TSTP Solution File: SWB031+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB031+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 : 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 20:13:00 EDT 2023
% Result : Unsatisfiable 0.18s 0.42s
% Output : Proof 0.18s
% 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 : SWB031+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
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 06:12:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.42 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.18/0.42
% 0.18/0.42 % SZS status Unsatisfiable
% 0.18/0.42
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 Take the following subset of the input axioms:
% 0.18/0.43 fof(owl_class_nothing_ext, axiom, ![X]: ~icext(uri_owl_Nothing, X)).
% 0.18/0.43 fof(owl_class_thing_ext, axiom, ![X2]: (icext(uri_owl_Thing, X2) <=> ir(X2))).
% 0.18/0.43 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))))).
% 0.18/0.43 fof(owl_eqdis_equivalentclass, axiom, ![C1, C2]: (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & (ic(C2) & ![X2]: (icext(C1, X2) <=> icext(C2, X2)))))).
% 0.18/0.43 fof(simple_ir, axiom, ![X2]: ir(X2)).
% 0.18/0.43 fof(testcase_premise_fullish_031_Large_Universe, axiom, ?[BNODE_x, BNODE_l]: (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & (iext(uri_owl_oneOf, BNODE_x, BNODE_l) & (iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))))).
% 0.18/0.43
% 0.18/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.43 fresh(y, y, x1...xn) = u
% 0.18/0.43 C => fresh(s, t, x1...xn) = v
% 0.18/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.43 variables of u and v.
% 0.18/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.43 input problem has no model of domain size 1).
% 0.18/0.43
% 0.18/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.43
% 0.18/0.43 Axiom 1 (simple_ir): ir(X) = true2.
% 0.18/0.43 Axiom 2 (testcase_premise_fullish_031_Large_Universe_3): iext(uri_owl_equivalentClass, uri_owl_Thing, bnode_x) = true2.
% 0.18/0.43 Axiom 3 (testcase_premise_fullish_031_Large_Universe): iext(uri_rdf_first, bnode_l, uri_ex_w) = true2.
% 0.18/0.43 Axiom 4 (testcase_premise_fullish_031_Large_Universe_1): iext(uri_rdf_rest, bnode_l, uri_rdf_nil) = true2.
% 0.18/0.43 Axiom 5 (testcase_premise_fullish_031_Large_Universe_2): iext(uri_owl_oneOf, bnode_x, bnode_l) = true2.
% 0.18/0.43 Axiom 6 (owl_class_thing_ext): fresh11(X, X, Y) = true2.
% 0.18/0.43 Axiom 7 (owl_enum_class_001_1): fresh23(X, X, Y, Z) = Y.
% 0.18/0.43 Axiom 8 (owl_class_thing_ext): fresh11(ir(X), true2, X) = icext(uri_owl_Thing, X).
% 0.18/0.43 Axiom 9 (owl_eqdis_equivalentclass): fresh6(X, X, Y, Z) = true2.
% 0.18/0.43 Axiom 10 (owl_enum_class_001_1): fresh21(X, X, Y, Z, W) = W.
% 0.18/0.43 Axiom 11 (owl_eqdis_equivalentclass): fresh7(X, X, Y, Z, W) = icext(Z, W).
% 0.18/0.43 Axiom 12 (owl_enum_class_001_1): fresh22(X, X, Y, Z, W, V) = fresh23(icext(Y, V), true2, W, V).
% 0.18/0.43 Axiom 13 (owl_enum_class_001_1): fresh20(X, X, Y, Z, W, V) = fresh21(iext(uri_rdf_first, Z, W), true2, Y, W, V).
% 0.18/0.43 Axiom 14 (owl_eqdis_equivalentclass): fresh7(iext(uri_owl_equivalentClass, X, Y), true2, X, Y, Z) = fresh6(icext(X, Z), true2, Y, Z).
% 0.18/0.43 Axiom 15 (owl_enum_class_001_1): fresh20(iext(uri_owl_oneOf, X, Y), true2, X, Y, Z, W) = fresh22(iext(uri_rdf_rest, Y, uri_rdf_nil), true2, X, Y, Z, W).
% 0.18/0.43
% 0.18/0.43 Lemma 16: fresh22(X, X, bnode_x, Y, Z, W) = Z.
% 0.18/0.43 Proof:
% 0.18/0.43 fresh22(X, X, bnode_x, Y, Z, W)
% 0.18/0.43 = { by axiom 12 (owl_enum_class_001_1) }
% 0.18/0.43 fresh23(icext(bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 11 (owl_eqdis_equivalentclass) R->L }
% 0.18/0.43 fresh23(fresh7(true2, true2, uri_owl_Thing, bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 2 (testcase_premise_fullish_031_Large_Universe_3) R->L }
% 0.18/0.43 fresh23(fresh7(iext(uri_owl_equivalentClass, uri_owl_Thing, bnode_x), true2, uri_owl_Thing, bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 14 (owl_eqdis_equivalentclass) }
% 0.18/0.43 fresh23(fresh6(icext(uri_owl_Thing, W), true2, bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 8 (owl_class_thing_ext) R->L }
% 0.18/0.43 fresh23(fresh6(fresh11(ir(W), true2, W), true2, bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 1 (simple_ir) }
% 0.18/0.43 fresh23(fresh6(fresh11(true2, true2, W), true2, bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 6 (owl_class_thing_ext) }
% 0.18/0.43 fresh23(fresh6(true2, true2, bnode_x, W), true2, Z, W)
% 0.18/0.43 = { by axiom 9 (owl_eqdis_equivalentclass) }
% 0.18/0.43 fresh23(true2, true2, Z, W)
% 0.18/0.43 = { by axiom 7 (owl_enum_class_001_1) }
% 0.18/0.43 Z
% 0.18/0.43
% 0.18/0.43 Lemma 17: fresh20(X, X, Y, bnode_l, uri_ex_w, Z) = Z.
% 0.18/0.43 Proof:
% 0.18/0.43 fresh20(X, X, Y, bnode_l, uri_ex_w, Z)
% 0.18/0.43 = { by axiom 13 (owl_enum_class_001_1) }
% 0.18/0.43 fresh21(iext(uri_rdf_first, bnode_l, uri_ex_w), true2, Y, uri_ex_w, Z)
% 0.18/0.43 = { by axiom 3 (testcase_premise_fullish_031_Large_Universe) }
% 0.18/0.43 fresh21(true2, true2, Y, uri_ex_w, Z)
% 0.18/0.43 = { by axiom 10 (owl_enum_class_001_1) }
% 0.18/0.43 Z
% 0.18/0.43
% 0.18/0.43 Lemma 18: fresh20(X, X, bnode_x, bnode_l, Y, Z) = fresh22(W, W, bnode_x, V, Y, Z).
% 0.18/0.43 Proof:
% 0.18/0.43 fresh20(X, X, bnode_x, bnode_l, Y, Z)
% 0.18/0.43 = { by axiom 13 (owl_enum_class_001_1) }
% 0.18/0.43 fresh21(iext(uri_rdf_first, bnode_l, Y), true2, bnode_x, Y, Z)
% 0.18/0.43 = { by axiom 13 (owl_enum_class_001_1) R->L }
% 0.18/0.43 fresh20(true2, true2, bnode_x, bnode_l, Y, Z)
% 0.18/0.43 = { by axiom 5 (testcase_premise_fullish_031_Large_Universe_2) R->L }
% 0.18/0.43 fresh20(iext(uri_owl_oneOf, bnode_x, bnode_l), true2, bnode_x, bnode_l, Y, Z)
% 0.18/0.43 = { by axiom 15 (owl_enum_class_001_1) }
% 0.18/0.43 fresh22(iext(uri_rdf_rest, bnode_l, uri_rdf_nil), true2, bnode_x, bnode_l, Y, Z)
% 0.18/0.43 = { by axiom 4 (testcase_premise_fullish_031_Large_Universe_1) }
% 0.18/0.43 fresh22(true2, true2, bnode_x, bnode_l, Y, Z)
% 0.18/0.43 = { by axiom 12 (owl_enum_class_001_1) }
% 0.18/0.43 fresh23(icext(bnode_x, Z), true2, Y, Z)
% 0.18/0.43 = { by axiom 12 (owl_enum_class_001_1) R->L }
% 0.18/0.43 fresh22(W, W, bnode_x, V, Y, Z)
% 0.18/0.43
% 0.18/0.43 Goal 1 (true_equals_false): true = false.
% 0.18/0.43 Proof:
% 0.18/0.43 true
% 0.18/0.43 = { by lemma 17 R->L }
% 0.18/0.43 fresh20(X, X, bnode_x, bnode_l, uri_ex_w, true)
% 0.18/0.43 = { by lemma 18 }
% 0.18/0.43 fresh22(Y, Y, bnode_x, Z, uri_ex_w, true)
% 0.18/0.43 = { by lemma 16 }
% 0.18/0.43 uri_ex_w
% 0.18/0.43 = { by lemma 16 R->L }
% 0.18/0.43 fresh22(W, W, bnode_x, V, uri_ex_w, false)
% 0.18/0.43 = { by lemma 18 R->L }
% 0.18/0.43 fresh20(U, U, bnode_x, bnode_l, uri_ex_w, false)
% 0.18/0.43 = { by lemma 17 }
% 0.18/0.43 false
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43
% 0.18/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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