uri_rdfs_domain, X, Y), $$true2, X, Y, Z, W) = $$fresh25(iext(X, Z, W), $$true2, Y, Z). 54.20/54.44 Axiom 489 (rdfs_cext_def_1): $$fresh30(icext(X, Y), $$true2, Y, X) = iext(uri_rdf_type, Y, X). 54.20/54.44 Axiom 490 (rdfs_cext_def): $$fresh31(iext(uri_rdf_type, X, Y), $$true2, X, Y) = icext(Y, X). 54.20/54.44 Axiom 577 (owl_bool_intersectionof_class_003_11): $$fresh131(sP1_owl_bool_intersectionof_class_003_equiv(X, Y, Z, W), $$true2, Z, W) = icext(Z, W). 54.20/54.44 Axiom 578 (owl_bool_intersectionof_class_003_10): $$fresh132(sP1_owl_bool_intersectionof_class_003_equiv(X, Y, Z, W), $$true2, Y, W) = icext(Y, W). 54.20/54.44 Axiom 582 (owl_bool_intersectionof_class_003_6): $$fresh215(icext(X, Y), $$true2, X, Z, W, V, U, T, S, Y) = $$fresh216(iext(uri_rdf_first, T, S), $$true2, X, Z, W, V, U, T, S, Y). 54.20/54.44 Axiom 626 (testcase_premise_fullish_012_Template_Class_12): iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)) = $$true2. 54.20/54.44 Axiom 627 (testcase_premise_fullish_012_Template_Class_11): iext(uri_owl_hasValue, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_foaf_Person) = $$true2. 54.20/54.44 Axiom 628 (testcase_premise_fullish_012_Template_Class_10): iext(uri_rdf_first, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r) = $$true2. 54.20/54.44 Axiom 629 (testcase_premise_fullish_012_Template_Class_9): iext(uri_rdf_first, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty) = $$true2. 54.20/54.44 Axiom 630 (testcase_premise_fullish_012_Template_Class_8): iext(uri_rdf_first, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty) = $$true2. 54.20/54.44 Axiom 631 (testcase_premise_fullish_012_Template_Class_7): iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1) = $$true2. 54.20/54.44 Axiom 633 (testcase_premise_fullish_012_Template_Class_5): iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) = $$true2. 54.20/54.44 Axiom 635 (testcase_premise_fullish_012_Template_Class_3): iext(uri_rdf_rest, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, uri_rdf_nil) = $$true2. 54.20/54.44 Axiom 636 (testcase_premise_fullish_012_Template_Class_2): iext(uri_rdf_rest, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2) = $$true2. 54.20/54.44 Axiom 637 (testcase_premise_fullish_012_Template_Class_1): iext(uri_rdf_rest, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3) = $$true2. 54.20/54.44 Axiom 638 (testcase_premise_fullish_012_Template_Class): iext(uri_owl_onProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain) = $$true2. 54.20/54.44 54.20/54.44 Lemma 639: sP1_owl_bool_intersectionof_class_003_equiv(uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) = $$true2. 54.20/54.44 Proof: 54.20/54.44 sP1_owl_bool_intersectionof_class_003_equiv(uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 113 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh219($$true2, $$true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 637 (testcase_premise_fullish_012_Template_Class_1) } 54.20/54.44 $$fresh219(iext(uri_rdf_rest, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3), $$true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 117 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh220($$true2, $$true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 631 (testcase_premise_fullish_012_Template_Class_7) } 54.20/54.44 $$fresh220(iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1), $$true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 118 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh217($$true2, $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 630 (testcase_premise_fullish_012_Template_Class_8) } 54.20/54.44 $$fresh217(iext(uri_rdf_first, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty), $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 120 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh215($$true2, $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 366 (rdfs_cext_def) } 54.20/54.44 $$fresh215($$fresh31($$true2, $$true2, uri_ex_name, uri_ex_PersonAttribute), $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 633 (testcase_premise_fullish_012_Template_Class_5) } 54.20/54.44 $$fresh215($$fresh31(iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute), $$true2, uri_ex_name, uri_ex_PersonAttribute), $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 490 (rdfs_cext_def) } 54.20/54.44 $$fresh215(icext(uri_ex_PersonAttribute, uri_ex_name), $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 582 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh216(iext(uri_rdf_first, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r), $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 628 (testcase_premise_fullish_012_Template_Class_10) } 54.20/54.44 $$fresh216($$true2, $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 119 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh218(iext(uri_rdf_first, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty), $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 629 (testcase_premise_fullish_012_Template_Class_9) } 54.20/54.44 $$fresh218($$true2, $$true2, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 116 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh222(iext(uri_rdf_rest, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, uri_rdf_nil), $$true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 635 (testcase_premise_fullish_012_Template_Class_3) } 54.20/54.44 $$fresh222($$true2, $$true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 115 (owl_bool_intersectionof_class_003_6) } 54.20/54.44 $$fresh221(iext(uri_rdf_rest, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2), $$true2, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 636 (testcase_premise_fullish_012_Template_Class_2) } 54.20/54.44 $$fresh221($$true2, $$true2, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 54.20/54.44 = { by axiom 114 (owl_bool_intersectionof_class_003_6) } 54.20/54.45 $$true2 54.20/54.45 54.20/54.45 Goal 1 (testcase_conclusion_fullish_012_Template_Class): tuple2(iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) = tuple2($$true2, $$true2). 54.20/54.45 Proof: 54.20/54.45 tuple2(iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 489 (rdfs_cext_def_1) } 54.20/54.45 tuple2($$fresh30(icext(uri_foaf_Person, uri_ex_alice), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 371 (rdfs_domain_main) } 54.20/54.45 tuple2($$fresh30($$fresh26($$true2, $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 352 (owl_restrict_hasvalue_1) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh337($$true2, $$true2, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 638 (testcase_premise_fullish_012_Template_Class) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh337(iext(uri_owl_onProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain), $$true2, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 353 (owl_restrict_hasvalue_1) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh338($$true2, $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 84 (owl_bool_intersectionof_class_003_11) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh338($$fresh131($$true2, $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name), $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by lemma 639 } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh338($$fresh131(sP1_owl_bool_intersectionof_class_003_equiv(uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name), $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name), $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 577 (owl_bool_intersectionof_class_003_11) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh338(icext(sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name), $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 453 (owl_restrict_hasvalue_1) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh36(iext(uri_owl_hasValue, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_foaf_Person), $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 627 (testcase_premise_fullish_012_Template_Class_11) } 54.20/54.45 tuple2($$fresh30($$fresh26($$fresh36($$true2, $$true2, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain, uri_foaf_Person, uri_ex_name), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 351 (owl_restrict_hasvalue_1) } 54.20/54.45 tuple2($$fresh30($$fresh26(iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person), $$true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 484 (rdfs_domain_main) } 54.20/54.45 tuple2($$fresh30($$fresh25(iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)), $$true2, uri_foaf_Person, uri_ex_alice), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 626 (testcase_premise_fullish_012_Template_Class_12) } 54.20/54.45 tuple2($$fresh30($$fresh25($$true2, $$true2, uri_foaf_Person, uri_ex_alice), $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 372 (rdfs_domain_main) } 54.20/54.45 tuple2($$fresh30($$true2, $$true2, uri_ex_alice, uri_foaf_Person), iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 367 (rdfs_cext_def_1) } 54.20/54.45 tuple2($$true2, iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 489 (rdfs_cext_def_1) } 54.20/54.45 tuple2($$true2, $$fresh30(icext(uri_owl_FunctionalProperty, uri_ex_name), $$true2, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 578 (owl_bool_intersectionof_class_003_10) } 54.20/54.45 tuple2($$true2, $$fresh30($$fresh132(sP1_owl_bool_intersectionof_class_003_equiv(uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name), $$true2, uri_owl_FunctionalProperty, uri_ex_name), $$true2, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by lemma 639 } 54.20/54.45 tuple2($$true2, $$fresh30($$fresh132($$true2, $$true2, uri_owl_FunctionalProperty, uri_ex_name), $$true2, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 83 (owl_bool_intersectionof_class_003_10) } 54.20/54.45 tuple2($$true2, $$fresh30($$true2, $$true2, uri_ex_name, uri_owl_FunctionalProperty)) 54.20/54.45 = { by axiom 367 (rdfs_cext_def_1) } 54.20/54.45 tuple2($$true2, $$true2) 54.20/54.45 % SZS output end Proof 54.20/54.45 54.20/54.45 RESULT: Theorem (the conjecture is true). 54.20/54.48 EOF