TSTP Solution File: SWB002+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWB002+3 : 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 : n017.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 20:12:40 EDT 2023
% Result : Theorem 5.76s 1.14s
% Output : Proof 5.76s
% 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 : SWB002+3 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 05:54:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 5.76/1.14 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 5.76/1.14
% 5.76/1.14 % SZS status Theorem
% 5.76/1.14
% 5.76/1.14 % SZS output start Proof
% 5.76/1.14 Take the following subset of the input axioms:
% 5.76/1.14 fof(owl_bool_complementof_class, axiom, ![Z, C]: (iext(uri_owl_complementOf, Z, C) => (ic(Z) & (ic(C) & ![X]: (icext(Z, X) <=> ~icext(C, X)))))).
% 5.76/1.14 fof(owl_bool_unionof_class_000, axiom, ![Z2]: (iext(uri_owl_unionOf, Z2, uri_rdf_nil) <=> (ic(Z2) & ![X2]: ~icext(Z2, X2)))).
% 5.76/1.14 fof(owl_class_nothing_ext, axiom, ![X2]: ~icext(uri_owl_Nothing, X2)).
% 5.76/1.14 fof(testcase_conclusion_fullish_002_Existential_Blank_Nodes, conjecture, ?[BNODE_x, BNODE_y]: (iext(uri_ex_p, BNODE_x, BNODE_y) & iext(uri_ex_q, BNODE_y, BNODE_x))).
% 5.76/1.14 fof(testcase_premise_fullish_002_Existential_Blank_Nodes, axiom, ?[BNODE_o]: (iext(uri_ex_p, uri_ex_s, BNODE_o) & iext(uri_ex_q, BNODE_o, uri_ex_s))).
% 5.76/1.14
% 5.76/1.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.76/1.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.76/1.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.76/1.14 fresh(y, y, x1...xn) = u
% 5.76/1.14 C => fresh(s, t, x1...xn) = v
% 5.76/1.14 where fresh is a fresh function symbol and x1..xn are the free
% 5.76/1.14 variables of u and v.
% 5.76/1.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.76/1.14 input problem has no model of domain size 1).
% 5.76/1.14
% 5.76/1.14 The encoding turns the above axioms into the following unit equations and goals:
% 5.76/1.14
% 5.76/1.14 Axiom 1 (testcase_premise_fullish_002_Existential_Blank_Nodes): iext(uri_ex_p, uri_ex_s, bnode_o) = true2.
% 5.76/1.14 Axiom 2 (testcase_premise_fullish_002_Existential_Blank_Nodes_1): iext(uri_ex_q, bnode_o, uri_ex_s) = true2.
% 5.76/1.14
% 5.76/1.14 Goal 1 (testcase_conclusion_fullish_002_Existential_Blank_Nodes): tuple2(iext(uri_ex_p, X, Y), iext(uri_ex_q, Y, X)) = tuple2(true2, true2).
% 5.76/1.14 The goal is true when:
% 5.76/1.14 X = uri_ex_s
% 5.76/1.14 Y = bnode_o
% 5.76/1.14
% 5.76/1.14 Proof:
% 5.76/1.14 tuple2(iext(uri_ex_p, uri_ex_s, bnode_o), iext(uri_ex_q, bnode_o, uri_ex_s))
% 5.76/1.14 = { by axiom 1 (testcase_premise_fullish_002_Existential_Blank_Nodes) }
% 5.76/1.14 tuple2(true2, iext(uri_ex_q, bnode_o, uri_ex_s))
% 5.76/1.14 = { by axiom 2 (testcase_premise_fullish_002_Existential_Blank_Nodes_1) }
% 5.76/1.14 tuple2(true2, true2)
% 5.76/1.14 % SZS output end Proof
% 5.76/1.14
% 5.76/1.14 RESULT: Theorem (the conjecture is true).
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