TSTP Solution File: SWB006+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWB006+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 : 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 20:12:43 EDT 2023
% Result : Theorem 95.22s 12.84s
% Output : Proof 95.22s
% 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 : SWB006+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
% 0.12/0.34 % Computer : n014.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 06:10:01 EDT 2023
% 0.12/0.34 % CPUTime :
% 95.22/12.84 Command-line arguments: --no-flatten-goal
% 95.22/12.84
% 95.22/12.84 % SZS status Theorem
% 95.22/12.84
% 95.22/12.85 % SZS output start Proof
% 95.22/12.85 Take the following subset of the input axioms:
% 95.22/12.85 fof(owl_eqdis_sameas, axiom, ![X, Y]: (iext(uri_owl_sameAs, X, Y) <=> X=Y)).
% 95.22/12.85 fof(testcase_conclusion_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes, conjecture, iext(uri_owl_sameAs, uri_ex_u, uri_ex_w)).
% 95.22/12.85 fof(testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes, axiom, ?[BNODE_x]: (iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc)) & (iext(uri_owl_sameAs, BNODE_x, literal_plain(dat_str_abc)) & iext(uri_owl_sameAs, BNODE_x, uri_ex_w)))).
% 95.22/12.85
% 95.22/12.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 95.22/12.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 95.22/12.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 95.22/12.85 fresh(y, y, x1...xn) = u
% 95.22/12.85 C => fresh(s, t, x1...xn) = v
% 95.22/12.85 where fresh is a fresh function symbol and x1..xn are the free
% 95.22/12.85 variables of u and v.
% 95.22/12.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 95.22/12.85 input problem has no model of domain size 1).
% 95.22/12.85
% 95.22/12.85 The encoding turns the above axioms into the following unit equations and goals:
% 95.22/12.85
% 95.22/12.85 Axiom 1 (owl_eqdis_sameas): iext(uri_owl_sameAs, X, X) = true2.
% 95.22/12.85 Axiom 2 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_1): iext(uri_owl_sameAs, bnode_x, uri_ex_w) = true2.
% 95.22/12.85 Axiom 3 (owl_eqdis_sameas_1): fresh(X, X, Y, Z) = Z.
% 95.22/12.85 Axiom 4 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes): iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc)) = true2.
% 95.22/12.85 Axiom 5 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_2): iext(uri_owl_sameAs, bnode_x, literal_plain(dat_str_abc)) = true2.
% 95.22/12.85 Axiom 6 (owl_eqdis_sameas_1): fresh(iext(uri_owl_sameAs, X, Y), true2, X, Y) = X.
% 95.22/12.85
% 95.22/12.85 Goal 1 (testcase_conclusion_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes): iext(uri_owl_sameAs, uri_ex_u, uri_ex_w) = true2.
% 95.22/12.85 Proof:
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, uri_ex_w)
% 95.22/12.85 = { by axiom 6 (owl_eqdis_sameas_1) R->L }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, uri_ex_w, literal_plain(dat_str_abc)), true2, uri_ex_w, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 3 (owl_eqdis_sameas_1) R->L }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, fresh(true2, true2, bnode_x, uri_ex_w), literal_plain(dat_str_abc)), true2, uri_ex_w, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 2 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_1) R->L }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, fresh(iext(uri_owl_sameAs, bnode_x, uri_ex_w), true2, bnode_x, uri_ex_w), literal_plain(dat_str_abc)), true2, uri_ex_w, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 6 (owl_eqdis_sameas_1) }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, bnode_x, literal_plain(dat_str_abc)), true2, uri_ex_w, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 5 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_2) }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(true2, true2, uri_ex_w, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 3 (owl_eqdis_sameas_1) }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc))
% 95.22/12.85 = { by axiom 3 (owl_eqdis_sameas_1) R->L }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(true2, true2, uri_ex_u, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 4 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes) R->L }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc)), true2, uri_ex_u, literal_plain(dat_str_abc)))
% 95.22/12.85 = { by axiom 6 (owl_eqdis_sameas_1) }
% 95.22/12.85 iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)
% 95.22/12.85 = { by axiom 1 (owl_eqdis_sameas) }
% 95.22/12.85 true2
% 95.22/12.85 % SZS output end Proof
% 95.22/12.85
% 95.22/12.85 RESULT: Theorem (the conjecture is true).
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