0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.13/0.34 % Computer : n014.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 11:33:39 EDT 2019 0.13/0.34 % CPUTime : 33.64/33.81 % SZS status Theorem 33.64/33.81 33.64/33.81 % SZS output start Proof 33.64/33.81 Take the following subset of the input axioms: 33.64/33.82 fof(owl_bool_intersectionof_class_003, axiom, ![Z, S1, C1, S2, C2, S3, C3]: (((ic(Z) & (ic(C3) & (![X]: (icext(Z, X) <=> (icext(C1, X) & (icext(C2, X) & icext(C3, X)))) & (ic(C2) & ic(C1))))) <=> iext(uri_owl_intersectionOf, Z, S1)) <= (iext(uri_rdf_rest, S1, S2) & (iext(uri_rdf_first, S2, C2) & (iext(uri_rdf_rest, S2, S3) & (iext(uri_rdf_rest, S3, uri_rdf_nil) & (iext(uri_rdf_first, S3, C3) & iext(uri_rdf_first, S1, C1)))))))). 33.64/33.82 fof(owl_restrict_hasvalue, axiom, ![Z, P, A]: (![X]: (icext(Z, X) <=> iext(P, X, A)) <= (iext(uri_owl_hasValue, Z, A) & iext(uri_owl_onProperty, Z, P)))). 33.64/33.82 fof(rdfs_cext_def, axiom, ![X, C]: (icext(C, X) <=> iext(uri_rdf_type, X, C))). 33.64/33.82 fof(rdfs_domain_main, axiom, ![X, C, Y, P]: ((iext(P, X, Y) & iext(uri_rdfs_domain, P, C)) => icext(C, X))). 33.64/33.82 fof(testcase_conclusion_fullish_012_Template_Class, conjecture, iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) & iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)). 33.64/33.82 fof(testcase_premise_fullish_012_Template_Class, axiom, ?[BNODE_l1, BNODE_l2, BNODE_l3, BNODE_r]: (iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & (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_ex_name, uri_ex_PersonAttribute) & (iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)) & (iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & (iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & (iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & (iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class)))))))))))))). 33.64/33.82 33.64/33.82 Now clausify the problem and encode Horn clauses using encoding 3 of 33.64/33.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 33.64/33.82 We repeatedly replace C & s=t => u=v by the two clauses: 33.64/33.82 fresh(y, y, x1...xn) = u 33.64/33.82 C => fresh(s, t, x1...xn) = v 33.64/33.82 where fresh is a fresh function symbol and x1..xn are the free 33.64/33.82 variables of u and v. 33.64/33.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the 33.64/33.82 input problem has no model of domain size 1). 33.64/33.82 33.64/33.82 The encoding turns the above axioms into the following unit equations and goals: 33.64/33.82 33.64/33.83 Axiom 1 (owl_bool_intersectionof_class_003_10): fresh132(X, X, Y, Z) = true2. 33.64/33.83 Axiom 2 (owl_bool_intersectionof_class_003_11): fresh131(X, X, Y, Z) = true2. 33.64/33.83 Axiom 3 (owl_bool_intersectionof_class_003_4): fresh256(X, X, Y, Z, W, V, U) = sP2_owl_bool_intersectionof_class_003_equiv(Z, W, V, U). 33.64/33.83 Axiom 4 (owl_bool_intersectionof_class_003_4): fresh258(X, X, Y, Z, W, V) = true2. 33.64/33.83 Axiom 5 (owl_bool_intersectionof_class_003_4): fresh257(X, X, Y, Z, W, V, U, T) = fresh258(iext(uri_rdf_first, Y, Z), true2, Z, V, U, T). 33.64/33.83 Axiom 6 (owl_bool_intersectionof_class_003_4): fresh254(X, X, Y, Z, W, V, U, T, S) = fresh257(iext(uri_rdf_first, U, T), true2, Y, Z, W, V, T, S). 33.64/33.83 Axiom 7 (owl_bool_intersectionof_class_003_4): fresh255(X, X, Y, Z, W, V, U, T, S) = fresh256(iext(uri_rdf_first, W, V), true2, Y, Z, V, T, S). 33.64/33.83 Axiom 8 (owl_bool_intersectionof_class_003_4): fresh253(X, X, Y, Z, W, V, U, T, S) = fresh255(iext(uri_rdf_rest, Y, W), true2, Y, Z, W, V, U, T, S). 33.64/33.83 Axiom 9 (owl_bool_intersectionof_class_003_4): fresh252(X, X, Y, Z, W, V, U, T, S) = fresh254(iext(uri_rdf_rest, W, U), true2, Y, Z, W, V, U, T, S). 33.64/33.83 Axiom 10 (owl_bool_intersectionof_class_003_4): fresh251(X, X, Y, Z, W, V, U, T, S, X2) = fresh253(iext(uri_rdf_rest, T, uri_rdf_nil), true2, Z, W, V, U, T, S, X2). 33.64/33.83 Axiom 11 (owl_restrict_hasvalue_1): fresh36(X, X, Y, Z, W, V) = iext(Z, V, W). 33.64/33.83 Axiom 12 (owl_restrict_hasvalue_1): fresh360(X, X, Y, Z, W) = true2. 33.64/33.83 Axiom 13 (owl_restrict_hasvalue_1): fresh359(X, X, Y, Z, W, V) = fresh360(iext(uri_owl_hasValue, Y, W), true2, Z, W, V). 33.64/33.83 Axiom 14 (rdfs_cext_def): fresh31(X, X, Y, Z) = true2. 33.64/33.83 Axiom 15 (rdfs_cext_def_1): fresh30(X, X, Y, Z) = true2. 33.64/33.83 Axiom 16 (rdfs_domain_main): fresh26(X, X, Y, Z, W, V) = icext(Z, W). 33.64/33.83 Axiom 17 (rdfs_domain_main): fresh25(X, X, Y, Z) = true2. 33.64/33.83 Axiom 18 (rdfs_domain_main): fresh26(iext(uri_rdfs_domain, X, Y), true2, X, Y, Z, W) = fresh25(iext(X, Z, W), true2, Y, Z). 33.64/33.83 Axiom 19 (rdfs_cext_def_1): fresh30(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X). 33.64/33.83 Axiom 20 (rdfs_cext_def): fresh31(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X). 33.64/33.83 Axiom 21 (owl_restrict_hasvalue_1): fresh359(icext(X, Y), true2, X, Z, W, Y) = fresh36(iext(uri_owl_onProperty, X, Z), true2, X, Z, W, Y). 33.64/33.83 Axiom 22 (owl_bool_intersectionof_class_003_11): fresh131(sP2_owl_bool_intersectionof_class_003_equiv(X, Y, Z, W), true2, Z, W) = icext(Z, W). 33.64/33.83 Axiom 23 (owl_bool_intersectionof_class_003_10): fresh132(sP2_owl_bool_intersectionof_class_003_equiv(X, Y, Z, W), true2, Y, W) = icext(Y, W). 33.64/33.83 Axiom 24 (owl_bool_intersectionof_class_003_4): fresh251(icext(X, Y), true2, X, Z, W, V, U, T, S, Y) = fresh252(iext(uri_owl_intersectionOf, X, Z), true2, Z, W, V, U, T, S, Y). 33.64/33.83 Axiom 25 (testcase_premise_fullish_012_Template_Class_12): iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)) = true2. 33.64/33.83 Axiom 26 (testcase_premise_fullish_012_Template_Class_11): iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1) = true2. 33.64/33.83 Axiom 27 (testcase_premise_fullish_012_Template_Class_10): iext(uri_owl_onProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain) = true2. 33.64/33.83 Axiom 28 (testcase_premise_fullish_012_Template_Class_9): iext(uri_owl_hasValue, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_foaf_Person) = true2. 33.64/33.83 Axiom 29 (testcase_premise_fullish_012_Template_Class_8): iext(uri_rdf_rest, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, uri_rdf_nil) = true2. 33.64/33.83 Axiom 30 (testcase_premise_fullish_012_Template_Class_7): iext(uri_rdf_rest, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2) = true2. 33.64/33.83 Axiom 31 (testcase_premise_fullish_012_Template_Class_6): iext(uri_rdf_rest, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3) = true2. 33.64/33.83 Axiom 32 (testcase_premise_fullish_012_Template_Class_5): iext(uri_rdf_first, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r) = true2. 33.64/33.83 Axiom 33 (testcase_premise_fullish_012_Template_Class_4): iext(uri_rdf_first, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty) = true2. 33.64/33.83 Axiom 34 (testcase_premise_fullish_012_Template_Class_3): iext(uri_rdf_first, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty) = true2. 33.64/33.83 Axiom 35 (testcase_premise_fullish_012_Template_Class): iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) = true2. 33.64/33.83 33.64/33.83 Lemma 36: sP2_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. 33.64/33.83 Proof: 33.64/33.83 sP2_owl_bool_intersectionof_class_003_equiv(uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 33.64/33.83 = { by axiom 3 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh256(true2, true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 33.64/33.83 = { by axiom 34 (testcase_premise_fullish_012_Template_Class_3) } 33.64/33.83 fresh256(iext(uri_rdf_first, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty), true2, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 33.64/33.83 = { by axiom 7 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh255(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) 33.64/33.83 = { by axiom 30 (testcase_premise_fullish_012_Template_Class_7) } 33.64/33.83 fresh255(iext(uri_rdf_rest, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2), 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) 33.64/33.83 = { by axiom 8 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh253(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) 33.64/33.83 = { by axiom 29 (testcase_premise_fullish_012_Template_Class_8) } 33.64/33.83 fresh253(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) 33.64/33.83 = { by axiom 10 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh251(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) 33.64/33.83 = { by axiom 14 (rdfs_cext_def) } 33.64/33.83 fresh251(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) 33.64/33.83 = { by axiom 35 (testcase_premise_fullish_012_Template_Class) } 33.64/33.83 fresh251(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) 33.64/33.83 = { by axiom 20 (rdfs_cext_def) } 33.64/33.83 fresh251(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) 33.64/33.83 = { by axiom 24 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh252(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) 33.64/33.83 = { by axiom 26 (testcase_premise_fullish_012_Template_Class_11) } 33.64/33.83 fresh252(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) 33.64/33.83 = { by axiom 9 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh254(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, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 33.64/33.83 = { by axiom 31 (testcase_premise_fullish_012_Template_Class_6) } 33.64/33.83 fresh254(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) 33.64/33.83 = { by axiom 6 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh257(iext(uri_rdf_first, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r), 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) 33.64/33.83 = { by axiom 32 (testcase_premise_fullish_012_Template_Class_5) } 33.64/33.83 fresh257(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) 33.64/33.83 = { by axiom 5 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 fresh258(iext(uri_rdf_first, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty), true2, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 33.64/33.83 = { by axiom 33 (testcase_premise_fullish_012_Template_Class_4) } 33.64/33.83 fresh258(true2, true2, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 33.64/33.83 = { by axiom 4 (owl_bool_intersectionof_class_003_4) } 33.64/33.83 true2 33.64/33.83 33.64/33.83 Goal 1 (testcase_conclusion_fullish_012_Template_Class): tuple2(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) = tuple2(true2, true2). 33.64/33.83 Proof: 33.64/33.83 tuple2(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by axiom 19 (rdfs_cext_def_1) } 33.64/33.83 tuple2(fresh30(icext(uri_owl_FunctionalProperty, uri_ex_name), true2, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by axiom 23 (owl_bool_intersectionof_class_003_10) } 33.64/33.83 tuple2(fresh30(fresh132(sP2_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), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by lemma 36 } 33.64/33.83 tuple2(fresh30(fresh132(true2, true2, uri_owl_FunctionalProperty, uri_ex_name), true2, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by axiom 1 (owl_bool_intersectionof_class_003_10) } 33.64/33.83 tuple2(fresh30(true2, true2, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by axiom 15 (rdfs_cext_def_1) } 33.64/33.83 tuple2(true2, iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by axiom 19 (rdfs_cext_def_1) } 33.64/33.83 tuple2(true2, fresh30(icext(uri_foaf_Person, uri_ex_alice), true2, uri_ex_alice, uri_foaf_Person)) 33.64/33.83 = { by axiom 16 (rdfs_domain_main) } 33.64/33.83 tuple2(true2, 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)) 33.64/33.83 = { by axiom 12 (owl_restrict_hasvalue_1) } 33.64/33.83 tuple2(true2, fresh30(fresh26(fresh360(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)) 33.64/33.83 = { by axiom 28 (testcase_premise_fullish_012_Template_Class_9) } 33.64/33.83 tuple2(true2, fresh30(fresh26(fresh360(iext(uri_owl_hasValue, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_foaf_Person), 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)) 33.64/33.83 = { by axiom 13 (owl_restrict_hasvalue_1) } 33.64/33.83 tuple2(true2, fresh30(fresh26(fresh359(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)) 33.64/33.83 = { by axiom 2 (owl_bool_intersectionof_class_003_11) } 33.64/33.83 tuple2(true2, fresh30(fresh26(fresh359(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)) 33.64/33.83 = { by lemma 36 } 33.64/33.83 tuple2(true2, fresh30(fresh26(fresh359(fresh131(sP2_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)) 33.64/33.83 = { by axiom 22 (owl_bool_intersectionof_class_003_11) } 33.64/33.84 tuple2(true2, fresh30(fresh26(fresh359(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)) 33.64/33.84 = { by axiom 21 (owl_restrict_hasvalue_1) } 33.64/33.84 tuple2(true2, fresh30(fresh26(fresh36(iext(uri_owl_onProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain), 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)) 33.64/33.84 = { by axiom 27 (testcase_premise_fullish_012_Template_Class_10) } 33.64/33.84 tuple2(true2, 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)) 33.64/33.84 = { by axiom 11 (owl_restrict_hasvalue_1) } 33.64/33.84 tuple2(true2, 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)) 33.64/33.84 = { by axiom 18 (rdfs_domain_main) } 33.64/33.84 tuple2(true2, 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)) 33.64/33.84 = { by axiom 25 (testcase_premise_fullish_012_Template_Class_12) } 33.64/33.84 tuple2(true2, fresh30(fresh25(true2, true2, uri_foaf_Person, uri_ex_alice), true2, uri_ex_alice, uri_foaf_Person)) 33.64/33.84 = { by axiom 17 (rdfs_domain_main) } 33.64/33.84 tuple2(true2, fresh30(true2, true2, uri_ex_alice, uri_foaf_Person)) 33.64/33.84 = { by axiom 15 (rdfs_cext_def_1) } 33.64/33.84 tuple2(true2, true2) 33.64/33.84 % SZS output end Proof 33.64/33.84 33.64/33.84 RESULT: Theorem (the conjecture is true). 33.64/33.85 EOF