TSTP Solution File: SWB008+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWB008+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 : n006.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 20:12:45 EDT 2023
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB008+2 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % 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 : n006.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 06:26:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.39 Command-line arguments: --no-flatten-goal
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(owl_char_inversefunctional, axiom, ![P]: (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![Y, X1, X2]: ((iext(P, X1, Y) & iext(P, X2, Y)) => X1=X2)))).
% 0.19/0.40 fof(owl_eqdis_sameas, axiom, ![X, Y2]: (iext(uri_owl_sameAs, X, Y2) <=> X=Y2)).
% 0.19/0.40 fof(rdfs_cext_def, axiom, ![C, X3]: (iext(uri_rdf_type, X3, C) <=> icext(C, X3))).
% 0.19/0.40 fof(testcase_conclusion_fullish_008_Inverse_Functional_Data_Properties, conjecture, iext(uri_owl_sameAs, uri_ex_bob, uri_ex_robert)).
% 0.19/0.40 fof(testcase_premise_fullish_008_Inverse_Functional_Data_Properties, axiom, iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_DatatypeProperty) & (iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty) & (iext(uri_foaf_mbox_sha1sum, uri_ex_bob, literal_plain(dat_str_xyz)) & iext(uri_foaf_mbox_sha1sum, uri_ex_robert, literal_plain(dat_str_xyz))))).
% 0.19/0.40
% 0.19/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.40 fresh(y, y, x1...xn) = u
% 0.19/0.40 C => fresh(s, t, x1...xn) = v
% 0.19/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.40 variables of u and v.
% 0.19/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.40 input problem has no model of domain size 1).
% 0.19/0.40
% 0.19/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.40
% 0.19/0.40 Axiom 1 (owl_eqdis_sameas): iext(uri_owl_sameAs, X, X) = true.
% 0.19/0.40 Axiom 2 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties): iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty) = true.
% 0.19/0.40 Axiom 3 (owl_char_inversefunctional_1): fresh9(X, X, Y, Z) = Z.
% 0.19/0.40 Axiom 4 (rdfs_cext_def): fresh4(X, X, Y, Z) = true.
% 0.19/0.40 Axiom 5 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_2): iext(uri_foaf_mbox_sha1sum, uri_ex_bob, literal_plain(dat_str_xyz)) = true.
% 0.19/0.40 Axiom 6 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_3): iext(uri_foaf_mbox_sha1sum, uri_ex_robert, literal_plain(dat_str_xyz)) = true.
% 0.19/0.40 Axiom 7 (owl_char_inversefunctional_1): fresh2(X, X, Y, Z, W, V) = Z.
% 0.19/0.40 Axiom 8 (owl_char_inversefunctional_1): fresh8(X, X, Y, Z, W, V) = fresh9(iext(Y, Z, V), true, Z, W).
% 0.19/0.40 Axiom 9 (rdfs_cext_def): fresh4(iext(uri_rdf_type, X, Y), true, X, Y) = icext(Y, X).
% 0.19/0.40 Axiom 10 (owl_char_inversefunctional_1): fresh8(icext(uri_owl_InverseFunctionalProperty, X), true, X, Y, Z, W) = fresh2(iext(X, Z, W), true, X, Y, Z, W).
% 0.19/0.40
% 0.19/0.40 Goal 1 (testcase_conclusion_fullish_008_Inverse_Functional_Data_Properties): iext(uri_owl_sameAs, uri_ex_bob, uri_ex_robert) = true.
% 0.19/0.40 Proof:
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, uri_ex_robert)
% 0.19/0.40 = { by axiom 7 (owl_char_inversefunctional_1) R->L }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh2(true, true, uri_foaf_mbox_sha1sum, uri_ex_robert, uri_ex_bob, literal_plain(dat_str_xyz)))
% 0.19/0.40 = { by axiom 5 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_2) R->L }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh2(iext(uri_foaf_mbox_sha1sum, uri_ex_bob, literal_plain(dat_str_xyz)), true, uri_foaf_mbox_sha1sum, uri_ex_robert, uri_ex_bob, literal_plain(dat_str_xyz)))
% 0.19/0.40 = { by axiom 10 (owl_char_inversefunctional_1) R->L }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh8(icext(uri_owl_InverseFunctionalProperty, uri_foaf_mbox_sha1sum), true, uri_foaf_mbox_sha1sum, uri_ex_robert, uri_ex_bob, literal_plain(dat_str_xyz)))
% 0.19/0.40 = { by axiom 9 (rdfs_cext_def) R->L }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh8(fresh4(iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty), true, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty), true, uri_foaf_mbox_sha1sum, uri_ex_robert, uri_ex_bob, literal_plain(dat_str_xyz)))
% 0.19/0.40 = { by axiom 2 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties) }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh8(fresh4(true, true, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty), true, uri_foaf_mbox_sha1sum, uri_ex_robert, uri_ex_bob, literal_plain(dat_str_xyz)))
% 0.19/0.40 = { by axiom 4 (rdfs_cext_def) }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh8(true, true, uri_foaf_mbox_sha1sum, uri_ex_robert, uri_ex_bob, literal_plain(dat_str_xyz)))
% 0.19/0.40 = { by axiom 8 (owl_char_inversefunctional_1) }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh9(iext(uri_foaf_mbox_sha1sum, uri_ex_robert, literal_plain(dat_str_xyz)), true, uri_ex_robert, uri_ex_bob))
% 0.19/0.40 = { by axiom 6 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_3) }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, fresh9(true, true, uri_ex_robert, uri_ex_bob))
% 0.19/0.40 = { by axiom 3 (owl_char_inversefunctional_1) }
% 0.19/0.40 iext(uri_owl_sameAs, uri_ex_bob, uri_ex_bob)
% 0.19/0.40 = { by axiom 1 (owl_eqdis_sameas) }
% 0.19/0.40 true
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Theorem (the conjecture is true).
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