0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof 0.14/0.34 % Computer : n025.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1200 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Jul 13 17:33:42 EDT 2021 0.14/0.34 % CPUTime : 17.21/2.55 % SZS status Theorem 17.21/2.55 17.21/2.57 % SZS output start Proof 17.21/2.57 Take the following subset of the input axioms: 17.79/2.59 fof(owl_chain_003, axiom, ![P1, P2, P, S1, S2, S3, P3]: ((iext(uri_rdf_rest, S1, S2) & (iext(uri_rdf_rest, S2, S3) & (iext(uri_rdf_first, S3, P3) & (iext(uri_rdf_rest, S3, uri_rdf_nil) & (iext(uri_rdf_first, S2, P2) & iext(uri_rdf_first, S1, P1)))))) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P2) & (ip(P3) & (![Y0, Y1, Y2, Y3]: ((iext(P1, Y0, Y1) & (iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) => iext(P, Y0, Y3)) & (ip(P1) & ip(P)))))))). 17.79/2.59 fof(owl_eqdis_sameas, axiom, ![X, Y]: (iext(uri_owl_sameAs, X, Y) <=> Y=X)). 17.79/2.59 fof(owl_inv, axiom, ![P1, P2]: ((![X, Y]: (iext(P1, X, Y) <=> iext(P2, Y, X)) & (ip(P2) & ip(P1))) <=> iext(uri_owl_inverseOf, P1, P2))). 17.79/2.59 fof(owl_rdfsext_subclassof, axiom, ![C1, C2]: ((ic(C2) & (![X]: (icext(C1, X) => icext(C2, X)) & ic(C1))) <=> iext(uri_rdfs_subClassOf, C1, C2))). 17.79/2.59 fof(owl_rdfsext_subpropertyof, axiom, ![P1, P2]: (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & (![X, Y]: (iext(P2, X, Y) <= iext(P1, X, Y)) & ip(P2))))). 17.79/2.59 fof(owl_restrict_somevaluesfrom, axiom, ![C, P, Z]: ((iext(uri_owl_onProperty, Z, P) & iext(uri_owl_someValuesFrom, Z, C)) => ![X]: (?[Y]: (icext(C, Y) & iext(P, X, Y)) <=> icext(Z, X)))). 17.79/2.59 fof(rdfs_cext_def, axiom, ![X, C]: (icext(C, X) <=> iext(uri_rdf_type, X, C))). 17.79/2.59 fof(testcase_conclusion_fullish_013_Cliques, conjecture, iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)). 17.79/2.59 fof(testcase_premise_fullish_013_Cliques, axiom, ?[BNODE_r, BNODE_i, BNODE_l1, BNODE_l2, BNODE_l3]: (iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & (iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & (iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & (iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & (iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & (iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & (iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & (iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang) & (iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & (iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & (iext(uri_rdf_first, BNODE_l3, BNODE_i) & (iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & (iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & (iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & (iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & (iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class)))))))))))))))))))). 17.79/2.59 17.79/2.59 Now clausify the problem and encode Horn clauses using encoding 3 of 17.79/2.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 17.79/2.59 We repeatedly replace C & s=t => u=v by the two clauses: 17.79/2.59 fresh(y, y, x1...xn) = u 17.79/2.59 C => fresh(s, t, x1...xn) = v 17.79/2.59 where fresh is a fresh function symbol and x1..xn are the free 17.79/2.59 variables of u and v. 17.79/2.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the 17.79/2.59 input problem has no model of domain size 1). 17.79/2.59 17.79/2.59 The encoding turns the above axioms into the following unit equations and goals: 17.79/2.59 17.79/2.59 Axiom 1 (testcase_premise_fullish_013_Cliques_10): iext(uri_rdf_first, bnode_l3, bnode_i) = true. 17.79/2.59 Axiom 2 (testcase_premise_fullish_013_Cliques_11): iext(uri_rdf_first, bnode_l2, uri_ex_sameCliqueAs) = true. 17.79/2.59 Axiom 3 (testcase_premise_fullish_013_Cliques_12): iext(uri_rdf_first, bnode_l1, uri_rdf_type) = true. 17.79/2.59 Axiom 4 (testcase_premise_fullish_013_Cliques_14): iext(uri_rdf_rest, bnode_l3, uri_rdf_nil) = true. 17.79/2.59 Axiom 5 (testcase_premise_fullish_013_Cliques_15): iext(uri_rdf_rest, bnode_l2, bnode_l3) = true. 17.79/2.59 Axiom 6 (testcase_premise_fullish_013_Cliques_16): iext(uri_rdf_rest, bnode_l1, bnode_l2) = true. 17.79/2.59 Axiom 7 (testcase_premise_fullish_013_Cliques_3): iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) = true. 17.79/2.59 Axiom 8 (testcase_premise_fullish_013_Cliques_4): iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang) = true. 17.79/2.59 Axiom 9 (testcase_premise_fullish_013_Cliques_5): iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) = true. 17.79/2.59 Axiom 10 (testcase_premise_fullish_013_Cliques_9): iext(uri_owl_propertyChainAxiom, uri_foaf_knows, bnode_l1) = true. 17.79/2.59 Axiom 11 (testcase_premise_fullish_013_Cliques_13): iext(uri_owl_inverseOf, bnode_i, uri_rdf_type) = true. 17.79/2.59 Axiom 12 (testcase_premise_fullish_013_Cliques): iext(uri_rdfs_subClassOf, uri_ex_Clique, bnode_r) = true. 17.79/2.59 Axiom 13 (testcase_premise_fullish_013_Cliques_7): iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) = true. 17.79/2.59 Axiom 14 (testcase_premise_fullish_013_Cliques_17): iext(uri_owl_someValuesFrom, bnode_r, uri_ex_Clique) = true. 17.79/2.59 Axiom 15 (testcase_premise_fullish_013_Cliques_18): iext(uri_owl_onProperty, bnode_r, uri_ex_sameCliqueAs) = true. 17.79/2.59 Axiom 16 (owl_eqdis_sameas_1): fresh(X, X, Y, Z) = Y. 17.79/2.59 Axiom 17 (owl_rdfsext_subclassof_2): fresh13(X, X, Y, Z) = true. 17.79/2.59 Axiom 18 (rdfs_cext_def_1): fresh2(X, X, Y, Z) = true. 17.79/2.59 Axiom 19 (owl_chain_003_1): fresh54(X, X, Y, Z, W) = true. 17.79/2.59 Axiom 20 (owl_restrict_somevaluesfrom_1): fresh30(X, X, Y, Z, W) = true. 17.79/2.59 Axiom 21 (owl_inv_2): fresh18(X, X, Y, Z, W) = true. 17.79/2.59 Axiom 22 (owl_rdfsext_subclassof_2): fresh14(X, X, Y, Z, W) = icext(Z, W). 17.79/2.59 Axiom 23 (owl_rdfsext_subpropertyof): fresh9(X, X, Y, Z, W) = true. 17.79/2.59 Axiom 24 (owl_inv_2): fresh19(X, X, Y, Z, W, V) = iext(Y, W, V). 17.79/2.59 Axiom 25 (owl_rdfsext_subpropertyof): fresh10(X, X, Y, Z, W, V) = iext(Z, W, V). 17.79/2.59 Axiom 26 (owl_restrict_somevaluesfrom_1): fresh4(X, X, Y, Z, W, V) = iext(Z, V, y2(Z, W, V)). 17.79/2.59 Axiom 27 (owl_eqdis_sameas_1): fresh(iext(uri_owl_sameAs, X, Y), true, X, Y) = Y. 17.79/2.59 Axiom 28 (owl_chain_003_1): fresh52(X, X, Y, Z, W, V, U) = iext(Y, W, U). 17.79/2.59 Axiom 29 (owl_restrict_somevaluesfrom_1): fresh29(X, X, Y, Z, W, V) = fresh30(icext(Y, V), true, Z, W, V). 17.79/2.59 Axiom 30 (rdfs_cext_def_1): fresh2(iext(uri_rdf_type, X, Y), true, X, Y) = icext(Y, X). 17.79/2.59 Axiom 31 (owl_rdfsext_subclassof_2): fresh14(iext(uri_rdfs_subClassOf, X, Y), true, X, Y, Z) = fresh13(icext(X, Z), true, Y, Z). 17.79/2.59 Axiom 32 (owl_chain_003_1): fresh53(X, X, Y, Z, W, V, U, T, S) = fresh54(iext(Z, V, U), true, Y, V, S). 17.79/2.59 Axiom 33 (owl_inv_2): fresh19(iext(uri_owl_inverseOf, X, Y), true, X, Y, Z, W) = fresh18(iext(Y, W, Z), true, X, Z, W). 17.79/2.59 Axiom 34 (owl_rdfsext_subpropertyof): fresh10(iext(uri_rdfs_subPropertyOf, X, Y), true, X, Y, Z, W) = fresh9(iext(X, Z, W), true, Y, Z, W). 17.79/2.59 Axiom 35 (owl_restrict_somevaluesfrom_1): fresh29(iext(uri_owl_onProperty, X, Y), true, X, Y, Z, W) = fresh4(iext(uri_owl_someValuesFrom, X, Z), true, X, Y, Z, W). 17.79/2.59 Axiom 36 (owl_chain_003_1): fresh51(X, X, Y, Z, W, V, U, T, S, X2) = fresh52(iext(W, T, S), true, Y, Z, U, T, X2). 17.79/2.59 Axiom 37 (owl_chain_003_1): fresh50(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh53(iext(U, X2, Y2), true, Y, W, V, T, S, X2, Y2). 17.79/2.59 Axiom 38 (owl_chain_003_1): fresh49(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh51(iext(uri_owl_propertyChainAxiom, Y, Z), true, Y, W, V, U, T, S, X2, Y2). 17.79/2.59 Axiom 39 (owl_chain_003_1): fresh48(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh50(iext(uri_rdf_first, Z, W), true, Y, Z, W, U, T, S, X2, Y2, Z2). 17.79/2.59 Axiom 40 (owl_chain_003_1): fresh47(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh49(iext(uri_rdf_first, V, U), true, Y, Z, W, U, S, X2, Y2, Z2, W2). 17.79/2.59 Axiom 41 (owl_chain_003_1): fresh46(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh48(iext(uri_rdf_first, T, S), true, Y, Z, W, V, U, S, X2, Y2, Z2, W2). 17.79/2.59 Axiom 42 (owl_chain_003_1): fresh45(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh47(iext(uri_rdf_rest, Z, V), true, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2). 17.79/2.59 Axiom 43 (owl_chain_003_1): fresh45(iext(uri_rdf_rest, X, uri_rdf_nil), true, Y, Z, W, V, U, X, T, S, X2, Y2, Z2) = fresh46(iext(uri_rdf_rest, V, X), true, Y, Z, W, V, U, X, T, S, X2, Y2, Z2). 17.79/2.59 17.79/2.59 Lemma 44: fresh4(X, X, Y, uri_ex_sameCliqueAs, uri_ex_Clique, Z) = fresh29(W, W, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, Z). 17.79/2.59 Proof: 17.79/2.59 fresh4(X, X, Y, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 = { by axiom 26 (owl_restrict_somevaluesfrom_1) } 17.79/2.59 iext(uri_ex_sameCliqueAs, Z, y2(uri_ex_sameCliqueAs, uri_ex_Clique, Z)) 17.79/2.59 = { by axiom 26 (owl_restrict_somevaluesfrom_1) R->L } 17.79/2.59 fresh4(true, true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 = { by axiom 14 (testcase_premise_fullish_013_Cliques_17) R->L } 17.79/2.59 fresh4(iext(uri_owl_someValuesFrom, bnode_r, uri_ex_Clique), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 = { by axiom 35 (owl_restrict_somevaluesfrom_1) R->L } 17.79/2.59 fresh29(iext(uri_owl_onProperty, bnode_r, uri_ex_sameCliqueAs), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 = { by axiom 15 (testcase_premise_fullish_013_Cliques_18) } 17.79/2.59 fresh29(true, true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 = { by axiom 29 (owl_restrict_somevaluesfrom_1) } 17.79/2.59 fresh30(icext(bnode_r, Z), true, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 = { by axiom 29 (owl_restrict_somevaluesfrom_1) R->L } 17.79/2.59 fresh29(W, W, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, Z) 17.79/2.59 17.79/2.59 Lemma 45: fresh29(X, X, bnode_r, Y, Z, uri_ex_JoesGang) = true. 17.79/2.59 Proof: 17.79/2.59 fresh29(X, X, bnode_r, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 29 (owl_restrict_somevaluesfrom_1) } 17.79/2.59 fresh30(icext(bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 22 (owl_rdfsext_subclassof_2) R->L } 17.79/2.59 fresh30(fresh14(true, true, uri_ex_Clique, bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 12 (testcase_premise_fullish_013_Cliques) R->L } 17.79/2.59 fresh30(fresh14(iext(uri_rdfs_subClassOf, uri_ex_Clique, bnode_r), true, uri_ex_Clique, bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 31 (owl_rdfsext_subclassof_2) } 17.79/2.59 fresh30(fresh13(icext(uri_ex_Clique, uri_ex_JoesGang), true, bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 30 (rdfs_cext_def_1) R->L } 17.79/2.59 fresh30(fresh13(fresh2(iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique), true, uri_ex_JoesGang, uri_ex_Clique), true, bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 7 (testcase_premise_fullish_013_Cliques_3) } 17.79/2.59 fresh30(fresh13(fresh2(true, true, uri_ex_JoesGang, uri_ex_Clique), true, bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 18 (rdfs_cext_def_1) } 17.79/2.59 fresh30(fresh13(true, true, bnode_r, uri_ex_JoesGang), true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 17 (owl_rdfsext_subclassof_2) } 17.79/2.59 fresh30(true, true, Y, Z, uri_ex_JoesGang) 17.79/2.59 = { by axiom 20 (owl_restrict_somevaluesfrom_1) } 17.79/2.59 true 17.79/2.59 17.79/2.59 Goal 1 (testcase_conclusion_fullish_013_Cliques): iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) = true. 17.79/2.59 Proof: 17.79/2.59 iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) 17.79/2.59 = { by axiom 28 (owl_chain_003_1) R->L } 17.79/2.59 fresh52(true, true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by lemma 45 R->L } 17.79/2.59 fresh52(fresh29(X, X, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by lemma 44 R->L } 17.79/2.59 fresh52(fresh4(Y, Y, Z, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 26 (owl_restrict_somevaluesfrom_1) } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 27 (owl_eqdis_sameas_1) R->L } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(iext(uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 25 (owl_rdfsext_subpropertyof) R->L } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh10(true, true, uri_ex_sameCliqueAs, uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 13 (testcase_premise_fullish_013_Cliques_7) R->L } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh10(iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs), true, uri_ex_sameCliqueAs, uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 34 (owl_rdfsext_subpropertyof) } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh9(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 26 (owl_restrict_somevaluesfrom_1) R->L } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh9(fresh4(W, W, V, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang), true, uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by lemma 44 } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh9(fresh29(U, U, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang), true, uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by lemma 45 } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh9(true, true, uri_owl_sameAs, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 23 (owl_rdfsext_subpropertyof) } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(true, true, uri_ex_JoesGang, y2(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 16 (owl_eqdis_sameas_1) } 17.79/2.59 fresh52(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 36 (owl_chain_003_1) R->L } 17.79/2.59 fresh51(true, true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 10 (testcase_premise_fullish_013_Cliques_9) R->L } 17.79/2.59 fresh51(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, bnode_l1), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 38 (owl_chain_003_1) R->L } 17.79/2.59 fresh49(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 2 (testcase_premise_fullish_013_Cliques_11) R->L } 17.79/2.59 fresh49(iext(uri_rdf_first, bnode_l2, uri_ex_sameCliqueAs), true, uri_foaf_knows, bnode_l1, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 40 (owl_chain_003_1) R->L } 17.79/2.59 fresh47(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 6 (testcase_premise_fullish_013_Cliques_16) R->L } 17.79/2.59 fresh47(iext(uri_rdf_rest, bnode_l1, bnode_l2), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 42 (owl_chain_003_1) R->L } 17.79/2.59 fresh45(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 4 (testcase_premise_fullish_013_Cliques_14) R->L } 17.79/2.59 fresh45(iext(uri_rdf_rest, bnode_l3, uri_rdf_nil), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 43 (owl_chain_003_1) } 17.79/2.59 fresh46(iext(uri_rdf_rest, bnode_l2, bnode_l3), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 5 (testcase_premise_fullish_013_Cliques_15) } 17.79/2.59 fresh46(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 41 (owl_chain_003_1) } 17.79/2.59 fresh48(iext(uri_rdf_first, bnode_l3, bnode_i), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 1 (testcase_premise_fullish_013_Cliques_10) } 17.79/2.59 fresh48(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 39 (owl_chain_003_1) } 17.79/2.59 fresh50(iext(uri_rdf_first, bnode_l1, uri_rdf_type), true, uri_foaf_knows, bnode_l1, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 3 (testcase_premise_fullish_013_Cliques_12) } 17.79/2.59 fresh50(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 37 (owl_chain_003_1) } 17.79/2.59 fresh53(iext(bnode_i, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 24 (owl_inv_2) R->L } 17.79/2.59 fresh53(fresh19(true, true, bnode_i, uri_rdf_type, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 11 (testcase_premise_fullish_013_Cliques_13) R->L } 17.79/2.59 fresh53(fresh19(iext(uri_owl_inverseOf, bnode_i, uri_rdf_type), true, bnode_i, uri_rdf_type, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 33 (owl_inv_2) } 17.79/2.59 fresh53(fresh18(iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang), true, bnode_i, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 8 (testcase_premise_fullish_013_Cliques_4) } 17.79/2.59 fresh53(fresh18(true, true, bnode_i, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 21 (owl_inv_2) } 17.79/2.59 fresh53(true, true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob) 17.79/2.59 = { by axiom 32 (owl_chain_003_1) } 17.79/2.59 fresh54(iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang), true, uri_foaf_knows, uri_ex_alice, uri_ex_bob) 17.79/2.59 = { by axiom 9 (testcase_premise_fullish_013_Cliques_5) } 17.79/2.59 fresh54(true, true, uri_foaf_knows, uri_ex_alice, uri_ex_bob) 17.79/2.59 = { by axiom 19 (owl_chain_003_1) } 17.79/2.59 true 17.79/2.59 % SZS output end Proof 17.79/2.59 17.79/2.59 RESULT: Theorem (the conjecture is true). 17.79/2.60 EOF