TSTP Solution File: SWB009+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB009+3 : 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 : n023.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 20:12:46 EDT 2023
% Result : Theorem 83.74s 10.88s
% Output : Proof 83.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB009+3 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 07:49:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 83.74/10.88 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 83.74/10.88
% 83.74/10.88 % SZS status Theorem
% 83.74/10.88
% 83.74/10.89 % SZS output start Proof
% 83.74/10.89 Take the following subset of the input axioms:
% 83.74/10.89 fof(owl_bool_complementof_class, axiom, ![Z, C]: (iext(uri_owl_complementOf, Z, C) => (ic(Z) & (ic(C) & ![X]: (icext(Z, X) <=> ~icext(C, X)))))).
% 83.74/10.89 fof(owl_bool_unionof_class_000, axiom, ![Z2]: (iext(uri_owl_unionOf, Z2, uri_rdf_nil) <=> (ic(Z2) & ![X2]: ~icext(Z2, X2)))).
% 83.74/10.89 fof(owl_class_nothing_ext, axiom, ![X2]: ~icext(uri_owl_Nothing, X2)).
% 83.74/10.89 fof(owl_restrict_somevaluesfrom, axiom, ![C2, P, Z2]: ((iext(uri_owl_someValuesFrom, Z2, C2) & iext(uri_owl_onProperty, Z2, P)) => ![X2]: (icext(Z2, X2) <=> ?[Y]: (iext(P, X2, Y) & icext(C2, Y))))).
% 83.74/10.89 fof(rdfs_cext_def, axiom, ![C2, X2]: (iext(uri_rdf_type, X2, C2) <=> icext(C2, X2))).
% 83.74/10.89 fof(testcase_conclusion_fullish_009_Existential_Restriction_Entailments, conjecture, ?[BNODE_x]: (iext(uri_ex_p, uri_ex_s, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_c))).
% 83.74/10.89 fof(testcase_premise_fullish_009_Existential_Restriction_Entailments, axiom, ?[BNODE_z]: (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & (iext(uri_rdf_type, uri_ex_s, BNODE_z) & (iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & (iext(uri_owl_onProperty, BNODE_z, uri_ex_p) & iext(uri_owl_someValuesFrom, BNODE_z, uri_ex_c))))))).
% 83.74/10.89
% 83.74/10.89 Now clausify the problem and encode Horn clauses using encoding 3 of
% 83.74/10.89 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 83.74/10.89 We repeatedly replace C & s=t => u=v by the two clauses:
% 83.74/10.89 fresh(y, y, x1...xn) = u
% 83.74/10.89 C => fresh(s, t, x1...xn) = v
% 83.74/10.89 where fresh is a fresh function symbol and x1..xn are the free
% 83.74/10.89 variables of u and v.
% 83.74/10.89 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 83.74/10.89 input problem has no model of domain size 1).
% 83.74/10.89
% 83.74/10.89 The encoding turns the above axioms into the following unit equations and goals:
% 83.74/10.89
% 83.74/10.89 Axiom 1 (testcase_premise_fullish_009_Existential_Restriction_Entailments_1): iext(uri_rdf_type, uri_ex_s, bnode_z) = true2.
% 83.74/10.89 Axiom 2 (testcase_premise_fullish_009_Existential_Restriction_Entailments_4): iext(uri_owl_onProperty, bnode_z, uri_ex_p) = true2.
% 83.74/10.89 Axiom 3 (testcase_premise_fullish_009_Existential_Restriction_Entailments_5): iext(uri_owl_someValuesFrom, bnode_z, uri_ex_c) = true2.
% 83.74/10.89 Axiom 4 (rdfs_cext_def): fresh31(X, X, Y, Z) = true2.
% 83.74/10.89 Axiom 5 (rdfs_cext_def_1): fresh30(X, X, Y, Z) = true2.
% 83.74/10.89 Axiom 6 (owl_restrict_somevaluesfrom_2): fresh154(X, X, Y, Z, W) = true2.
% 83.74/10.89 Axiom 7 (owl_restrict_somevaluesfrom_1): fresh152(X, X, Y, Z, W) = true2.
% 83.74/10.89 Axiom 8 (rdfs_cext_def_1): fresh30(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X).
% 83.74/10.89 Axiom 9 (owl_restrict_somevaluesfrom_1): fresh35(X, X, Y, Z, W, V) = iext(Z, V, y(Z, W, V)).
% 83.74/10.89 Axiom 10 (owl_restrict_somevaluesfrom_2): fresh34(X, X, Y, Z, W, V) = icext(W, y(Z, W, V)).
% 83.74/10.89 Axiom 11 (rdfs_cext_def): fresh31(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X).
% 83.74/10.89 Axiom 12 (owl_restrict_somevaluesfrom_2): fresh153(X, X, Y, Z, W, V) = fresh154(iext(uri_owl_onProperty, Y, Z), true2, Z, W, V).
% 83.74/10.89 Axiom 13 (owl_restrict_somevaluesfrom_1): fresh151(X, X, Y, Z, W, V) = fresh152(iext(uri_owl_onProperty, Y, Z), true2, Z, W, V).
% 83.74/10.89 Axiom 14 (owl_restrict_somevaluesfrom_1): fresh151(icext(X, Y), true2, X, Z, W, Y) = fresh35(iext(uri_owl_someValuesFrom, X, W), true2, X, Z, W, Y).
% 83.74/10.89 Axiom 15 (owl_restrict_somevaluesfrom_2): fresh153(icext(X, Y), true2, X, Z, W, Y) = fresh34(iext(uri_owl_someValuesFrom, X, W), true2, X, Z, W, Y).
% 83.74/10.89
% 83.74/10.89 Lemma 16: icext(bnode_z, uri_ex_s) = true2.
% 83.74/10.89 Proof:
% 83.74/10.89 icext(bnode_z, uri_ex_s)
% 83.74/10.89 = { by axiom 11 (rdfs_cext_def) R->L }
% 83.74/10.89 fresh31(iext(uri_rdf_type, uri_ex_s, bnode_z), true2, uri_ex_s, bnode_z)
% 83.74/10.89 = { by axiom 1 (testcase_premise_fullish_009_Existential_Restriction_Entailments_1) }
% 83.74/10.89 fresh31(true2, true2, uri_ex_s, bnode_z)
% 83.74/10.89 = { by axiom 4 (rdfs_cext_def) }
% 83.74/10.89 true2
% 83.74/10.89
% 83.74/10.89 Goal 1 (testcase_conclusion_fullish_009_Existential_Restriction_Entailments): tuple2(iext(uri_rdf_type, X, uri_ex_c), iext(uri_ex_p, uri_ex_s, X)) = tuple2(true2, true2).
% 83.74/10.89 The goal is true when:
% 83.74/10.89 X = y(uri_ex_p, uri_ex_c, uri_ex_s)
% 83.74/10.89
% 83.74/10.89 Proof:
% 83.74/10.89 tuple2(iext(uri_rdf_type, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 8 (rdfs_cext_def_1) R->L }
% 83.74/10.89 tuple2(fresh30(icext(uri_ex_c, y(uri_ex_p, uri_ex_c, uri_ex_s)), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 10 (owl_restrict_somevaluesfrom_2) R->L }
% 83.74/10.89 tuple2(fresh30(fresh34(true2, true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 3 (testcase_premise_fullish_009_Existential_Restriction_Entailments_5) R->L }
% 83.74/10.89 tuple2(fresh30(fresh34(iext(uri_owl_someValuesFrom, bnode_z, uri_ex_c), true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 15 (owl_restrict_somevaluesfrom_2) R->L }
% 83.74/10.89 tuple2(fresh30(fresh153(icext(bnode_z, uri_ex_s), true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by lemma 16 }
% 83.74/10.89 tuple2(fresh30(fresh153(true2, true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 12 (owl_restrict_somevaluesfrom_2) }
% 83.74/10.89 tuple2(fresh30(fresh154(iext(uri_owl_onProperty, bnode_z, uri_ex_p), true2, uri_ex_p, uri_ex_c, uri_ex_s), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 2 (testcase_premise_fullish_009_Existential_Restriction_Entailments_4) }
% 83.74/10.89 tuple2(fresh30(fresh154(true2, true2, uri_ex_p, uri_ex_c, uri_ex_s), true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 6 (owl_restrict_somevaluesfrom_2) }
% 83.74/10.89 tuple2(fresh30(true2, true2, y(uri_ex_p, uri_ex_c, uri_ex_s), uri_ex_c), iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.89 = { by axiom 5 (rdfs_cext_def_1) }
% 83.74/10.90 tuple2(true2, iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 83.74/10.90 = { by axiom 9 (owl_restrict_somevaluesfrom_1) R->L }
% 83.74/10.90 tuple2(true2, fresh35(true2, true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 83.74/10.90 = { by axiom 3 (testcase_premise_fullish_009_Existential_Restriction_Entailments_5) R->L }
% 83.74/10.90 tuple2(true2, fresh35(iext(uri_owl_someValuesFrom, bnode_z, uri_ex_c), true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 83.74/10.90 = { by axiom 14 (owl_restrict_somevaluesfrom_1) R->L }
% 83.74/10.90 tuple2(true2, fresh151(icext(bnode_z, uri_ex_s), true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 83.74/10.90 = { by lemma 16 }
% 83.74/10.90 tuple2(true2, fresh151(true2, true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 83.74/10.90 = { by axiom 13 (owl_restrict_somevaluesfrom_1) }
% 83.74/10.90 tuple2(true2, fresh152(iext(uri_owl_onProperty, bnode_z, uri_ex_p), true2, uri_ex_p, uri_ex_c, uri_ex_s))
% 83.74/10.90 = { by axiom 2 (testcase_premise_fullish_009_Existential_Restriction_Entailments_4) }
% 83.74/10.90 tuple2(true2, fresh152(true2, true2, uri_ex_p, uri_ex_c, uri_ex_s))
% 83.74/10.90 = { by axiom 7 (owl_restrict_somevaluesfrom_1) }
% 83.74/10.90 tuple2(true2, true2)
% 83.74/10.90 % SZS output end Proof
% 83.74/10.90
% 83.74/10.90 RESULT: Theorem (the conjecture is true).
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