TSTP Solution File: SWB009+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB009+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 : n032.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 0.12s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB009+2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n032.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 07:08:59 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39
% 0.17/0.40 % SZS output start Proof
% 0.17/0.40 Take the following subset of the input axioms:
% 0.17/0.40 fof(owl_restrict_somevaluesfrom, axiom, ![C, Z, P]: ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X]: (icext(Z, X) <=> ?[Y]: (iext(P, X, Y) & icext(C, Y))))).
% 0.17/0.40 fof(rdfs_cext_def, axiom, ![X2, C2]: (iext(uri_rdf_type, X2, C2) <=> icext(C2, X2))).
% 0.17/0.40 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))).
% 0.17/0.40 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))))))).
% 0.17/0.40
% 0.17/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.40 fresh(y, y, x1...xn) = u
% 0.17/0.40 C => fresh(s, t, x1...xn) = v
% 0.17/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.40 variables of u and v.
% 0.17/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.40 input problem has no model of domain size 1).
% 0.17/0.40
% 0.17/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.40
% 0.17/0.40 Axiom 1 (testcase_premise_fullish_009_Existential_Restriction_Entailments_1): iext(uri_rdf_type, uri_ex_s, bnode_z) = true2.
% 0.17/0.40 Axiom 2 (testcase_premise_fullish_009_Existential_Restriction_Entailments_4): iext(uri_owl_someValuesFrom, bnode_z, uri_ex_c) = true2.
% 0.17/0.40 Axiom 3 (testcase_premise_fullish_009_Existential_Restriction_Entailments_5): iext(uri_owl_onProperty, bnode_z, uri_ex_p) = true2.
% 0.17/0.40 Axiom 4 (rdfs_cext_def_1): fresh(X, X, Y, Z) = true2.
% 0.17/0.40 Axiom 5 (rdfs_cext_def): fresh2(X, X, Y, Z) = true2.
% 0.17/0.40 Axiom 6 (owl_restrict_somevaluesfrom_2): fresh12(X, X, Y, Z, W) = true2.
% 0.17/0.40 Axiom 7 (owl_restrict_somevaluesfrom_1): fresh10(X, X, Y, Z, W) = true2.
% 0.17/0.40 Axiom 8 (rdfs_cext_def_1): fresh(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X).
% 0.17/0.40 Axiom 9 (owl_restrict_somevaluesfrom_1): fresh4(X, X, Y, Z, W, V) = iext(Z, V, y(Z, W, V)).
% 0.17/0.40 Axiom 10 (owl_restrict_somevaluesfrom_2): fresh3(X, X, Y, Z, W, V) = icext(W, y(Z, W, V)).
% 0.17/0.40 Axiom 11 (rdfs_cext_def): fresh2(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X).
% 0.17/0.40 Axiom 12 (owl_restrict_somevaluesfrom_2): fresh11(X, X, Y, Z, W, V) = fresh12(iext(uri_owl_someValuesFrom, Y, W), true2, Z, W, V).
% 0.17/0.40 Axiom 13 (owl_restrict_somevaluesfrom_1): fresh9(X, X, Y, Z, W, V) = fresh10(iext(uri_owl_someValuesFrom, Y, W), true2, Z, W, V).
% 0.17/0.40 Axiom 14 (owl_restrict_somevaluesfrom_1): fresh9(icext(X, Y), true2, X, Z, W, Y) = fresh4(iext(uri_owl_onProperty, X, Z), true2, X, Z, W, Y).
% 0.17/0.40 Axiom 15 (owl_restrict_somevaluesfrom_2): fresh11(icext(X, Y), true2, X, Z, W, Y) = fresh3(iext(uri_owl_onProperty, X, Z), true2, X, Z, W, Y).
% 0.17/0.40
% 0.17/0.40 Lemma 16: icext(bnode_z, uri_ex_s) = true2.
% 0.17/0.40 Proof:
% 0.17/0.40 icext(bnode_z, uri_ex_s)
% 0.17/0.40 = { by axiom 11 (rdfs_cext_def) R->L }
% 0.17/0.40 fresh2(iext(uri_rdf_type, uri_ex_s, bnode_z), true2, uri_ex_s, bnode_z)
% 0.17/0.40 = { by axiom 1 (testcase_premise_fullish_009_Existential_Restriction_Entailments_1) }
% 0.17/0.40 fresh2(true2, true2, uri_ex_s, bnode_z)
% 0.17/0.40 = { by axiom 5 (rdfs_cext_def) }
% 0.17/0.40 true2
% 0.17/0.40
% 0.17/0.40 Goal 1 (testcase_conclusion_fullish_009_Existential_Restriction_Entailments): tuple(iext(uri_rdf_type, X, uri_ex_c), iext(uri_ex_p, uri_ex_s, X)) = tuple(true2, true2).
% 0.17/0.40 The goal is true when:
% 0.17/0.40 X = y(uri_ex_p, uri_ex_c, uri_ex_s)
% 0.17/0.40
% 0.17/0.40 Proof:
% 0.17/0.40 tuple(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)))
% 0.17/0.40 = { by axiom 8 (rdfs_cext_def_1) R->L }
% 0.17/0.40 tuple(fresh(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)))
% 0.17/0.40 = { by axiom 10 (owl_restrict_somevaluesfrom_2) R->L }
% 0.17/0.40 tuple(fresh(fresh3(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)))
% 0.17/0.40 = { by axiom 3 (testcase_premise_fullish_009_Existential_Restriction_Entailments_5) R->L }
% 0.17/0.41 tuple(fresh(fresh3(iext(uri_owl_onProperty, bnode_z, uri_ex_p), 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)))
% 0.17/0.41 = { by axiom 15 (owl_restrict_somevaluesfrom_2) R->L }
% 0.17/0.41 tuple(fresh(fresh11(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)))
% 0.17/0.41 = { by lemma 16 }
% 0.17/0.41 tuple(fresh(fresh11(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)))
% 0.17/0.41 = { by axiom 12 (owl_restrict_somevaluesfrom_2) }
% 0.17/0.41 tuple(fresh(fresh12(iext(uri_owl_someValuesFrom, bnode_z, uri_ex_c), 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)))
% 0.17/0.41 = { by axiom 2 (testcase_premise_fullish_009_Existential_Restriction_Entailments_4) }
% 0.17/0.41 tuple(fresh(fresh12(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)))
% 0.17/0.41 = { by axiom 6 (owl_restrict_somevaluesfrom_2) }
% 0.17/0.41 tuple(fresh(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)))
% 0.17/0.41 = { by axiom 4 (rdfs_cext_def_1) }
% 0.17/0.41 tuple(true2, iext(uri_ex_p, uri_ex_s, y(uri_ex_p, uri_ex_c, uri_ex_s)))
% 0.17/0.41 = { by axiom 9 (owl_restrict_somevaluesfrom_1) R->L }
% 0.17/0.41 tuple(true2, fresh4(true2, true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 0.17/0.41 = { by axiom 3 (testcase_premise_fullish_009_Existential_Restriction_Entailments_5) R->L }
% 0.17/0.41 tuple(true2, fresh4(iext(uri_owl_onProperty, bnode_z, uri_ex_p), true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 0.17/0.41 = { by axiom 14 (owl_restrict_somevaluesfrom_1) R->L }
% 0.17/0.41 tuple(true2, fresh9(icext(bnode_z, uri_ex_s), true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 0.17/0.41 = { by lemma 16 }
% 0.17/0.41 tuple(true2, fresh9(true2, true2, bnode_z, uri_ex_p, uri_ex_c, uri_ex_s))
% 0.17/0.41 = { by axiom 13 (owl_restrict_somevaluesfrom_1) }
% 0.17/0.41 tuple(true2, fresh10(iext(uri_owl_someValuesFrom, bnode_z, uri_ex_c), true2, uri_ex_p, uri_ex_c, uri_ex_s))
% 0.17/0.41 = { by axiom 2 (testcase_premise_fullish_009_Existential_Restriction_Entailments_4) }
% 0.17/0.41 tuple(true2, fresh10(true2, true2, uri_ex_p, uri_ex_c, uri_ex_s))
% 0.17/0.41 = { by axiom 7 (owl_restrict_somevaluesfrom_1) }
% 0.17/0.41 tuple(true2, true2)
% 0.17/0.41 % SZS output end Proof
% 0.17/0.41
% 0.17/0.41 RESULT: Theorem (the conjecture is true).
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