TSTP Solution File: SWB005+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB005+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:12:42 EDT 2023
% Result : Theorem 135.10s 17.85s
% Output : Proof 135.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWB005+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n019.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 : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 07:23:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 135.10/17.85 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 135.10/17.85
% 135.10/17.85 % SZS status Theorem
% 135.10/17.85
% 135.10/17.86 % SZS output start Proof
% 135.10/17.86 Take the following subset of the input axioms:
% 135.10/17.86 fof(owl_class_objectproperty_ext, axiom, ![X]: (icext(uri_owl_ObjectProperty, X) <=> ip(X))).
% 135.10/17.86 fof(owl_class_thing_ext, axiom, ![X2]: (icext(uri_owl_Thing, X2) <=> ir(X2))).
% 135.10/17.86 fof(owl_parts_ip_def, axiom, ![X2]: (ip(X2) <=> iext(uri_rdf_type, X2, uri_rdf_Property))).
% 135.10/17.86 fof(owl_parts_ir_def, axiom, ![X2]: (ir(X2) <=> iext(uri_rdf_type, X2, uri_rdfs_Resource))).
% 135.10/17.86 fof(rdfs_cext_def, axiom, ![C, X2]: (iext(uri_rdf_type, X2, C) <=> icext(C, X2))).
% 135.10/17.86 fof(simple_iext_property, axiom, ![S, P, O]: (iext(P, S, O) => ip(P))).
% 135.10/17.86 fof(simple_ir, axiom, ![X2]: ir(X2)).
% 135.10/17.86 fof(testcase_conclusion_fullish_005_Everything_is_a_Resource, conjecture, iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) & (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) & (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) & (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) & (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) & (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & (iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) & iext(uri_rdf_type, uri_ex_o, uri_owl_Thing)))))))).
% 135.10/17.86 fof(testcase_premise_fullish_005_Everything_is_a_Resource, axiom, iext(uri_ex_p, uri_ex_s, uri_ex_o)).
% 135.10/17.86
% 135.10/17.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 135.10/17.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 135.10/17.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 135.10/17.86 fresh(y, y, x1...xn) = u
% 135.10/17.86 C => fresh(s, t, x1...xn) = v
% 135.10/17.86 where fresh is a fresh function symbol and x1..xn are the free
% 135.10/17.86 variables of u and v.
% 135.10/17.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 135.10/17.86 input problem has no model of domain size 1).
% 135.10/17.86
% 135.10/17.86 The encoding turns the above axioms into the following unit equations and goals:
% 135.10/17.86
% 135.10/17.86 Axiom 1 (simple_ir): ir(X) = true2.
% 135.10/17.86 Axiom 2 (testcase_premise_fullish_005_Everything_is_a_Resource): iext(uri_ex_p, uri_ex_s, uri_ex_o) = true2.
% 135.10/17.86 Axiom 3 (owl_class_objectproperty_ext): fresh448(X, X, Y) = true2.
% 135.10/17.86 Axiom 4 (owl_class_thing_ext): fresh435(X, X, Y) = true2.
% 135.10/17.86 Axiom 5 (owl_parts_ip_def_1): fresh260(X, X, Y) = true2.
% 135.10/17.86 Axiom 6 (owl_parts_ir_def_1): fresh258(X, X, Y) = true2.
% 135.10/17.86 Axiom 7 (simple_iext_property): fresh6(X, X, Y) = true2.
% 135.10/17.86 Axiom 8 (owl_class_objectproperty_ext): fresh448(ip(X), true2, X) = icext(uri_owl_ObjectProperty, X).
% 135.10/17.86 Axiom 9 (owl_class_thing_ext): fresh435(ir(X), true2, X) = icext(uri_owl_Thing, X).
% 135.10/17.86 Axiom 10 (owl_parts_ip_def_1): fresh260(ip(X), true2, X) = iext(uri_rdf_type, X, uri_rdf_Property).
% 135.10/17.86 Axiom 11 (owl_parts_ir_def_1): fresh258(ir(X), true2, X) = iext(uri_rdf_type, X, uri_rdfs_Resource).
% 135.10/17.86 Axiom 12 (rdfs_cext_def_1): fresh34(X, X, Y, Z) = true2.
% 135.10/17.86 Axiom 13 (rdfs_cext_def_1): fresh34(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X).
% 135.10/17.86 Axiom 14 (simple_iext_property): fresh6(iext(X, Y, Z), true2, X) = ip(X).
% 135.10/17.86
% 135.10/17.86 Lemma 15: ip(uri_ex_p) = true2.
% 135.10/17.86 Proof:
% 135.10/17.86 ip(uri_ex_p)
% 135.10/17.86 = { by axiom 14 (simple_iext_property) R->L }
% 135.10/17.86 fresh6(iext(uri_ex_p, uri_ex_s, uri_ex_o), true2, uri_ex_p)
% 135.10/17.86 = { by axiom 2 (testcase_premise_fullish_005_Everything_is_a_Resource) }
% 135.10/17.86 fresh6(true2, true2, uri_ex_p)
% 135.10/17.86 = { by axiom 7 (simple_iext_property) }
% 135.10/17.86 true2
% 135.10/17.86
% 135.10/17.86 Lemma 16: iext(uri_rdf_type, X, uri_rdfs_Resource) = true2.
% 135.10/17.86 Proof:
% 135.10/17.86 iext(uri_rdf_type, X, uri_rdfs_Resource)
% 135.10/17.86 = { by axiom 11 (owl_parts_ir_def_1) R->L }
% 135.10/17.86 fresh258(ir(X), true2, X)
% 135.10/17.86 = { by axiom 1 (simple_ir) }
% 135.10/17.86 fresh258(true2, true2, X)
% 135.10/17.86 = { by axiom 6 (owl_parts_ir_def_1) }
% 135.10/17.86 true2
% 135.10/17.86
% 135.10/17.86 Lemma 17: iext(uri_rdf_type, X, uri_owl_Thing) = true2.
% 135.10/17.86 Proof:
% 135.10/17.86 iext(uri_rdf_type, X, uri_owl_Thing)
% 135.10/17.86 = { by axiom 13 (rdfs_cext_def_1) R->L }
% 135.10/17.86 fresh34(icext(uri_owl_Thing, X), true2, X, uri_owl_Thing)
% 135.10/17.86 = { by axiom 9 (owl_class_thing_ext) R->L }
% 135.10/17.86 fresh34(fresh435(ir(X), true2, X), true2, X, uri_owl_Thing)
% 135.10/17.86 = { by axiom 1 (simple_ir) }
% 135.10/17.86 fresh34(fresh435(true2, true2, X), true2, X, uri_owl_Thing)
% 135.10/17.86 = { by axiom 4 (owl_class_thing_ext) }
% 135.10/17.86 fresh34(true2, true2, X, uri_owl_Thing)
% 135.10/17.86 = { by axiom 12 (rdfs_cext_def_1) }
% 135.10/17.86 true2
% 135.10/17.86
% 135.10/17.86 Goal 1 (testcase_conclusion_fullish_005_Everything_is_a_Resource): tuple2(iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_s, uri_owl_Thing), iext(uri_rdf_type, uri_ex_p, uri_rdf_Property), iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing)) = tuple2(true2, true2, true2, true2, true2, true2, true2, true2).
% 135.10/17.86 Proof:
% 135.10/17.86 tuple2(iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_s, uri_owl_Thing), iext(uri_rdf_type, uri_ex_p, uri_rdf_Property), iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 16 }
% 135.10/17.86 tuple2(true2, iext(uri_rdf_type, uri_ex_s, uri_owl_Thing), iext(uri_rdf_type, uri_ex_p, uri_rdf_Property), iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 17 }
% 135.10/17.86 tuple2(true2, true2, iext(uri_rdf_type, uri_ex_p, uri_rdf_Property), iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by axiom 10 (owl_parts_ip_def_1) R->L }
% 135.10/17.86 tuple2(true2, true2, fresh260(ip(uri_ex_p), true2, uri_ex_p), iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 15 }
% 135.10/17.86 tuple2(true2, true2, fresh260(true2, true2, uri_ex_p), iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by axiom 5 (owl_parts_ip_def_1) }
% 135.10/17.86 tuple2(true2, true2, true2, iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 16 }
% 135.10/17.86 tuple2(true2, true2, true2, true2, iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), iext(uri_rdf_type, uri_ex_p, uri_owl_Thing), iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 17 }
% 135.10/17.86 tuple2(true2, true2, true2, true2, iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), true2, iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource), iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 16 }
% 135.10/17.86 tuple2(true2, true2, true2, true2, iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), true2, true2, iext(uri_rdf_type, uri_ex_o, uri_owl_Thing))
% 135.10/17.86 = { by lemma 17 }
% 135.10/17.86 tuple2(true2, true2, true2, true2, iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty), true2, true2, true2)
% 135.10/17.86 = { by axiom 13 (rdfs_cext_def_1) R->L }
% 135.10/17.86 tuple2(true2, true2, true2, true2, fresh34(icext(uri_owl_ObjectProperty, uri_ex_p), true2, uri_ex_p, uri_owl_ObjectProperty), true2, true2, true2)
% 135.10/17.86 = { by axiom 8 (owl_class_objectproperty_ext) R->L }
% 135.10/17.86 tuple2(true2, true2, true2, true2, fresh34(fresh448(ip(uri_ex_p), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ObjectProperty), true2, true2, true2)
% 135.10/17.86 = { by lemma 15 }
% 135.10/17.86 tuple2(true2, true2, true2, true2, fresh34(fresh448(true2, true2, uri_ex_p), true2, uri_ex_p, uri_owl_ObjectProperty), true2, true2, true2)
% 135.10/17.86 = { by axiom 3 (owl_class_objectproperty_ext) }
% 135.10/17.86 tuple2(true2, true2, true2, true2, fresh34(true2, true2, uri_ex_p, uri_owl_ObjectProperty), true2, true2, true2)
% 135.10/17.86 = { by axiom 12 (rdfs_cext_def_1) }
% 135.10/17.86 tuple2(true2, true2, true2, true2, true2, true2, true2, true2)
% 135.10/17.86 % SZS output end Proof
% 135.10/17.86
% 135.10/17.86 RESULT: Theorem (the conjecture is true).
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