0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.14/0.35 % Computer : n004.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Thu Jul 2 07:12:43 EDT 2020 0.14/0.35 % CPUTime : 327.84/41.54 % SZS status Theorem 327.84/41.55 327.84/41.55 % SZS output start Proof 327.84/41.55 Take the following subset of the input axioms: 327.84/41.55 fof(conclusion_rdfbased_sem_class_thing_term, conjecture, iext(uri_rdfs_subClassOf, uri_ex_c, uri_owl_Thing)). 327.84/41.55 fof(owl_class_classowl_ext, axiom, ![X]: (icext(uri_owl_Class, X) <=> ic(X))). 327.84/41.55 fof(owl_class_thing_ext, axiom, ![X]: (ir(X) <=> icext(uri_owl_Thing, X))). 327.84/41.55 fof(owl_class_thing_type, axiom, ic(uri_owl_Thing)). 327.84/41.55 fof(owl_rdfsext_subclassof, axiom, ![C1, C2]: ((ic(C1) & (ic(C2) & ![X]: (icext(C2, X) <= icext(C1, X)))) <=> iext(uri_rdfs_subClassOf, C1, C2))). 327.84/41.55 fof(premise_rdfbased_sem_class_thing_term, axiom, iext(uri_rdf_type, uri_ex_c, uri_owl_Class)). 327.84/41.55 fof(rdfs_cext_def, axiom, ![X, C]: (iext(uri_rdf_type, X, C) <=> icext(C, X))). 327.84/41.55 fof(simple_ir, axiom, ![X]: ir(X)). 327.84/41.55 327.84/41.55 Now clausify the problem and encode Horn clauses using encoding 3 of 327.84/41.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 327.84/41.55 We repeatedly replace C & s=t => u=v by the two clauses: 327.84/41.55 fresh(y, y, x1...xn) = u 327.84/41.55 C => fresh(s, t, x1...xn) = v 327.84/41.55 where fresh is a fresh function symbol and x1..xn are the free 327.84/41.55 variables of u and v. 327.84/41.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the 327.84/41.55 input problem has no model of domain size 1). 327.84/41.55 327.84/41.55 The encoding turns the above axioms into the following unit equations and goals: 327.84/41.55 327.84/41.55 Axiom 1 (owl_class_classowl_ext): fresh437(X, X, Y) = true2. 327.84/41.55 Axiom 2 (owl_class_thing_ext_1): fresh404(X, X, Y) = true2. 327.84/41.55 Axiom 3 (owl_rdfsext_subclassof_1): fresh963(X, X, Y, Z) = iext(uri_rdfs_subClassOf, Y, Z). 327.84/41.55 Axiom 4 (owl_rdfsext_subclassof_1): fresh99(X, X, Y, Z) = true2. 327.84/41.55 Axiom 5 (owl_rdfsext_subclassof_1): fresh962(X, X, Y, Z) = fresh963(ic(Y), true2, Y, Z). 327.84/41.55 Axiom 6 (rdfs_cext_def_1): fresh34(X, X, Y, Z) = true2. 327.84/41.55 Axiom 7 (owl_class_thing_ext_1): fresh404(ir(X), true2, X) = icext(uri_owl_Thing, X). 327.84/41.55 Axiom 8 (owl_class_thing_type): ic(uri_owl_Thing) = true2. 327.84/41.55 Axiom 9 (simple_ir): ir(X) = true2. 327.84/41.55 Axiom 10 (owl_rdfsext_subclassof_1): fresh962(ic(X), true2, Y, X) = fresh99(icext(X, sK49_owl_rdfsext_subclassof_X(Y, X)), true2, Y, X). 327.84/41.55 Axiom 11 (owl_class_classowl_ext): fresh437(icext(uri_owl_Class, X), true2, X) = ic(X). 327.84/41.55 Axiom 12 (rdfs_cext_def_1): fresh34(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X). 327.84/41.55 Axiom 13 (premise_rdfbased_sem_class_thing_term): iext(uri_rdf_type, uri_ex_c, uri_owl_Class) = true2. 327.84/41.55 327.84/41.55 Goal 1 (conclusion_rdfbased_sem_class_thing_term): iext(uri_rdfs_subClassOf, uri_ex_c, uri_owl_Thing) = true2. 327.84/41.55 Proof: 327.84/41.55 iext(uri_rdfs_subClassOf, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 3 (owl_rdfsext_subclassof_1) } 327.84/41.55 fresh963(true2, true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 1 (owl_class_classowl_ext) } 327.84/41.55 fresh963(fresh437(true2, true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 6 (rdfs_cext_def_1) } 327.84/41.55 fresh963(fresh437(fresh34(true2, true2, uri_ex_c, uri_owl_Class), true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 13 (premise_rdfbased_sem_class_thing_term) } 327.84/41.55 fresh963(fresh437(fresh34(iext(uri_rdf_type, uri_ex_c, uri_owl_Class), true2, uri_ex_c, uri_owl_Class), true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 12 (rdfs_cext_def_1) } 327.84/41.55 fresh963(fresh437(icext(uri_owl_Class, uri_ex_c), true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 11 (owl_class_classowl_ext) } 327.84/41.55 fresh963(ic(uri_ex_c), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 5 (owl_rdfsext_subclassof_1) } 327.84/41.55 fresh962(true2, true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 8 (owl_class_thing_type) } 327.84/41.55 fresh962(ic(uri_owl_Thing), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 10 (owl_rdfsext_subclassof_1) } 327.84/41.55 fresh99(icext(uri_owl_Thing, sK49_owl_rdfsext_subclassof_X(uri_ex_c, uri_owl_Thing)), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 7 (owl_class_thing_ext_1) } 327.84/41.55 fresh99(fresh404(ir(sK49_owl_rdfsext_subclassof_X(uri_ex_c, uri_owl_Thing)), true2, sK49_owl_rdfsext_subclassof_X(uri_ex_c, uri_owl_Thing)), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 9 (simple_ir) } 327.84/41.55 fresh99(fresh404(true2, true2, sK49_owl_rdfsext_subclassof_X(uri_ex_c, uri_owl_Thing)), true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 2 (owl_class_thing_ext_1) } 327.84/41.55 fresh99(true2, true2, uri_ex_c, uri_owl_Thing) 327.84/41.55 = { by axiom 4 (owl_rdfsext_subclassof_1) } 327.84/41.55 true2 327.84/41.55 % SZS output end Proof 327.84/41.55 327.84/41.55 RESULT: Theorem (the conjecture is true). 327.84/41.60 EOF