TSTP Solution File: SWB029+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB029+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 : n003.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 20:12:59 EDT 2023
% Result : Theorem 0.19s 0.49s
% 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 : SWB029+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 : n003.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 06:48:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.49 Command-line arguments: --no-flatten-goal
% 0.19/0.49
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Take the following subset of the input axioms:
% 0.19/0.50 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)))))).
% 0.19/0.50 fof(owl_bool_intersectionof_class_002, axiom, ![S1, C1, S2, C2, Z2]: ((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_intersectionOf, Z2, S1) <=> (ic(Z2) & (ic(C1) & (ic(C2) & ![X2]: (icext(Z2, X2) <=> (icext(C1, X2) & icext(C2, X2))))))))).
% 0.19/0.50 fof(rdfs_cext_def, axiom, ![X2, C3]: (iext(uri_rdf_type, X2, C3) <=> icext(C3, X2))).
% 0.19/0.50 fof(testcase_premise_fullish_029_Ex_Falso_Quodlibet, axiom, ?[BNODE_x, BNODE_y, BNODE_l1, BNODE_l2]: (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & (iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & (iext(uri_rdf_type, uri_ex_w, BNODE_x) & (iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & (iext(uri_rdf_first, BNODE_l1, uri_ex_A) & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & (iext(uri_rdf_first, BNODE_l2, BNODE_y) & (iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)))))))))).
% 0.19/0.50
% 0.19/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.50 fresh(y, y, x1...xn) = u
% 0.19/0.50 C => fresh(s, t, x1...xn) = v
% 0.19/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.50 variables of u and v.
% 0.19/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.50 input problem has no model of domain size 1).
% 0.19/0.50
% 0.19/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.50
% 0.19/0.50 Axiom 1 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_3): iext(uri_owl_complementOf, bnode_y, uri_ex_A) = true2.
% 0.19/0.50 Axiom 2 (testcase_premise_fullish_029_Ex_Falso_Quodlibet): iext(uri_rdf_type, uri_ex_w, bnode_x) = true2.
% 0.19/0.50 Axiom 3 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_8): iext(uri_owl_intersectionOf, bnode_x, bnode_l1) = true2.
% 0.19/0.50 Axiom 4 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_4): iext(uri_rdf_first, bnode_l1, uri_ex_A) = true2.
% 0.19/0.50 Axiom 5 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_5): iext(uri_rdf_first, bnode_l2, bnode_y) = true2.
% 0.19/0.50 Axiom 6 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_6): iext(uri_rdf_rest, bnode_l1, bnode_l2) = true2.
% 0.19/0.50 Axiom 7 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_7): iext(uri_rdf_rest, bnode_l2, uri_rdf_nil) = true2.
% 0.19/0.50 Axiom 8 (owl_bool_intersectionof_class_002_8): fresh4(X, X, Y, Z) = true2.
% 0.19/0.50 Axiom 9 (owl_bool_intersectionof_class_002_9): fresh3(X, X, Y, Z) = true2.
% 0.19/0.50 Axiom 10 (rdfs_cext_def): fresh2(X, X, Y, Z) = true2.
% 0.19/0.50 Axiom 11 (owl_bool_intersectionof_class_002_3): fresh29(X, X, Y, Z, W) = true2.
% 0.19/0.50 Axiom 12 (owl_bool_intersectionof_class_002_3): fresh27(X, X, Y, Z, W, V) = equiv(Z, W, V).
% 0.19/0.50 Axiom 13 (owl_bool_intersectionof_class_002_8): fresh4(equiv(X, Y, Z), true2, X, Z) = icext(X, Z).
% 0.19/0.50 Axiom 14 (owl_bool_intersectionof_class_002_9): fresh3(equiv(X, Y, Z), true2, Y, Z) = icext(Y, Z).
% 0.19/0.50 Axiom 15 (rdfs_cext_def): fresh2(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X).
% 0.19/0.50 Axiom 16 (owl_bool_intersectionof_class_002_3): fresh28(X, X, Y, Z, W, V, U) = fresh29(iext(uri_rdf_first, Y, Z), true2, Z, V, U).
% 0.19/0.50 Axiom 17 (owl_bool_intersectionof_class_002_3): fresh26(X, X, Y, Z, W, V, U) = fresh27(iext(uri_rdf_first, W, V), true2, Y, Z, V, U).
% 0.19/0.50 Axiom 18 (owl_bool_intersectionof_class_002_3): fresh25(X, X, Y, Z, W, V, U) = fresh28(iext(uri_rdf_rest, Y, W), true2, Y, Z, W, V, U).
% 0.19/0.50 Axiom 19 (owl_bool_intersectionof_class_002_3): fresh24(X, X, Y, Z, W, V, U, T) = fresh26(iext(uri_rdf_rest, V, uri_rdf_nil), true2, Z, W, V, U, T).
% 0.19/0.50 Axiom 20 (owl_bool_intersectionof_class_002_3): fresh24(icext(X, Y), true2, X, Z, W, V, U, Y) = fresh25(iext(uri_owl_intersectionOf, X, Z), true2, Z, W, V, U, Y).
% 0.19/0.50
% 0.19/0.50 Lemma 21: equiv(uri_ex_A, bnode_y, uri_ex_w) = true2.
% 0.19/0.50 Proof:
% 0.19/0.50 equiv(uri_ex_A, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 12 (owl_bool_intersectionof_class_002_3) R->L }
% 0.19/0.50 fresh27(true2, true2, bnode_l1, uri_ex_A, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 5 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_5) R->L }
% 0.19/0.50 fresh27(iext(uri_rdf_first, bnode_l2, bnode_y), true2, bnode_l1, uri_ex_A, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 17 (owl_bool_intersectionof_class_002_3) R->L }
% 0.19/0.50 fresh26(true2, true2, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 7 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_7) R->L }
% 0.19/0.50 fresh26(iext(uri_rdf_rest, bnode_l2, uri_rdf_nil), true2, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 19 (owl_bool_intersectionof_class_002_3) R->L }
% 0.19/0.50 fresh24(true2, true2, bnode_x, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 10 (rdfs_cext_def) R->L }
% 0.19/0.50 fresh24(fresh2(true2, true2, uri_ex_w, bnode_x), true2, bnode_x, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 2 (testcase_premise_fullish_029_Ex_Falso_Quodlibet) R->L }
% 0.19/0.50 fresh24(fresh2(iext(uri_rdf_type, uri_ex_w, bnode_x), true2, uri_ex_w, bnode_x), true2, bnode_x, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 15 (rdfs_cext_def) }
% 0.19/0.50 fresh24(icext(bnode_x, uri_ex_w), true2, bnode_x, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 20 (owl_bool_intersectionof_class_002_3) }
% 0.19/0.50 fresh25(iext(uri_owl_intersectionOf, bnode_x, bnode_l1), true2, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 3 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_8) }
% 0.19/0.50 fresh25(true2, true2, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 18 (owl_bool_intersectionof_class_002_3) }
% 0.19/0.50 fresh28(iext(uri_rdf_rest, bnode_l1, bnode_l2), true2, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 6 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_6) }
% 0.19/0.50 fresh28(true2, true2, bnode_l1, uri_ex_A, bnode_l2, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 16 (owl_bool_intersectionof_class_002_3) }
% 0.19/0.50 fresh29(iext(uri_rdf_first, bnode_l1, uri_ex_A), true2, uri_ex_A, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 4 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_4) }
% 0.19/0.50 fresh29(true2, true2, uri_ex_A, bnode_y, uri_ex_w)
% 0.19/0.50 = { by axiom 11 (owl_bool_intersectionof_class_002_3) }
% 0.19/0.50 true2
% 0.19/0.50
% 0.19/0.50 Goal 1 (owl_bool_complementof_class_3): tuple(iext(uri_owl_complementOf, X, Y), icext(X, Z), icext(Y, Z)) = tuple(true2, true2, true2).
% 0.19/0.50 The goal is true when:
% 0.19/0.50 X = bnode_y
% 0.19/0.50 Y = uri_ex_A
% 0.19/0.50 Z = uri_ex_w
% 0.19/0.50
% 0.19/0.50 Proof:
% 0.19/0.50 tuple(iext(uri_owl_complementOf, bnode_y, uri_ex_A), icext(bnode_y, uri_ex_w), icext(uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by axiom 1 (testcase_premise_fullish_029_Ex_Falso_Quodlibet_3) }
% 0.19/0.50 tuple(true2, icext(bnode_y, uri_ex_w), icext(uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by axiom 14 (owl_bool_intersectionof_class_002_9) R->L }
% 0.19/0.50 tuple(true2, fresh3(equiv(uri_ex_A, bnode_y, uri_ex_w), true2, bnode_y, uri_ex_w), icext(uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by lemma 21 }
% 0.19/0.50 tuple(true2, fresh3(true2, true2, bnode_y, uri_ex_w), icext(uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by axiom 9 (owl_bool_intersectionof_class_002_9) }
% 0.19/0.50 tuple(true2, true2, icext(uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by axiom 13 (owl_bool_intersectionof_class_002_8) R->L }
% 0.19/0.50 tuple(true2, true2, fresh4(equiv(uri_ex_A, bnode_y, uri_ex_w), true2, uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by lemma 21 }
% 0.19/0.50 tuple(true2, true2, fresh4(true2, true2, uri_ex_A, uri_ex_w))
% 0.19/0.50 = { by axiom 8 (owl_bool_intersectionof_class_002_8) }
% 0.19/0.50 tuple(true2, true2, true2)
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Theorem (the conjecture is true).
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