TSTP Solution File: SWB023+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB023+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 : n019.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 20:12:55 EDT 2023
% Result : Theorem 0.19s 0.43s
% 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
% 0.00/0.12 % Problem : SWB023+2 : 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
% 0.13/0.34 % Computer : n019.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 06:35:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.43 Command-line arguments: --no-flatten-goal
% 0.19/0.43
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Take the following subset of the input axioms:
% 0.19/0.44 fof(owl_char_functional, axiom, ![P]: (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X, Y1, Y2]: ((iext(P, X, Y1) & iext(P, X, Y2)) => Y1=Y2)))).
% 0.19/0.44 fof(owl_enum_class_001, axiom, ![Z, S1, A1]: ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X2]: (icext(Z, X2) <=> X2=A1))))).
% 0.19/0.44 fof(owl_eqdis_sameas, axiom, ![Y, X2]: (iext(uri_owl_sameAs, X2, Y) <=> X2=Y)).
% 0.19/0.44 fof(rdfs_cext_def, axiom, ![C, X2]: (iext(uri_rdf_type, X2, C) <=> icext(C, X2))).
% 0.19/0.44 fof(testcase_conclusion_fullish_023_Unique_List_Components, conjecture, iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)).
% 0.19/0.44 fof(testcase_premise_fullish_023_Unique_List_Components, axiom, ?[BNODE_o, BNODE_l]: (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & (iext(uri_rdf_type, uri_ex_w, BNODE_o) & (iext(uri_rdf_type, BNODE_o, uri_owl_Class) & (iext(uri_owl_oneOf, BNODE_o, BNODE_l) & (iext(uri_rdf_first, BNODE_l, uri_ex_u) & (iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)))))))).
% 0.19/0.44
% 0.19/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.44 fresh(y, y, x1...xn) = u
% 0.19/0.44 C => fresh(s, t, x1...xn) = v
% 0.19/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.44 variables of u and v.
% 0.19/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.44 input problem has no model of domain size 1).
% 0.19/0.44
% 0.19/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.44
% 0.19/0.44 Axiom 1 (owl_eqdis_sameas): iext(uri_owl_sameAs, X, X) = true.
% 0.19/0.44 Axiom 2 (testcase_premise_fullish_023_Unique_List_Components_1): iext(uri_rdf_type, uri_ex_w, bnode_o) = true.
% 0.19/0.44 Axiom 3 (testcase_premise_fullish_023_Unique_List_Components): iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) = true.
% 0.19/0.44 Axiom 4 (testcase_premise_fullish_023_Unique_List_Components_5): iext(uri_rdf_rest, bnode_l, uri_rdf_nil) = true.
% 0.19/0.44 Axiom 5 (testcase_premise_fullish_023_Unique_List_Components_6): iext(uri_owl_oneOf, bnode_o, bnode_l) = true.
% 0.19/0.44 Axiom 6 (testcase_premise_fullish_023_Unique_List_Components_3): iext(uri_rdf_first, bnode_l, uri_ex_u) = true.
% 0.19/0.44 Axiom 7 (testcase_premise_fullish_023_Unique_List_Components_4): iext(uri_rdf_first, bnode_l, uri_ex_v) = true.
% 0.19/0.44 Axiom 8 (owl_enum_class_001_3): fresh24(X, X, Y, Z) = Y.
% 0.19/0.44 Axiom 9 (owl_char_functional_1): fresh11(X, X, Y, Z) = Z.
% 0.19/0.44 Axiom 10 (rdfs_cext_def): fresh4(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 11 (owl_enum_class_001_3): fresh22(X, X, Y, Z, W) = W.
% 0.19/0.44 Axiom 12 (owl_char_functional_1): fresh2(X, X, Y, Z, W, V) = W.
% 0.19/0.44 Axiom 13 (owl_enum_class_001_3): fresh23(X, X, Y, Z, W) = fresh24(iext(uri_rdf_first, Y, Z), true, Z, W).
% 0.19/0.44 Axiom 14 (owl_char_functional_1): fresh10(X, X, Y, Z, W, V) = fresh11(iext(Y, Z, W), true, W, V).
% 0.19/0.44 Axiom 15 (rdfs_cext_def): fresh4(iext(uri_rdf_type, X, Y), true, X, Y) = icext(Y, X).
% 0.19/0.44 Axiom 16 (owl_enum_class_001_3): fresh21(X, X, Y, Z, W, V) = fresh22(iext(uri_rdf_rest, Z, uri_rdf_nil), true, Z, W, V).
% 0.19/0.44 Axiom 17 (owl_enum_class_001_3): fresh21(icext(X, Y), true, X, Z, W, Y) = fresh23(iext(uri_owl_oneOf, X, Z), true, Z, W, Y).
% 0.19/0.44 Axiom 18 (owl_char_functional_1): fresh10(icext(uri_owl_FunctionalProperty, X), true, X, Y, Z, W) = fresh2(iext(X, Y, W), true, X, Y, Z, W).
% 0.19/0.44
% 0.19/0.44 Lemma 19: uri_ex_w = uri_ex_u.
% 0.19/0.44 Proof:
% 0.19/0.44 uri_ex_w
% 0.19/0.44 = { by axiom 11 (owl_enum_class_001_3) R->L }
% 0.19/0.44 fresh22(true, true, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 4 (testcase_premise_fullish_023_Unique_List_Components_5) R->L }
% 0.19/0.44 fresh22(iext(uri_rdf_rest, bnode_l, uri_rdf_nil), true, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 16 (owl_enum_class_001_3) R->L }
% 0.19/0.44 fresh21(true, true, bnode_o, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 10 (rdfs_cext_def) R->L }
% 0.19/0.44 fresh21(fresh4(true, true, uri_ex_w, bnode_o), true, bnode_o, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 2 (testcase_premise_fullish_023_Unique_List_Components_1) R->L }
% 0.19/0.44 fresh21(fresh4(iext(uri_rdf_type, uri_ex_w, bnode_o), true, uri_ex_w, bnode_o), true, bnode_o, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 15 (rdfs_cext_def) }
% 0.19/0.44 fresh21(icext(bnode_o, uri_ex_w), true, bnode_o, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 17 (owl_enum_class_001_3) }
% 0.19/0.44 fresh23(iext(uri_owl_oneOf, bnode_o, bnode_l), true, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 5 (testcase_premise_fullish_023_Unique_List_Components_6) }
% 0.19/0.44 fresh23(true, true, bnode_l, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 13 (owl_enum_class_001_3) }
% 0.19/0.44 fresh24(iext(uri_rdf_first, bnode_l, uri_ex_u), true, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 6 (testcase_premise_fullish_023_Unique_List_Components_3) }
% 0.19/0.44 fresh24(true, true, uri_ex_u, uri_ex_w)
% 0.19/0.44 = { by axiom 8 (owl_enum_class_001_3) }
% 0.19/0.44 uri_ex_u
% 0.19/0.44
% 0.19/0.44 Goal 1 (testcase_conclusion_fullish_023_Unique_List_Components): tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)) = tuple(true, true).
% 0.19/0.44 Proof:
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))
% 0.19/0.44 = { by axiom 12 (owl_char_functional_1) R->L }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh2(true, true, uri_rdf_first, bnode_l, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 6 (testcase_premise_fullish_023_Unique_List_Components_3) R->L }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh2(iext(uri_rdf_first, bnode_l, uri_ex_u), true, uri_rdf_first, bnode_l, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 18 (owl_char_functional_1) R->L }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh10(icext(uri_owl_FunctionalProperty, uri_rdf_first), true, uri_rdf_first, bnode_l, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 15 (rdfs_cext_def) R->L }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh10(fresh4(iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty), true, uri_rdf_first, uri_owl_FunctionalProperty), true, uri_rdf_first, bnode_l, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 3 (testcase_premise_fullish_023_Unique_List_Components) }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh10(fresh4(true, true, uri_rdf_first, uri_owl_FunctionalProperty), true, uri_rdf_first, bnode_l, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 10 (rdfs_cext_def) }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh10(true, true, uri_rdf_first, bnode_l, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 14 (owl_char_functional_1) }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh11(iext(uri_rdf_first, bnode_l, uri_ex_v), true, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 7 (testcase_premise_fullish_023_Unique_List_Components_4) }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, fresh11(true, true, uri_ex_v, uri_ex_u)))
% 0.19/0.44 = { by axiom 9 (owl_char_functional_1) }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, uri_ex_u))
% 0.19/0.44 = { by lemma 19 }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_u, uri_ex_u), iext(uri_owl_sameAs, uri_ex_w, uri_ex_u))
% 0.19/0.44 = { by lemma 19 }
% 0.19/0.44 tuple(iext(uri_owl_sameAs, uri_ex_u, uri_ex_u), iext(uri_owl_sameAs, uri_ex_u, uri_ex_u))
% 0.19/0.44 = { by axiom 1 (owl_eqdis_sameas) }
% 0.19/0.44 tuple(true, iext(uri_owl_sameAs, uri_ex_u, uri_ex_u))
% 0.19/0.44 = { by axiom 1 (owl_eqdis_sameas) }
% 0.19/0.44 tuple(true, true)
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Theorem (the conjecture is true).
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