TSTP Solution File: SWB002+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB002+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 : n014.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 20:12:40 EDT 2023
% Result : Theorem 87.71s 11.62s
% Output : Proof 87.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB002+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 06:19:16 EDT 2023
% 0.12/0.34 % CPUTime :
% 87.71/11.62 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 87.71/11.62
% 87.71/11.62 % SZS status Theorem
% 87.71/11.62
% 87.71/11.62 % SZS output start Proof
% 87.71/11.62 Take the following subset of the input axioms:
% 87.71/11.66 fof(owl_bool_complementof_class, axiom, ![C, Z]: (iext(uri_owl_complementOf, Z, C) => (ic(Z) & (ic(C) & ![X]: (icext(Z, X) <=> ~icext(C, X)))))).
% 87.71/11.66 fof(owl_bool_datatypecomplementof, axiom, ![D, Z2]: (iext(uri_owl_datatypeComplementOf, Z2, D) => ![X2]: (icext(Z2, X2) <=> (lv(X2) & ~icext(D, X2))))).
% 87.71/11.66 fof(owl_bool_unionof_class_000, axiom, ![Z2]: (iext(uri_owl_unionOf, Z2, uri_rdf_nil) <=> (ic(Z2) & ![X2]: ~icext(Z2, X2)))).
% 87.71/11.66 fof(owl_char_asymmetric, axiom, ![P]: (icext(uri_owl_AsymmetricProperty, P) <=> (ip(P) & ![Y, X2]: (iext(P, X2, Y) => ~iext(P, Y, X2))))).
% 87.71/11.66 fof(owl_char_irreflexive, axiom, ![P4]: (icext(uri_owl_IrreflexiveReflexiveProperty, P4) <=> (ip(P4) & ![X2]: ~iext(P4, X2, X2)))).
% 87.71/11.66 fof(owl_class_nothing_ext, axiom, ![X2]: ~icext(uri_owl_Nothing, X2)).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_base64binary, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_xsd_base64Binary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_boolean, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_xsd_boolean, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_datetime, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_xsd_dateTime, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_double, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_xsd_double, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_float, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_xsd_float, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_hexbinary, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_xsd_hexBinary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_real, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_anyuri_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_anyURI, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_boolean, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_xsd_boolean, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_datetime, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_xsd_dateTime, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_double, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_xsd_double, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_float, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_xsd_float, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_hexbinary, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_xsd_hexBinary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_real, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_base64binary_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_base64Binary, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_datetime, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_xsd_dateTime, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_double, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_xsd_double, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_float, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_xsd_float, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_hexbinary, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_xsd_hexBinary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_real, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_boolean_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_boolean, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_datetime_double, axiom, ![X2]: ~(icext(uri_xsd_dateTime, X2) & icext(uri_xsd_double, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_datetime_float, axiom, ![X2]: ~(icext(uri_xsd_dateTime, X2) & icext(uri_xsd_float, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_datetime_hexbinary, axiom, ![X2]: ~(icext(uri_xsd_dateTime, X2) & icext(uri_xsd_hexBinary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_datetime_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_dateTime, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_datetime_real, axiom, ![X2]: ~(icext(uri_xsd_dateTime, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_datetime_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_dateTime, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_double_float, axiom, ![X2]: ~(icext(uri_xsd_double, X2) & icext(uri_xsd_float, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_double_hexbinary, axiom, ![X2]: ~(icext(uri_xsd_double, X2) & icext(uri_xsd_hexBinary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_double_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_double, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_double_real, axiom, ![X2]: ~(icext(uri_xsd_double, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_double_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_double, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_float_hexbinary, axiom, ![X2]: ~(icext(uri_xsd_float, X2) & icext(uri_xsd_hexBinary, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_float_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_float, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_float_real, axiom, ![X2]: ~(icext(uri_xsd_float, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_float_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_float, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_hexbinary_plainliteral, axiom, ![X2]: ~(icext(uri_xsd_hexBinary, X2) & icext(uri_rdf_PlainLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_hexbinary_real, axiom, ![X2]: ~(icext(uri_xsd_hexBinary, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_hexbinary_xmlliteral, axiom, ![X2]: ~(icext(uri_xsd_hexBinary, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_plainliteral_real, axiom, ![X2]: ~(icext(uri_rdf_PlainLiteral, X2) & icext(uri_owl_real, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_plainliteral_xmlliteral, axiom, ![X2]: ~(icext(uri_rdf_PlainLiteral, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_dat_dtype_relation_disjoint_real_xmlliteral, axiom, ![X2]: ~(icext(uri_owl_real, X2) & icext(uri_rdf_XMLLiteral, X2))).
% 87.71/11.66 fof(owl_enum_class_000, axiom, ![Z2]: (iext(uri_owl_oneOf, Z2, uri_rdf_nil) <=> (ic(Z2) & ![X2]: ~icext(Z2, X2)))).
% 87.71/11.66 fof(owl_eqdis_differentfrom, axiom, ![X2, Y5]: (iext(uri_owl_differentFrom, X2, Y5) <=> X2!=Y5)).
% 87.71/11.66 fof(owl_eqdis_disjointunionof_000, axiom, ![C4]: (iext(uri_owl_disjointUnionOf, C4, uri_rdf_nil) <=> (ic(C4) & ![X2]: ~icext(C4, X2)))).
% 87.71/11.66 fof(owl_eqdis_disjointunionof_002, axiom, ![S1, C1, S2, C2, C4]: ((iext(uri_rdf_first, S1, C1) & (iext(uri_rdf_rest, S1, S2) & (iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))) => (iext(uri_owl_disjointUnionOf, C4, S1) <=> (ic(C4) & (ic(C1) & (ic(C2) & ![X2]: (icext(C4, X2) <=> ((icext(C1, X2) | icext(C2, X2)) & ~(icext(C1, X2) & icext(C2, X2)))))))))).
% 87.71/11.66 fof(owl_eqdis_disjointunionof_003, axiom, ![S3, C3, C4, S1_2, S2_2, C1_2, C2_2]: ((iext(uri_rdf_first, S1_2, C1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, C2_2) & (iext(uri_rdf_rest, S2_2, S3) & (iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))))) => (iext(uri_owl_disjointUnionOf, C4, S1_2) <=> (ic(C4) & (ic(C1_2) & (ic(C2_2) & (ic(C3) & ![X2]: (icext(C4, X2) <=> ((icext(C1_2, X2) | (icext(C2_2, X2) | icext(C3, X2))) & (~(icext(C1_2, X2) & icext(C2_2, X2)) & (~(icext(C1_2, X2) & icext(C3, X2)) & ~(icext(C2_2, X2) & icext(C3, X2))))))))))))).
% 87.71/11.66 fof(owl_eqdis_disjointwith, axiom, ![C1_2, C2_2]: (iext(uri_owl_disjointWith, C1_2, C2_2) <=> (ic(C1_2) & (ic(C2_2) & ![X2]: ~(icext(C1_2, X2) & icext(C2_2, X2)))))).
% 87.71/11.66 fof(owl_eqdis_propertydisjointwith, axiom, ![P1, P2]: (iext(uri_owl_propertyDisjointWith, P1, P2) <=> (ip(P1) & (ip(P2) & ![X2, Y5]: ~(iext(P1, X2, Y5) & iext(P2, X2, Y5)))))).
% 87.71/11.66 fof(owl_ndis_alldifferent_distinctmembers_if_002, axiom, ![A1, A2, Z2, S1_2, S2_2]: ((iext(uri_rdf_first, S1_2, A1) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, A2) & (iext(uri_rdf_rest, S2_2, uri_rdf_nil) & (icext(uri_owl_AllDifferent, Z2) & iext(uri_owl_distinctMembers, Z2, S1_2)))))) => A1!=A2)).
% 87.71/11.66 fof(owl_ndis_alldifferent_distinctmembers_if_003, axiom, ![A3, Z2, A1_2, A2_2, S1_2, S2_2, S3_2]: ((iext(uri_rdf_first, S1_2, A1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, A2_2) & (iext(uri_rdf_rest, S2_2, S3_2) & (iext(uri_rdf_first, S3_2, A3) & (iext(uri_rdf_rest, S3_2, uri_rdf_nil) & (icext(uri_owl_AllDifferent, Z2) & iext(uri_owl_distinctMembers, Z2, S1_2)))))))) => (A1_2!=A2_2 & (A1_2!=A3 & A2_2!=A3)))).
% 87.71/11.66 fof(owl_ndis_alldifferent_members_if_002, axiom, ![Z2, A1_2, A2_2, S1_2, S2_2]: ((iext(uri_rdf_first, S1_2, A1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, A2_2) & (iext(uri_rdf_rest, S2_2, uri_rdf_nil) & (icext(uri_owl_AllDifferent, Z2) & iext(uri_owl_members, Z2, S1_2)))))) => A1_2!=A2_2)).
% 87.71/11.66 fof(owl_ndis_alldifferent_members_if_003, axiom, ![Z2, A1_2, A2_2, S1_2, S2_2, S3_2, A3_2]: ((iext(uri_rdf_first, S1_2, A1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, A2_2) & (iext(uri_rdf_rest, S2_2, S3_2) & (iext(uri_rdf_first, S3_2, A3_2) & (iext(uri_rdf_rest, S3_2, uri_rdf_nil) & (icext(uri_owl_AllDifferent, Z2) & iext(uri_owl_members, Z2, S1_2)))))))) => (A1_2!=A2_2 & (A1_2!=A3_2 & A2_2!=A3_2)))).
% 87.71/11.66 fof(owl_ndis_alldisjointclasses_if_002, axiom, ![Z2, S1_2, S2_2, C1_2, C2_2]: ((iext(uri_rdf_first, S1_2, C1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, C2_2) & (iext(uri_rdf_rest, S2_2, uri_rdf_nil) & (icext(uri_owl_AllDisjointClasses, Z2) & iext(uri_owl_members, Z2, S1_2)))))) => ![X2]: ~(icext(C1_2, X2) & icext(C2_2, X2)))).
% 87.71/11.66 fof(owl_ndis_alldisjointclasses_if_003, axiom, ![Z2, S1_2, S2_2, S3_2, C1_2, C2_2, C3_2]: ((iext(uri_rdf_first, S1_2, C1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, C2_2) & (iext(uri_rdf_rest, S2_2, S3_2) & (iext(uri_rdf_first, S3_2, C3_2) & (iext(uri_rdf_rest, S3_2, uri_rdf_nil) & (icext(uri_owl_AllDisjointClasses, Z2) & iext(uri_owl_members, Z2, S1_2)))))))) => (![X2]: ~(icext(C1_2, X2) & icext(C2_2, X2)) & (![X2]: ~(icext(C1_2, X2) & icext(C3_2, X2)) & ![X2]: ~(icext(C2_2, X2) & icext(C3_2, X2)))))).
% 87.71/11.66 fof(owl_ndis_alldisjointproperties_if_002, axiom, ![Z2, S1_2, S2_2, P1_2, P2_2]: ((iext(uri_rdf_first, S1_2, P1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, P2_2) & (iext(uri_rdf_rest, S2_2, uri_rdf_nil) & (icext(uri_owl_AllDisjointProperties, Z2) & iext(uri_owl_members, Z2, S1_2)))))) => ![X2, Y5]: ~(iext(P1_2, X2, Y5) & iext(P2_2, X2, Y5)))).
% 87.71/11.66 fof(owl_ndis_alldisjointproperties_if_003, axiom, ![P3, Z2, S1_2, S2_2, S3_2, P1_2, P2_2]: ((iext(uri_rdf_first, S1_2, P1_2) & (iext(uri_rdf_rest, S1_2, S2_2) & (iext(uri_rdf_first, S2_2, P2_2) & (iext(uri_rdf_rest, S2_2, S3_2) & (iext(uri_rdf_first, S3_2, P3) & (iext(uri_rdf_rest, S3_2, uri_rdf_nil) & (icext(uri_owl_AllDisjointProperties, Z2) & iext(uri_owl_members, Z2, S1_2)))))))) => (![X2, Y5]: ~(iext(P1_2, X2, Y5) & iext(P2_2, X2, Y5)) & (![X2, Y5]: ~(iext(P1_2, X2, Y5) & iext(P3, X2, Y5)) & ![X2, Y5]: ~(iext(P2_2, X2, Y5) & iext(P3, X2, Y5)))))).
% 87.71/11.66 fof(owl_npa_data_if, axiom, ![V, Z2, P4, A2_2]: ((iext(uri_owl_sourceIndividual, Z2, A2_2) & (iext(uri_owl_assertionProperty, Z2, P4) & iext(uri_owl_targetValue, Z2, V))) => (iodp(P4) & ~iext(P4, A2_2, V)))).
% 87.71/11.66 fof(owl_npa_object_if, axiom, ![Z2, P4, A1_2, A2_2]: ((iext(uri_owl_sourceIndividual, Z2, A1_2) & (iext(uri_owl_assertionProperty, Z2, P4) & iext(uri_owl_targetIndividual, Z2, A2_2))) => ~iext(P4, A1_2, A2_2))).
% 87.71/11.66 fof(owl_prop_bottomdataproperty_ext, axiom, ![X2, Y5]: ~iext(uri_owl_bottomDataProperty, X2, Y5)).
% 87.71/11.66 fof(owl_prop_bottomobjectproperty_ext, axiom, ![X2, Y5]: ~iext(uri_owl_bottomObjectProperty, X2, Y5)).
% 87.71/11.66 fof(owl_restrict_exactcard_000, axiom, ![Z2, P4]: ((iext(uri_owl_cardinality, Z2, literal_typed(dat_str_0, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P4)) => ![X2]: (icext(Z2, X2) <=> ~?[Y5]: iext(P4, X2, Y5)))).
% 87.71/11.66 fof(owl_restrict_exactcard_002, axiom, ![Z2, P4]: ((iext(uri_owl_cardinality, Z2, literal_typed(dat_str_2, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P4)) => ![X2]: (icext(Z2, X2) <=> (?[Y1, Y2]: (iext(P4, X2, Y1) & (iext(P4, X2, Y2) & Y1!=Y2)) & ![Y3, Y1_2, Y2_2]: ((iext(P4, X2, Y1_2) & (iext(P4, X2, Y2_2) & iext(P4, X2, Y3))) => (Y3=Y1_2 | Y3=Y2_2)))))).
% 87.71/11.66 fof(owl_restrict_exactcard_003, axiom, ![Z2, P4]: ((iext(uri_owl_cardinality, Z2, literal_typed(dat_str_3, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P4)) => ![X2]: (icext(Z2, X2) <=> (?[Y1_2, Y2_2, Y3_2]: (iext(P4, X2, Y1_2) & (iext(P4, X2, Y2_2) & (iext(P4, X2, Y3_2) & (Y1_2!=Y2_2 & (Y1_2!=Y3_2 & Y2_2!=Y3_2))))) & ![Y4, Y1_2, Y2_2, Y3_2]: ((iext(P4, X2, Y1_2) & (iext(P4, X2, Y2_2) & (iext(P4, X2, Y3_2) & iext(P4, X2, Y4)))) => (Y4=Y1_2 | (Y4=Y2_2 | Y4=Y3_2))))))).
% 87.71/11.66 fof(owl_restrict_exactqcr_data_000, axiom, ![D2, Z2, P4]: ((iext(uri_owl_qualifiedCardinality, Z2, literal_typed(dat_str_0, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onDataRange, Z2, D2))) => (iodp(P4) & ![X2]: (icext(Z2, X2) <=> ~?[Y5]: (lv(Y5) & (iext(P4, X2, Y5) & icext(D2, Y5))))))).
% 87.71/11.66 fof(owl_restrict_exactqcr_data_002, axiom, ![D2, Z2, P4]: ((iext(uri_owl_qualifiedCardinality, Z2, literal_typed(dat_str_2, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onDataRange, Z2, D2))) => (iodp(P4) & ![X2]: (icext(Z2, X2) <=> (?[Y1_2, Y2_2]: (lv(Y1_2) & (iext(P4, X2, Y1_2) & (icext(D2, Y1_2) & (lv(Y2_2) & (iext(P4, X2, Y2_2) & (icext(D2, Y2_2) & Y1_2!=Y2_2)))))) & ![Y1_2, Y2_2, Y3_2]: ((lv(Y1_2) & (iext(P4, X2, Y1_2) & (icext(D2, Y1_2) & (lv(Y2_2) & (iext(P4, X2, Y2_2) & (icext(D2, Y2_2) & (lv(Y3_2) & (iext(P4, X2, Y3_2) & icext(D2, Y3_2))))))))) => (Y3_2=Y1_2 | Y3_2=Y2_2))))))).
% 87.71/11.67 fof(owl_restrict_exactqcr_data_003, axiom, ![D2, Z2, P4]: ((iext(uri_owl_qualifiedCardinality, Z2, literal_typed(dat_str_3, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onDataRange, Z2, D2))) => (iodp(P4) & ![X2]: (icext(Z2, X2) <=> (?[Y1_2, Y2_2, Y3_2]: (lv(Y1_2) & (iext(P4, X2, Y1_2) & (icext(D2, Y1_2) & (lv(Y2_2) & (iext(P4, X2, Y2_2) & (icext(D2, Y2_2) & (lv(Y3_2) & (iext(P4, X2, Y3_2) & (icext(D2, Y3_2) & (Y1_2!=Y2_2 & (Y1_2!=Y3_2 & Y2_2!=Y3_2))))))))))) & ![Y1_2, Y2_2, Y3_2, Y4_2]: ((lv(Y1_2) & (iext(P4, X2, Y1_2) & (icext(D2, Y1_2) & (lv(Y2_2) & (iext(P4, X2, Y2_2) & (icext(D2, Y2_2) & (lv(Y3_2) & (iext(P4, X2, Y3_2) & (icext(D2, Y3_2) & (lv(Y4_2) & (iext(P4, X2, Y4_2) & icext(D2, Y4_2)))))))))))) => (Y4_2=Y1_2 | (Y4_2=Y2_2 | Y4_2=Y3_2)))))))).
% 87.71/11.67 fof(owl_restrict_exactqcr_object_000, axiom, ![Z2, P4, C4]: ((iext(uri_owl_qualifiedCardinality, Z2, literal_typed(dat_str_0, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onClass, Z2, C4))) => ![X2]: (icext(Z2, X2) <=> ~?[Y5]: (iext(P4, X2, Y5) & icext(C4, Y5))))).
% 87.71/11.67 fof(owl_restrict_exactqcr_object_002, axiom, ![Z2, P4, C4]: ((iext(uri_owl_qualifiedCardinality, Z2, literal_typed(dat_str_2, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onClass, Z2, C4))) => ![X2]: (icext(Z2, X2) <=> (?[Y1_2, Y2_2]: (iext(P4, X2, Y1_2) & (icext(C4, Y1_2) & (iext(P4, X2, Y2_2) & (icext(C4, Y2_2) & Y1_2!=Y2_2)))) & ![Y1_2, Y2_2, Y3_2]: ((iext(P4, X2, Y1_2) & (icext(C4, Y1_2) & (iext(P4, X2, Y2_2) & (icext(C4, Y2_2) & (iext(P4, X2, Y3_2) & icext(C4, Y3_2)))))) => (Y3_2=Y1_2 | Y3_2=Y2_2)))))).
% 87.71/11.67 fof(owl_restrict_exactqcr_object_003, axiom, ![Z2, P4, C4]: ((iext(uri_owl_qualifiedCardinality, Z2, literal_typed(dat_str_3, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onClass, Z2, C4))) => ![X2]: (icext(Z2, X2) <=> (?[Y1_2, Y2_2, Y3_2]: (iext(P4, X2, Y1_2) & (icext(C4, Y1_2) & (iext(P4, X2, Y2_2) & (icext(C4, Y2_2) & (iext(P4, X2, Y3_2) & (icext(C4, Y3_2) & (Y1_2!=Y2_2 & (Y1_2!=Y3_2 & Y2_2!=Y3_2)))))))) & ![Y1_2, Y2_2, Y3_2, Y4_2]: ((iext(P4, X2, Y1_2) & (icext(C4, Y1_2) & (iext(P4, X2, Y2_2) & (icext(C4, Y2_2) & (iext(P4, X2, Y3_2) & (icext(C4, Y3_2) & (iext(P4, X2, Y4_2) & icext(C4, Y4_2)))))))) => (Y4_2=Y1_2 | (Y4_2=Y2_2 | Y4_2=Y3_2))))))).
% 87.71/11.67 fof(owl_restrict_maxcard_000, axiom, ![Z2, P4]: ((iext(uri_owl_maxCardinality, Z2, literal_typed(dat_str_0, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P4)) => ![X2]: (icext(Z2, X2) <=> ~?[Y5]: iext(P4, X2, Y5)))).
% 87.71/11.67 fof(owl_restrict_maxqcr_data_000, axiom, ![D2, Z2, P4]: ((iext(uri_owl_maxQualifiedCardinality, Z2, literal_typed(dat_str_0, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onDataRange, Z2, D2))) => (iodp(P4) & ![X2]: (icext(Z2, X2) <=> ~?[Y5]: (lv(Y5) & (iext(P4, X2, Y5) & icext(D2, Y5))))))).
% 87.71/11.67 fof(owl_restrict_maxqcr_object_000, axiom, ![Z2, P4, C4]: ((iext(uri_owl_maxQualifiedCardinality, Z2, literal_typed(dat_str_0, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onClass, Z2, C4))) => ![X2]: (icext(Z2, X2) <=> ~?[Y5]: (iext(P4, X2, Y5) & icext(C4, Y5))))).
% 87.71/11.67 fof(owl_restrict_mincard_002, axiom, ![Z2, P4]: ((iext(uri_owl_minCardinality, Z2, literal_typed(dat_str_2, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P4)) => ![X2]: (icext(Z2, X2) <=> ?[Y1_2, Y2_2]: (iext(P4, X2, Y1_2) & (iext(P4, X2, Y2_2) & Y1_2!=Y2_2))))).
% 87.71/11.67 fof(owl_restrict_mincard_003, axiom, ![Z2, P4]: ((iext(uri_owl_minCardinality, Z2, literal_typed(dat_str_3, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z2, P4)) => ![X2]: (icext(Z2, X2) <=> ?[Y1_2, Y2_2, Y3_2]: (iext(P4, X2, Y1_2) & (iext(P4, X2, Y2_2) & (iext(P4, X2, Y3_2) & (Y1_2!=Y2_2 & (Y1_2!=Y3_2 & Y2_2!=Y3_2)))))))).
% 87.71/11.67 fof(owl_restrict_minqcr_data_002, axiom, ![D2, Z2, P4]: ((iext(uri_owl_minQualifiedCardinality, Z2, literal_typed(dat_str_2, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onDataRange, Z2, D2))) => (iodp(P4) & ![X2]: (icext(Z2, X2) <=> ?[Y1_2, Y2_2]: (lv(Y1_2) & (iext(P4, X2, Y1_2) & (icext(D2, Y1_2) & (lv(Y2_2) & (iext(P4, X2, Y2_2) & (icext(D2, Y2_2) & Y1_2!=Y2_2)))))))))).
% 87.71/11.67 fof(owl_restrict_minqcr_data_003, axiom, ![D2, Z2, P4]: ((iext(uri_owl_minQualifiedCardinality, Z2, literal_typed(dat_str_3, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onDataRange, Z2, D2))) => (iodp(P4) & ![X2]: (icext(Z2, X2) <=> ?[Y1_2, Y2_2, Y3_2]: (lv(Y1_2) & (iext(P4, X2, Y1_2) & (icext(D2, Y1_2) & (lv(Y2_2) & (iext(P4, X2, Y2_2) & (icext(D2, Y2_2) & (lv(Y3_2) & (iext(P4, X2, Y3_2) & (icext(D2, Y3_2) & (Y1_2!=Y2_2 & (Y1_2!=Y3_2 & Y2_2!=Y3_2))))))))))))))).
% 87.71/11.67 fof(owl_restrict_minqcr_object_002, axiom, ![Z2, P4, C4]: ((iext(uri_owl_minQualifiedCardinality, Z2, literal_typed(dat_str_2, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onClass, Z2, C4))) => ![X2]: (icext(Z2, X2) <=> ?[Y1_2, Y2_2]: (iext(P4, X2, Y1_2) & (icext(C4, Y1_2) & (iext(P4, X2, Y2_2) & (icext(C4, Y2_2) & Y1_2!=Y2_2))))))).
% 87.71/11.67 fof(owl_restrict_minqcr_object_003, axiom, ![Z2, P4, C4]: ((iext(uri_owl_minQualifiedCardinality, Z2, literal_typed(dat_str_3, uri_xsd_nonNegativeInteger)) & (iext(uri_owl_onProperty, Z2, P4) & iext(uri_owl_onClass, Z2, C4))) => ![X2]: (icext(Z2, X2) <=> ?[Y1_2, Y2_2, Y3_2]: (iext(P4, X2, Y1_2) & (icext(C4, Y1_2) & (iext(P4, X2, Y2_2) & (icext(C4, Y2_2) & (iext(P4, X2, Y3_2) & (icext(C4, Y3_2) & (Y1_2!=Y2_2 & (Y1_2!=Y3_2 & Y2_2!=Y3_2))))))))))).
% 87.71/11.67 fof(testcase_conclusion_fullish_002_Existential_Blank_Nodes, conjecture, ?[BNODE_x, BNODE_y]: (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))).
% 87.71/11.67 fof(testcase_premise_fullish_002_Existential_Blank_Nodes, axiom, ?[BNODE_o]: (iext(uri_ex_p, uri_ex_s, BNODE_o) & iext(uri_ex_q, BNODE_o, uri_ex_s))).
% 87.71/11.67
% 87.71/11.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 87.71/11.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 87.71/11.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 87.71/11.67 fresh(y, y, x1...xn) = u
% 87.71/11.67 C => fresh(s, t, x1...xn) = v
% 87.71/11.67 where fresh is a fresh function symbol and x1..xn are the free
% 87.71/11.67 variables of u and v.
% 87.71/11.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 87.71/11.67 input problem has no model of domain size 1).
% 87.71/11.67
% 87.71/11.67 The encoding turns the above axioms into the following unit equations and goals:
% 87.71/11.67
% 87.71/11.67 Axiom 1 (testcase_premise_fullish_002_Existential_Blank_Nodes): iext(uri_ex_p, uri_ex_s, bnode_o) = true2.
% 87.71/11.67 Axiom 2 (testcase_premise_fullish_002_Existential_Blank_Nodes_1): iext(uri_ex_q, bnode_o, uri_ex_s) = true2.
% 87.71/11.67
% 87.71/11.67 Goal 1 (testcase_conclusion_fullish_002_Existential_Blank_Nodes): tuple7(iext(uri_ex_p, X, Y), iext(uri_ex_q, Y, X)) = tuple7(true2, true2).
% 87.71/11.67 The goal is true when:
% 87.71/11.67 X = uri_ex_s
% 87.71/11.67 Y = bnode_o
% 87.71/11.67
% 87.71/11.67 Proof:
% 87.71/11.67 tuple7(iext(uri_ex_p, uri_ex_s, bnode_o), iext(uri_ex_q, bnode_o, uri_ex_s))
% 87.71/11.67 = { by axiom 1 (testcase_premise_fullish_002_Existential_Blank_Nodes) }
% 87.71/11.67 tuple7(true2, iext(uri_ex_q, bnode_o, uri_ex_s))
% 87.71/11.67 = { by axiom 2 (testcase_premise_fullish_002_Existential_Blank_Nodes_1) }
% 87.71/11.67 tuple7(true2, true2)
% 87.71/11.67 % SZS output end Proof
% 87.71/11.67
% 87.71/11.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------