0.00/0.04 % 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 0.03/0.23 % Computer : n155.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:19:25 CDT 2018 0.03/0.23 % CPUTime : 26.63/26.90 % SZS status Theorem 26.63/26.90 26.73/26.90 % SZS output start Proof 26.73/26.90 Take the following subset of the input axioms: 26.73/26.91 fof(owl_bool_complementof_class, axiom, 26.73/26.91 ![Z, C]: 26.73/26.91 ((ic(Z) & (ic(C) & ![X]: (~icext(C, X) <=> icext(Z, X)))) 26.73/26.91 <= iext(uri_owl_complementOf, Z, C))). 26.73/26.91 fof(owl_bool_intersectionof_class_002, axiom, 26.73/26.91 ![Z, S1, C1, C2, S2]: 26.73/26.91 ((iext(uri_owl_intersectionOf, Z, S1) 26.73/26.91 <=> (![X]: ((icext(C2, X) & icext(C1, X)) <=> icext(Z, X)) 26.73/26.91 & (ic(C2) & (ic(C1) & ic(Z))))) 26.73/26.91 <= (iext(uri_rdf_first, S1, C1) 26.73/26.91 & (iext(uri_rdf_rest, S1, S2) 26.73/26.91 & (iext(uri_rdf_rest, S2, uri_rdf_nil) 26.73/26.91 & iext(uri_rdf_first, S2, C2)))))). 26.73/26.91 fof(owl_bool_unionof_class_000, axiom, 26.73/26.91 ![Z]: 26.73/26.91 ((ic(Z) & ![X]: ~icext(Z, X)) 26.73/26.91 <=> iext(uri_owl_unionOf, Z, uri_rdf_nil))). 26.73/26.91 fof(owl_class_nothing_ext, axiom, 26.73/26.91 ![X]: ~icext(uri_owl_Nothing, X)). 26.73/26.91 fof(rdfs_cext_def, axiom, 26.73/26.91 ![X, C]: (iext(uri_rdf_type, X, C) <=> icext(C, X))). 26.73/26.91 fof(testcase_premise_fullish_029_Ex_Falso_Quodlibet, axiom, 26.73/26.91 ?[BNODE_x, BNODE_y, BNODE_l1, BNODE_l2]: 26.73/26.91 (iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) 26.73/26.91 & (iext(uri_rdf_first, BNODE_l1, uri_ex_A) 26.73/26.91 & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) 26.73/26.91 & (iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) 26.73/26.91 & (iext(uri_owl_complementOf, BNODE_y, uri_ex_A) 26.73/26.91 & (iext(uri_rdf_first, BNODE_l2, BNODE_y) 26.73/26.91 & (iext(uri_rdf_type, uri_ex_w, BNODE_x) 26.73/26.91 & (iext(uri_rdf_type, uri_ex_B, uri_owl_Class) 26.73/26.91 & iext(uri_rdf_type, uri_ex_A, uri_owl_Class)))))))))). 26.73/26.91 26.73/26.91 Now clausify the problem and encode Horn clauses using encoding 3 of 26.73/26.91 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 26.73/26.91 We repeatedly replace C & s=t => u=v by the two clauses: 26.73/26.91 $$fresh(y, y, x1...xn) = u 26.73/26.91 C => $$fresh(s, t, x1...xn) = v 26.73/26.91 where $$fresh is a fresh function symbol and x1..xn are the free 26.73/26.91 variables of u and v. 26.73/26.91 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 26.73/26.91 input problem has no model of domain size 1). 26.73/26.91 26.73/26.91 The encoding turns the above axioms into the following unit equations and goals: 26.73/26.91 26.73/26.91 Axiom 55 (owl_bool_intersectionof_class_002_5): $$fresh259(X, X, Y, Z, W, V, U) = sP2_owl_bool_intersectionof_class_002_equiv(Z, V, U). 26.73/26.91 Axiom 56 (owl_bool_intersectionof_class_002_5): $$fresh261(X, X, Y, Z, W) = $$true2. 26.73/26.91 Axiom 57 (owl_bool_intersectionof_class_002_5): $$fresh262(X, X, Y, Z, W, V, U) = $$fresh261(iext(uri_rdf_rest, Y, W), $$true2, Z, V, U). 26.73/26.91 Axiom 58 (owl_bool_intersectionof_class_002_5): $$fresh258(X, X, Y, Z, W, V, U, T) = $$fresh262(iext(uri_owl_intersectionOf, Y, Z), $$true2, Z, W, V, U, T). 26.73/26.91 Axiom 59 (owl_bool_intersectionof_class_002_5): $$fresh260(X, X, Y, Z, W, V, U, T) = $$fresh259(iext(uri_rdf_rest, V, uri_rdf_nil), $$true2, Z, W, V, U, T). 26.73/26.91 Axiom 60 (owl_bool_intersectionof_class_002_5): $$fresh257(X, X, Y, Z, W, V, U, T) = $$fresh260(iext(uri_rdf_first, Z, W), $$true2, Y, Z, W, V, U, T). 26.73/26.91 Axiom 69 (owl_bool_intersectionof_class_002_8): $$fresh134(X, X, Y, Z) = $$true2. 26.73/26.91 Axiom 70 (owl_bool_intersectionof_class_002_9): $$fresh133(X, X, Y, Z) = $$true2. 26.73/26.91 Axiom 366 (rdfs_cext_def): $$fresh31(X, X, Y, Z) = $$true2. 26.73/26.91 Axiom 490 (rdfs_cext_def): $$fresh31(iext(uri_rdf_type, X, Y), $$true2, X, Y) = icext(Y, X). 26.73/26.91 Axiom 566 (owl_bool_intersectionof_class_002_9): $$fresh133(sP2_owl_bool_intersectionof_class_002_equiv(X, Y, Z), $$true2, Y, Z) = icext(Y, Z). 26.73/26.91 Axiom 567 (owl_bool_intersectionof_class_002_8): $$fresh134(sP2_owl_bool_intersectionof_class_002_equiv(X, Y, Z), $$true2, X, Z) = icext(X, Z). 26.73/26.91 Axiom 570 (owl_bool_intersectionof_class_002_5): $$fresh257(icext(X, Y), $$true2, X, Z, W, V, U, Y) = $$fresh258(iext(uri_rdf_first, V, U), $$true2, X, Z, W, V, U, Y). 26.73/26.91 Axiom 626 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_8): iext(uri_rdf_first, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y) = $$true2. 26.73/26.91 Axiom 627 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_7): iext(uri_rdf_first, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A) = $$true2. 26.73/26.91 Axiom 628 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_6): iext(uri_owl_intersectionOf, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1) = $$true2. 26.73/26.91 Axiom 630 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_4): iext(uri_rdf_type, uri_ex_w, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x) = $$true2. 26.73/26.91 Axiom 632 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_2): iext(uri_rdf_rest, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, uri_rdf_nil) = $$true2. 26.73/26.91 Axiom 633 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_1): iext(uri_rdf_rest, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2) = $$true2. 26.73/26.91 Axiom 634 (testcase_premise_fullish_029_Ex_Falso_Quodlibet): iext(uri_owl_complementOf, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_A) = $$true2. 26.73/26.91 26.73/26.91 Lemma 635: sP2_owl_bool_intersectionof_class_002_equiv(uri_ex_A, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) = $$true2. 26.73/26.91 Proof: 26.73/26.91 sP2_owl_bool_intersectionof_class_002_equiv(uri_ex_A, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 55 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$fresh259($$true2, $$true2, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 632 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_2) } 26.73/26.91 $$fresh259(iext(uri_rdf_rest, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, uri_rdf_nil), $$true2, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 59 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$fresh260($$true2, $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 627 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_7) } 26.73/26.91 $$fresh260(iext(uri_rdf_first, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A), $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 60 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$fresh257($$true2, $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 366 (rdfs_cext_def) } 26.73/26.91 $$fresh257($$fresh31($$true2, $$true2, uri_ex_w, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x), $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 630 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_4) } 26.73/26.91 $$fresh257($$fresh31(iext(uri_rdf_type, uri_ex_w, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x), $$true2, uri_ex_w, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x), $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 490 (rdfs_cext_def) } 26.73/26.91 $$fresh257(icext(sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, uri_ex_w), $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 570 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$fresh258(iext(uri_rdf_first, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y), $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 626 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_8) } 26.73/26.91 $$fresh258($$true2, $$true2, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 58 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$fresh262(iext(uri_owl_intersectionOf, sK3_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_x, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1), $$true2, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 628 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_6) } 26.73/26.91 $$fresh262($$true2, $$true2, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, uri_ex_A, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 57 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$fresh261(iext(uri_rdf_rest, sK4_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l1, sK2_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_l2), $$true2, uri_ex_A, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 633 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_1) } 26.73/26.91 $$fresh261($$true2, $$true2, uri_ex_A, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w) 26.73/26.91 = { by axiom 56 (owl_bool_intersectionof_class_002_5) } 26.73/26.91 $$true2 26.73/26.91 26.73/26.91 Goal 1 (owl_bool_complementof_class_3): tuple(iext(uri_owl_complementOf, X, Y), icext(X, Z), icext(Y, Z)) = tuple($$true2, $$true2, $$true2). 26.73/26.91 The goal is true when: 26.73/26.91 X = sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y 26.73/26.91 Y = uri_ex_A 26.73/26.91 Z = uri_ex_w 26.73/26.91 26.73/26.91 Proof: 26.73/26.91 tuple(iext(uri_owl_complementOf, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_A), icext(sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w), icext(uri_ex_A, uri_ex_w)) 26.73/26.91 = { by axiom 634 (testcase_premise_fullish_029_Ex_Falso_Quodlibet) } 26.73/26.91 tuple($$true2, icext(sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w), icext(uri_ex_A, uri_ex_w)) 26.73/26.91 = { by axiom 566 (owl_bool_intersectionof_class_002_9) } 26.73/26.91 tuple($$true2, $$fresh133(sP2_owl_bool_intersectionof_class_002_equiv(uri_ex_A, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w), $$true2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w), icext(uri_ex_A, uri_ex_w)) 26.73/26.91 = { by lemma 635 } 26.73/26.91 tuple($$true2, $$fresh133($$true2, $$true2, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w), icext(uri_ex_A, uri_ex_w)) 26.73/26.91 = { by axiom 70 (owl_bool_intersectionof_class_002_9) } 26.73/26.91 tuple($$true2, $$true2, icext(uri_ex_A, uri_ex_w)) 26.73/26.91 = { by axiom 567 (owl_bool_intersectionof_class_002_8) } 26.73/26.91 tuple($$true2, $$true2, $$fresh134(sP2_owl_bool_intersectionof_class_002_equiv(uri_ex_A, sK1_testcase_premise_fullish_029_Ex_Falso_Quodlibet_BNODE_y, uri_ex_w), $$true2, uri_ex_A, uri_ex_w)) 26.73/26.91 = { by lemma 635 } 26.73/26.91 tuple($$true2, $$true2, $$fresh134($$true2, $$true2, uri_ex_A, uri_ex_w)) 26.73/26.91 = { by axiom 69 (owl_bool_intersectionof_class_002_8) } 26.73/26.91 tuple($$true2, $$true2, $$true2) 26.73/26.91 % SZS output end Proof 26.73/26.91 26.73/26.91 RESULT: Theorem (the conjecture is true). 26.73/26.93 EOF