TSTP Solution File: SWB024+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB024+2 : 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 : n020.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 20:12:56 EDT 2023
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% 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 : SWB024+2 : 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 : n020.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 06:18:44 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.46 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.46
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 Take the following subset of the input axioms:
% 0.21/0.47 fof(owl_char_transitive, axiom, ![P]: (icext(uri_owl_TransitiveProperty, P) <=> (ip(P) & ![X, Z, Y]: ((iext(P, X, Y) & iext(P, Y, Z)) => iext(P, X, Z))))).
% 0.21/0.47 fof(owl_rdfsext_subclassof, axiom, ![C1, C2]: (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & (ic(C2) & ![X2]: (icext(C1, X2) => icext(C2, X2)))))).
% 0.21/0.47 fof(owl_restrict_mincard_001, axiom, ![Z2, P2]: ((iext(uri_owl_minCardinality, Z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P2)) => ![X2]: (icext(Z2, X2) <=> ?[Y2]: iext(P2, X2, Y2)))).
% 0.21/0.47 fof(rdfs_cext_def, axiom, ![C, X2]: (iext(uri_rdf_type, X2, C) <=> icext(C, X2))).
% 0.21/0.47 fof(testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties, conjecture, ?[BNODE_x]: (iext(uri_ex_hasAncestor, uri_ex_bob, BNODE_x) & iext(uri_ex_hasAncestor, uri_ex_alice, BNODE_x))).
% 0.21/0.47 fof(testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties, axiom, ?[BNODE_z]: (iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) & (iext(uri_rdfs_subClassOf, uri_ex_Person, BNODE_z) & (iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & (iext(uri_owl_onProperty, BNODE_z, uri_ex_hasAncestor) & (iext(uri_owl_minCardinality, BNODE_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & (iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) & (iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) & iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob))))))))).
% 0.21/0.47
% 0.21/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.47 fresh(y, y, x1...xn) = u
% 0.21/0.47 C => fresh(s, t, x1...xn) = v
% 0.21/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.47 variables of u and v.
% 0.21/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.47 input problem has no model of domain size 1).
% 0.21/0.47
% 0.21/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.47
% 0.21/0.47 Axiom 1 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties): iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) = true2.
% 0.21/0.47 Axiom 2 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_1): iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) = true2.
% 0.21/0.48 Axiom 3 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_6): iext(uri_rdfs_subClassOf, uri_ex_Person, bnode_z) = true2.
% 0.21/0.48 Axiom 4 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_7): iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob) = true2.
% 0.21/0.48 Axiom 5 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_5): iext(uri_owl_onProperty, bnode_z, uri_ex_hasAncestor) = true2.
% 0.21/0.48 Axiom 6 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_4): iext(uri_owl_minCardinality, bnode_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) = true2.
% 0.21/0.48 Axiom 7 (owl_rdfsext_subclassof_2): fresh6(X, X, Y, Z) = true2.
% 0.21/0.48 Axiom 8 (owl_restrict_mincard_001_1): fresh3(X, X, Y, Z) = true2.
% 0.21/0.48 Axiom 9 (rdfs_cext_def): fresh2(X, X, Y, Z) = true2.
% 0.21/0.48 Axiom 10 (owl_restrict_mincard_001_1): fresh21(X, X, Y, Z, W) = iext(Z, W, y2(Z, W)).
% 0.21/0.48 Axiom 11 (owl_char_transitive): fresh15(X, X, Y, Z, W) = true2.
% 0.21/0.48 Axiom 12 (owl_rdfsext_subclassof_2): fresh7(X, X, Y, Z, W) = icext(Z, W).
% 0.21/0.48 Axiom 13 (owl_char_transitive): fresh13(X, X, Y, Z, W, V) = iext(Y, Z, V).
% 0.21/0.48 Axiom 14 (owl_rdfsext_subclassof_2): fresh7(icext(X, Y), true2, X, Z, Y) = fresh6(iext(uri_rdfs_subClassOf, X, Z), true2, Z, Y).
% 0.21/0.48 Axiom 15 (rdfs_cext_def): fresh2(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X).
% 0.21/0.48 Axiom 16 (owl_restrict_mincard_001_1): fresh20(X, X, Y, Z, W) = fresh21(iext(uri_owl_onProperty, Y, Z), true2, Y, Z, W).
% 0.21/0.48 Axiom 17 (owl_char_transitive): fresh14(X, X, Y, Z, W, V) = fresh15(iext(Y, Z, W), true2, Y, Z, V).
% 0.21/0.48 Axiom 18 (owl_restrict_mincard_001_1): fresh20(icext(X, Y), true2, X, Z, Y) = fresh3(iext(uri_owl_minCardinality, X, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)), true2, Z, Y).
% 0.21/0.48 Axiom 19 (owl_char_transitive): fresh14(icext(uri_owl_TransitiveProperty, X), true2, X, Y, Z, W) = fresh13(iext(X, Z, W), true2, X, Y, Z, W).
% 0.21/0.48
% 0.21/0.48 Lemma 20: iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)) = true2.
% 0.21/0.48 Proof:
% 0.21/0.48 iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob))
% 0.21/0.48 = { by axiom 10 (owl_restrict_mincard_001_1) R->L }
% 0.21/0.48 fresh21(true2, true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 5 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_5) R->L }
% 0.21/0.48 fresh21(iext(uri_owl_onProperty, bnode_z, uri_ex_hasAncestor), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 16 (owl_restrict_mincard_001_1) R->L }
% 0.21/0.48 fresh20(true2, true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 7 (owl_rdfsext_subclassof_2) R->L }
% 0.21/0.48 fresh20(fresh6(true2, true2, bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 3 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_6) R->L }
% 0.21/0.48 fresh20(fresh6(iext(uri_rdfs_subClassOf, uri_ex_Person, bnode_z), true2, bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 14 (owl_rdfsext_subclassof_2) R->L }
% 0.21/0.48 fresh20(fresh7(icext(uri_ex_Person, uri_ex_bob), true2, uri_ex_Person, bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 15 (rdfs_cext_def) R->L }
% 0.21/0.48 fresh20(fresh7(fresh2(iext(uri_rdf_type, uri_ex_bob, uri_ex_Person), true2, uri_ex_bob, uri_ex_Person), true2, uri_ex_Person, bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 2 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_1) }
% 0.21/0.48 fresh20(fresh7(fresh2(true2, true2, uri_ex_bob, uri_ex_Person), true2, uri_ex_Person, bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 9 (rdfs_cext_def) }
% 0.21/0.48 fresh20(fresh7(true2, true2, uri_ex_Person, bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 12 (owl_rdfsext_subclassof_2) }
% 0.21/0.48 fresh20(icext(bnode_z, uri_ex_bob), true2, bnode_z, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 18 (owl_restrict_mincard_001_1) }
% 0.21/0.48 fresh3(iext(uri_owl_minCardinality, bnode_z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)), true2, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 6 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_4) }
% 0.21/0.48 fresh3(true2, true2, uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48 = { by axiom 8 (owl_restrict_mincard_001_1) }
% 0.21/0.48 true2
% 0.21/0.48
% 0.21/0.48 Goal 1 (testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties): tuple(iext(uri_ex_hasAncestor, uri_ex_bob, X), iext(uri_ex_hasAncestor, uri_ex_alice, X)) = tuple(true2, true2).
% 0.21/0.48 The goal is true when:
% 0.21/0.48 X = y2(uri_ex_hasAncestor, uri_ex_bob)
% 0.21/0.48
% 0.21/0.48 Proof:
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), iext(uri_ex_hasAncestor, uri_ex_alice, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 13 (owl_char_transitive) R->L }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh13(true2, true2, uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by lemma 20 R->L }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh13(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), true2, uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 19 (owl_char_transitive) R->L }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh14(icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor), true2, uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 15 (rdfs_cext_def) R->L }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh14(fresh2(iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty), true2, uri_ex_hasAncestor, uri_owl_TransitiveProperty), true2, uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 1 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties) }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh14(fresh2(true2, true2, uri_ex_hasAncestor, uri_owl_TransitiveProperty), true2, uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 9 (rdfs_cext_def) }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh14(true2, true2, uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 17 (owl_char_transitive) }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh15(iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob), true2, uri_ex_hasAncestor, uri_ex_alice, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 4 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties_7) }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), fresh15(true2, true2, uri_ex_hasAncestor, uri_ex_alice, y2(uri_ex_hasAncestor, uri_ex_bob)))
% 0.21/0.48 = { by axiom 11 (owl_char_transitive) }
% 0.21/0.48 tuple(iext(uri_ex_hasAncestor, uri_ex_bob, y2(uri_ex_hasAncestor, uri_ex_bob)), true2)
% 0.21/0.48 = { by lemma 20 }
% 0.21/0.48 tuple(true2, true2)
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48
% 0.21/0.48 RESULT: Theorem (the conjecture is true).
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