TSTP Solution File: SWB007+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWB007+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 : n008.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 20:12:44 EDT 2023
% Result : Theorem 0.18s 0.38s
% 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
% 0.00/0.13 % Problem : SWB007+2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n008.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Sun Aug 27 06:34:17 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.38 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.18/0.38
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 Take the following subset of the input axioms:
% 0.18/0.39 fof(owl_eqdis_sameas, axiom, ![X, Y]: (iext(uri_owl_sameAs, X, Y) <=> X=Y)).
% 0.18/0.39 fof(testcase_conclusion_fullish_007_Equal_Classes, conjecture, iext(uri_rdf_type, uri_ex_w, uri_ex_c2) & (iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2) & iext(uri_rdfs_range, uri_ex_p, uri_ex_c2))).
% 0.18/0.39 fof(testcase_premise_fullish_007_Equal_Classes, axiom, iext(uri_owl_sameAs, uri_ex_c1, uri_ex_c2) & (iext(uri_rdf_type, uri_ex_w, uri_ex_c1) & (iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c1) & iext(uri_rdfs_range, uri_ex_p, uri_ex_c1)))).
% 0.18/0.39
% 0.18/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.39 fresh(y, y, x1...xn) = u
% 0.18/0.39 C => fresh(s, t, x1...xn) = v
% 0.18/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.39 variables of u and v.
% 0.18/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.39 input problem has no model of domain size 1).
% 0.18/0.39
% 0.18/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.39
% 0.18/0.39 Axiom 1 (testcase_premise_fullish_007_Equal_Classes_1): iext(uri_rdf_type, uri_ex_w, uri_ex_c1) = true.
% 0.18/0.39 Axiom 2 (testcase_premise_fullish_007_Equal_Classes_2): iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c1) = true.
% 0.18/0.39 Axiom 3 (testcase_premise_fullish_007_Equal_Classes_3): iext(uri_rdfs_range, uri_ex_p, uri_ex_c1) = true.
% 0.18/0.39 Axiom 4 (testcase_premise_fullish_007_Equal_Classes): iext(uri_owl_sameAs, uri_ex_c1, uri_ex_c2) = true.
% 0.18/0.39 Axiom 5 (owl_eqdis_sameas_1): fresh(X, X, Y, Z) = Z.
% 0.18/0.39 Axiom 6 (owl_eqdis_sameas_1): fresh(iext(uri_owl_sameAs, X, Y), true, X, Y) = X.
% 0.18/0.39
% 0.18/0.39 Lemma 7: uri_ex_c1 = uri_ex_c2.
% 0.18/0.39 Proof:
% 0.18/0.39 uri_ex_c1
% 0.18/0.39 = { by axiom 6 (owl_eqdis_sameas_1) R->L }
% 0.18/0.39 fresh(iext(uri_owl_sameAs, uri_ex_c1, uri_ex_c2), true, uri_ex_c1, uri_ex_c2)
% 0.18/0.39 = { by axiom 4 (testcase_premise_fullish_007_Equal_Classes) }
% 0.18/0.39 fresh(true, true, uri_ex_c1, uri_ex_c2)
% 0.18/0.39 = { by axiom 5 (owl_eqdis_sameas_1) }
% 0.18/0.39 uri_ex_c2
% 0.18/0.39
% 0.18/0.39 Goal 1 (testcase_conclusion_fullish_007_Equal_Classes): tuple(iext(uri_rdf_type, uri_ex_w, uri_ex_c2), iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2), iext(uri_rdfs_range, uri_ex_p, uri_ex_c2)) = tuple(true, true, true).
% 0.18/0.39 Proof:
% 0.18/0.39 tuple(iext(uri_rdf_type, uri_ex_w, uri_ex_c2), iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2), iext(uri_rdfs_range, uri_ex_p, uri_ex_c2))
% 0.18/0.39 = { by lemma 7 R->L }
% 0.18/0.39 tuple(iext(uri_rdf_type, uri_ex_w, uri_ex_c2), iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2), iext(uri_rdfs_range, uri_ex_p, uri_ex_c1))
% 0.18/0.39 = { by axiom 3 (testcase_premise_fullish_007_Equal_Classes_3) }
% 0.18/0.39 tuple(iext(uri_rdf_type, uri_ex_w, uri_ex_c2), iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2), true)
% 0.18/0.39 = { by lemma 7 R->L }
% 0.18/0.39 tuple(iext(uri_rdf_type, uri_ex_w, uri_ex_c1), iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2), true)
% 0.18/0.39 = { by axiom 1 (testcase_premise_fullish_007_Equal_Classes_1) }
% 0.18/0.39 tuple(true, iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c2), true)
% 0.18/0.39 = { by lemma 7 R->L }
% 0.18/0.39 tuple(true, iext(uri_rdfs_subClassOf, uri_ex_c, uri_ex_c1), true)
% 0.18/0.39 = { by axiom 2 (testcase_premise_fullish_007_Equal_Classes_2) }
% 0.18/0.39 tuple(true, true, true)
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Theorem (the conjecture is true).
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