0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.12/0.31 % Computer : n012.cluster.edu 0.12/0.31 % Model : x86_64 x86_64 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.31 % Memory : 8042.1875MB 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.31 % CPULimit : 960 0.12/0.31 % WCLimit : 120 0.12/0.31 % DateTime : Thu Jul 2 07:17:06 EDT 2020 0.12/0.31 % CPUTime : 768.21/97.79 % SZS status Theorem 768.21/97.79 768.21/97.79 % SZS output start Proof 768.21/97.79 Take the following subset of the input axioms: 768.21/97.81 fof(owl_bool_intersectionof_class_003, axiom, ![Z, S1, C1, S2, C2, S3, C3]: ((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) & iext(uri_rdf_rest, S1, S2)))))) => (iext(uri_owl_intersectionOf, Z, S1) <=> (![X]: (icext(Z, X) <=> (icext(C3, X) & (icext(C2, X) & icext(C1, X)))) & (ic(C1) & (ic(C3) & (ic(C2) & ic(Z)))))))). 768.21/97.81 fof(owl_rdfsext_domain, axiom, ![C, P]: (iext(uri_rdfs_domain, P, C) <=> (![X, Y]: (iext(P, X, Y) => icext(C, X)) & (ip(P) & ic(C))))). 768.21/97.81 fof(owl_restrict_hasvalue, axiom, ![Z, P, A]: (![X]: (iext(P, X, A) <=> icext(Z, X)) <= (iext(uri_owl_onProperty, Z, P) & iext(uri_owl_hasValue, Z, A)))). 768.21/97.81 fof(rdfs_cext_def, axiom, ![X, C]: (icext(C, X) <=> iext(uri_rdf_type, X, C))). 768.21/97.81 fof(testcase_conclusion_fullish_012_Template_Class, conjecture, iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)). 768.21/97.81 fof(testcase_premise_fullish_012_Template_Class, axiom, ?[BNODE_l1, BNODE_l2, BNODE_l3, BNODE_r]: (iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & (iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)) & (iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & (iext(uri_owl_hasValue, BNODE_r, uri_foaf_Person) & (iext(uri_owl_onProperty, BNODE_r, uri_rdfs_domain) & (iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & (iext(uri_rdf_first, BNODE_l3, BNODE_r) & (iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & (iext(uri_rdf_first, BNODE_l2, uri_owl_FunctionalProperty) & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & (iext(uri_rdf_first, BNODE_l1, uri_owl_DatatypeProperty) & (iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, BNODE_l1) & iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class)))))))))))))). 768.21/97.81 768.21/97.81 Now clausify the problem and encode Horn clauses using encoding 3 of 768.21/97.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 768.21/97.81 We repeatedly replace C & s=t => u=v by the two clauses: 768.21/97.81 fresh(y, y, x1...xn) = u 768.21/97.81 C => fresh(s, t, x1...xn) = v 768.21/97.81 where fresh is a fresh function symbol and x1..xn are the free 768.21/97.81 variables of u and v. 768.21/97.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the 768.21/97.81 input problem has no model of domain size 1). 768.21/97.81 768.21/97.81 The encoding turns the above axioms into the following unit equations and goals: 768.21/97.81 768.21/97.81 Axiom 1 (owl_bool_intersectionof_class_003_10): fresh132(X, X, Y, Z) = true2. 768.21/97.81 Axiom 2 (owl_bool_intersectionof_class_003_11): fresh131(X, X, Y, Z) = true2. 768.21/97.81 Axiom 3 (owl_bool_intersectionof_class_003_4): fresh180(X, X, Y, Z, W, V, U, T) = sP1_owl_bool_intersectionof_class_003_equiv(Z, V, U, T). 768.21/97.81 Axiom 4 (owl_bool_intersectionof_class_003_4): fresh182(X, X, Y, Z, W, V) = true2. 768.21/97.81 Axiom 5 (owl_bool_intersectionof_class_003_4): fresh181(X, X, Y, Z, W, V, U, T, S) = fresh182(iext(uri_rdf_rest, Y, W), true2, Z, V, T, S). 768.21/97.81 Axiom 6 (owl_bool_intersectionof_class_003_4): fresh178(X, X, Y, Z, W, V, U, T, S) = fresh181(iext(uri_rdf_rest, U, uri_rdf_nil), true2, Y, Z, W, V, U, T, S). 768.21/97.81 Axiom 7 (owl_bool_intersectionof_class_003_4): fresh179(X, X, Y, Z, W, V, U, T, S) = fresh180(iext(uri_rdf_rest, W, U), true2, Y, Z, W, V, T, S). 768.21/97.81 Axiom 8 (owl_bool_intersectionof_class_003_4): fresh177(X, X, Y, Z, W, V, U, T, S) = fresh179(iext(uri_rdf_first, Y, Z), true2, Y, Z, W, V, U, T, S). 768.21/97.81 Axiom 9 (owl_bool_intersectionof_class_003_4): fresh176(X, X, Y, Z, W, V, U, T, S) = fresh178(iext(uri_rdf_first, W, V), true2, Y, Z, W, V, U, T, S). 768.21/97.81 Axiom 10 (owl_bool_intersectionof_class_003_4): fresh175(X, X, Y, Z, W, V, U, T, S, X2) = fresh177(iext(uri_rdf_first, T, S), true2, Z, W, V, U, T, S, X2). 768.21/97.81 Axiom 11 (owl_rdfsext_domain): fresh58(X, X, Y, Z, W, V) = icext(Z, W). 768.21/97.81 Axiom 12 (owl_rdfsext_domain): fresh57(X, X, Y, Z) = true2. 768.21/97.81 Axiom 13 (owl_restrict_hasvalue_1): fresh36(X, X, Y, Z, W, V) = iext(Z, V, W). 768.21/97.81 Axiom 14 (owl_restrict_hasvalue_1): fresh342(X, X, Y, Z, W) = true2. 768.21/97.81 Axiom 15 (owl_restrict_hasvalue_1): fresh341(X, X, Y, Z, W, V) = fresh342(iext(uri_owl_onProperty, Y, Z), true2, Z, W, V). 768.21/97.81 Axiom 16 (rdfs_cext_def): fresh31(X, X, Y, Z) = true2. 768.21/97.81 Axiom 17 (rdfs_cext_def_1): fresh30(X, X, Y, Z) = true2. 768.21/97.81 Axiom 18 (owl_rdfsext_domain): fresh58(iext(uri_rdfs_domain, X, Y), true2, X, Y, Z, W) = fresh57(iext(X, Z, W), true2, Y, Z). 768.21/97.81 Axiom 19 (rdfs_cext_def_1): fresh30(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X). 768.21/97.81 Axiom 20 (rdfs_cext_def): fresh31(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X). 768.21/97.81 Axiom 21 (owl_restrict_hasvalue_1): fresh341(icext(X, Y), true2, X, Z, W, Y) = fresh36(iext(uri_owl_hasValue, X, W), true2, X, Z, W, Y). 768.21/97.81 Axiom 22 (owl_bool_intersectionof_class_003_11): fresh131(sP1_owl_bool_intersectionof_class_003_equiv(X, Y, Z, W), true2, Z, W) = icext(Z, W). 768.21/97.81 Axiom 23 (owl_bool_intersectionof_class_003_10): fresh132(sP1_owl_bool_intersectionof_class_003_equiv(X, Y, Z, W), true2, Y, W) = icext(Y, W). 768.21/97.81 Axiom 24 (owl_bool_intersectionof_class_003_4): fresh175(icext(X, Y), true2, X, Z, W, V, U, T, S, Y) = fresh176(iext(uri_owl_intersectionOf, X, Z), true2, Z, W, V, U, T, S, Y). 768.21/97.81 Axiom 25 (testcase_premise_fullish_012_Template_Class_12): iext(uri_ex_name, uri_ex_alice, literal_plain(dat_str_alice)) = true2. 768.21/97.81 Axiom 26 (testcase_premise_fullish_012_Template_Class_11): iext(uri_owl_hasValue, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_foaf_Person) = true2. 768.21/97.81 Axiom 27 (testcase_premise_fullish_012_Template_Class_10): iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1) = true2. 768.21/97.81 Axiom 28 (testcase_premise_fullish_012_Template_Class_9): iext(uri_rdf_first, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r) = true2. 768.21/97.81 Axiom 29 (testcase_premise_fullish_012_Template_Class_8): iext(uri_rdf_first, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty) = true2. 768.21/97.81 Axiom 30 (testcase_premise_fullish_012_Template_Class_7): iext(uri_rdf_first, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, uri_owl_FunctionalProperty) = true2. 768.21/97.81 Axiom 31 (testcase_premise_fullish_012_Template_Class_6): iext(uri_rdf_rest, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, uri_rdf_nil) = true2. 768.21/97.81 Axiom 32 (testcase_premise_fullish_012_Template_Class_5): iext(uri_rdf_rest, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2) = true2. 768.21/97.81 Axiom 33 (testcase_premise_fullish_012_Template_Class_4): iext(uri_rdf_rest, sK4_testcase_premise_fullish_012_Template_Class_BNODE_l2, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3) = true2. 768.21/97.81 Axiom 34 (testcase_premise_fullish_012_Template_Class_3): iext(uri_owl_onProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_rdfs_domain) = true2. 768.21/97.82 Axiom 35 (testcase_premise_fullish_012_Template_Class): iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) = true2. 768.21/97.82 768.21/97.82 Lemma 36: 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. 768.21/97.82 Proof: 768.21/97.82 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) 768.21/97.82 = { by axiom 3 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh180(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) 768.21/97.82 = { by axiom 33 (testcase_premise_fullish_012_Template_Class_4) } 768.21/97.82 fresh180(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) 768.21/97.82 = { by axiom 7 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh179(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) 768.21/97.82 = { by axiom 29 (testcase_premise_fullish_012_Template_Class_8) } 768.21/97.82 fresh179(iext(uri_rdf_first, sK3_testcase_premise_fullish_012_Template_Class_BNODE_l1, uri_owl_DatatypeProperty), 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) 768.21/97.82 = { by axiom 8 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh177(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) 768.21/97.82 = { by axiom 28 (testcase_premise_fullish_012_Template_Class_9) } 768.21/97.82 fresh177(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, sK1_testcase_premise_fullish_012_Template_Class_BNODE_l3, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 768.21/97.82 = { by axiom 10 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh175(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) 768.21/97.82 = { by axiom 16 (rdfs_cext_def) } 768.21/97.82 fresh175(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) 768.21/97.82 = { by axiom 35 (testcase_premise_fullish_012_Template_Class) } 768.21/97.82 fresh175(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) 768.21/97.82 = { by axiom 20 (rdfs_cext_def) } 768.21/97.82 fresh175(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) 768.21/97.82 = { by axiom 24 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh176(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) 768.21/97.82 = { by axiom 27 (testcase_premise_fullish_012_Template_Class_10) } 768.21/97.82 fresh176(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) 768.21/97.82 = { by axiom 9 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh178(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, 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) 768.21/97.82 = { by axiom 30 (testcase_premise_fullish_012_Template_Class_7) } 768.21/97.82 fresh178(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) 768.21/97.82 = { by axiom 6 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh181(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) 768.21/97.82 = { by axiom 31 (testcase_premise_fullish_012_Template_Class_6) } 768.21/97.82 fresh181(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) 768.21/97.82 = { by axiom 5 (owl_bool_intersectionof_class_003_4) } 768.21/97.82 fresh182(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) 768.21/97.82 = { by axiom 32 (testcase_premise_fullish_012_Template_Class_5) } 768.21/97.82 fresh182(true2, true2, uri_owl_DatatypeProperty, uri_owl_FunctionalProperty, sK2_testcase_premise_fullish_012_Template_Class_BNODE_r, uri_ex_name) 768.21/97.82 = { by axiom 4 (owl_bool_intersectionof_class_003_4) } 768.21/97.83 true2 768.21/97.83 768.21/97.83 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). 768.21/97.83 Proof: 768.21/97.83 tuple2(iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 19 (rdfs_cext_def_1) } 768.21/97.83 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)) 768.21/97.83 = { by axiom 23 (owl_bool_intersectionof_class_003_10) } 768.21/97.83 tuple2(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), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by lemma 36 } 768.21/97.83 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)) 768.21/97.83 = { by axiom 1 (owl_bool_intersectionof_class_003_10) } 768.21/97.83 tuple2(fresh30(true2, true2, uri_ex_name, uri_owl_FunctionalProperty), iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 17 (rdfs_cext_def_1) } 768.21/97.83 tuple2(true2, iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 19 (rdfs_cext_def_1) } 768.21/97.83 tuple2(true2, fresh30(icext(uri_foaf_Person, uri_ex_alice), true2, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 11 (owl_rdfsext_domain) } 768.21/97.83 tuple2(true2, fresh30(fresh58(true2, true2, uri_ex_name, uri_foaf_Person, uri_ex_alice, literal_plain(dat_str_alice)), true2, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 14 (owl_restrict_hasvalue_1) } 768.21/97.83 tuple2(true2, fresh30(fresh58(fresh342(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)) 768.21/97.83 = { by axiom 34 (testcase_premise_fullish_012_Template_Class_3) } 768.21/97.83 tuple2(true2, fresh30(fresh58(fresh342(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)) 768.21/97.83 = { by axiom 15 (owl_restrict_hasvalue_1) } 768.21/97.83 tuple2(true2, fresh30(fresh58(fresh341(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)) 768.21/97.83 = { by axiom 2 (owl_bool_intersectionof_class_003_11) } 768.21/97.83 tuple2(true2, fresh30(fresh58(fresh341(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)) 768.21/97.83 = { by lemma 36 } 768.21/97.83 tuple2(true2, fresh30(fresh58(fresh341(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)) 768.21/97.83 = { by axiom 22 (owl_bool_intersectionof_class_003_11) } 768.21/97.83 tuple2(true2, fresh30(fresh58(fresh341(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)) 768.21/97.83 = { by axiom 21 (owl_restrict_hasvalue_1) } 768.21/97.83 tuple2(true2, fresh30(fresh58(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)) 768.21/97.83 = { by axiom 26 (testcase_premise_fullish_012_Template_Class_11) } 768.21/97.83 tuple2(true2, fresh30(fresh58(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)) 768.21/97.83 = { by axiom 13 (owl_restrict_hasvalue_1) } 768.21/97.83 tuple2(true2, fresh30(fresh58(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)) 768.21/97.83 = { by axiom 18 (owl_rdfsext_domain) } 768.21/97.83 tuple2(true2, fresh30(fresh57(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)) 768.21/97.83 = { by axiom 25 (testcase_premise_fullish_012_Template_Class_12) } 768.21/97.83 tuple2(true2, fresh30(fresh57(true2, true2, uri_foaf_Person, uri_ex_alice), true2, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 12 (owl_rdfsext_domain) } 768.21/97.83 tuple2(true2, fresh30(true2, true2, uri_ex_alice, uri_foaf_Person)) 768.21/97.83 = { by axiom 17 (rdfs_cext_def_1) } 768.21/97.83 tuple2(true2, true2) 768.21/97.83 % SZS output end Proof 768.21/97.83 768.21/97.83 RESULT: Theorem (the conjecture is true). 768.21/97.89 EOF