TSTP Solution File: SWB054+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWB054+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 : n018.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 20:13:04 EDT 2023
% Result : Theorem 284.13s 36.87s
% Output : Proof 284.13s
% 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 : SWB054+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
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 07:46:45 EDT 2023
% 0.14/0.35 % CPUTime :
% 284.13/36.87 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 284.13/36.87
% 284.13/36.87 % SZS status Theorem
% 284.13/36.87
% 284.13/36.87 % SZS output start Proof
% 284.13/36.87 Take the following subset of the input axioms:
% 284.13/36.87 fof(conclusion_rdfbased_sem_class_thing_term, conjecture, iext(uri_rdfs_subClassOf, uri_ex_c, uri_owl_Thing)).
% 284.13/36.87 fof(owl_class_classowl_ext, axiom, ![X]: (icext(uri_owl_Class, X) <=> ic(X))).
% 284.13/36.87 fof(owl_class_thing_ext, axiom, ![X2]: (icext(uri_owl_Thing, X2) <=> ir(X2))).
% 284.13/36.87 fof(owl_class_thing_type, axiom, ic(uri_owl_Thing)).
% 284.13/36.87 fof(owl_rdfsext_subclassof, axiom, ![C1, C2]: (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & (ic(C2) & ![X2]: (icext(C1, X2) => icext(C2, X2)))))).
% 284.13/36.87 fof(premise_rdfbased_sem_class_thing_term, axiom, iext(uri_rdf_type, uri_ex_c, uri_owl_Class)).
% 284.13/36.87 fof(rdfs_cext_def, axiom, ![C, X2]: (iext(uri_rdf_type, X2, C) <=> icext(C, X2))).
% 284.13/36.87 fof(simple_ir, axiom, ![X2]: ir(X2)).
% 284.13/36.87
% 284.13/36.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 284.13/36.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 284.13/36.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 284.13/36.87 fresh(y, y, x1...xn) = u
% 284.13/36.87 C => fresh(s, t, x1...xn) = v
% 284.13/36.87 where fresh is a fresh function symbol and x1..xn are the free
% 284.13/36.87 variables of u and v.
% 284.13/36.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 284.13/36.87 input problem has no model of domain size 1).
% 284.13/36.87
% 284.13/36.87 The encoding turns the above axioms into the following unit equations and goals:
% 284.13/36.87
% 284.13/36.87 Axiom 1 (owl_class_thing_type): ic(uri_owl_Thing) = true2.
% 284.13/36.87 Axiom 2 (simple_ir): ir(X) = true2.
% 284.13/36.87 Axiom 3 (premise_rdfbased_sem_class_thing_term): iext(uri_rdf_type, uri_ex_c, uri_owl_Class) = true2.
% 284.13/36.87 Axiom 4 (owl_class_classowl_ext): fresh467(X, X, Y) = true2.
% 284.13/36.87 Axiom 5 (owl_class_thing_ext): fresh435(X, X, Y) = true2.
% 284.13/36.87 Axiom 6 (owl_rdfsext_subclassof_3): fresh859(X, X, Y, Z) = iext(uri_rdfs_subClassOf, Y, Z).
% 284.13/36.87 Axiom 7 (owl_class_classowl_ext): fresh467(icext(uri_owl_Class, X), true2, X) = ic(X).
% 284.13/36.87 Axiom 8 (owl_class_thing_ext): fresh435(ir(X), true2, X) = icext(uri_owl_Thing, X).
% 284.13/36.87 Axiom 9 (owl_rdfsext_subclassof_3): fresh129(X, X, Y, Z) = true2.
% 284.13/36.87 Axiom 10 (rdfs_cext_def): fresh35(X, X, Y, Z) = true2.
% 284.13/36.88 Axiom 11 (owl_rdfsext_subclassof_3): fresh858(X, X, Y, Z) = fresh859(ic(Y), true2, Y, Z).
% 284.13/36.88 Axiom 12 (owl_rdfsext_subclassof_3): fresh858(ic(X), true2, Y, X) = fresh129(icext(X, x21(Y, X)), true2, Y, X).
% 284.13/36.88 Axiom 13 (rdfs_cext_def): fresh35(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X).
% 284.13/36.88
% 284.13/36.88 Goal 1 (conclusion_rdfbased_sem_class_thing_term): iext(uri_rdfs_subClassOf, uri_ex_c, uri_owl_Thing) = true2.
% 284.13/36.88 Proof:
% 284.13/36.88 iext(uri_rdfs_subClassOf, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 6 (owl_rdfsext_subclassof_3) R->L }
% 284.13/36.88 fresh859(true2, true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 4 (owl_class_classowl_ext) R->L }
% 284.13/36.88 fresh859(fresh467(true2, true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 10 (rdfs_cext_def) R->L }
% 284.13/36.88 fresh859(fresh467(fresh35(true2, true2, uri_ex_c, uri_owl_Class), true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 3 (premise_rdfbased_sem_class_thing_term) R->L }
% 284.13/36.88 fresh859(fresh467(fresh35(iext(uri_rdf_type, uri_ex_c, uri_owl_Class), true2, uri_ex_c, uri_owl_Class), true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 13 (rdfs_cext_def) }
% 284.13/36.88 fresh859(fresh467(icext(uri_owl_Class, uri_ex_c), true2, uri_ex_c), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 7 (owl_class_classowl_ext) }
% 284.13/36.88 fresh859(ic(uri_ex_c), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 11 (owl_rdfsext_subclassof_3) R->L }
% 284.13/36.88 fresh858(true2, true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 1 (owl_class_thing_type) R->L }
% 284.13/36.88 fresh858(ic(uri_owl_Thing), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 12 (owl_rdfsext_subclassof_3) }
% 284.13/36.88 fresh129(icext(uri_owl_Thing, x21(uri_ex_c, uri_owl_Thing)), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 8 (owl_class_thing_ext) R->L }
% 284.13/36.88 fresh129(fresh435(ir(x21(uri_ex_c, uri_owl_Thing)), true2, x21(uri_ex_c, uri_owl_Thing)), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 2 (simple_ir) }
% 284.13/36.88 fresh129(fresh435(true2, true2, x21(uri_ex_c, uri_owl_Thing)), true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 5 (owl_class_thing_ext) }
% 284.13/36.88 fresh129(true2, true2, uri_ex_c, uri_owl_Thing)
% 284.13/36.88 = { by axiom 9 (owl_rdfsext_subclassof_3) }
% 284.13/36.88 true2
% 284.13/36.88 % SZS output end Proof
% 284.13/36.88
% 284.13/36.88 RESULT: Theorem (the conjecture is true).
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