TSTP Solution File: SWB013+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWB013+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 : 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 20:12:48 EDT 2023
% Result : Theorem 16.97s 2.60s
% Output : Proof 16.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB013+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
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 07:31:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.97/2.60 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 16.97/2.60
% 16.97/2.60 % SZS status Theorem
% 16.97/2.60
% 16.97/2.62 % SZS output start Proof
% 16.97/2.62 Take the following subset of the input axioms:
% 16.97/2.63 fof(owl_chain_003, axiom, ![P, P1, P2, S1, S2, S3, P3]: ((iext(uri_rdf_first, S1, P1) & (iext(uri_rdf_rest, S1, S2) & (iext(uri_rdf_first, S2, P2) & (iext(uri_rdf_rest, S2, S3) & (iext(uri_rdf_first, S3, P3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))))) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & (ip(P1) & (ip(P2) & (ip(P3) & ![Y0, Y1, Y2, Y3]: ((iext(P1, Y0, Y1) & (iext(P2, Y1, Y2) & iext(P3, Y2, Y3))) => iext(P, Y0, Y3))))))))).
% 16.97/2.63 fof(owl_eqdis_sameas, axiom, ![X, Y]: (iext(uri_owl_sameAs, X, Y) <=> X=Y)).
% 16.97/2.63 fof(owl_inv, axiom, ![P1_2, P2_2]: (iext(uri_owl_inverseOf, P1_2, P2_2) <=> (ip(P1_2) & (ip(P2_2) & ![X2, Y4]: (iext(P1_2, X2, Y4) <=> iext(P2_2, Y4, X2)))))).
% 16.97/2.63 fof(owl_rdfsext_subclassof, axiom, ![C1, C2]: (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & (ic(C2) & ![X2]: (icext(C1, X2) => icext(C2, X2)))))).
% 16.97/2.63 fof(owl_rdfsext_subpropertyof, axiom, ![P1_2, P2_2]: (iext(uri_rdfs_subPropertyOf, P1_2, P2_2) <=> (ip(P1_2) & (ip(P2_2) & ![X2, Y4]: (iext(P1_2, X2, Y4) => iext(P2_2, X2, Y4)))))).
% 16.97/2.63 fof(owl_restrict_somevaluesfrom, axiom, ![C, Z, P4]: ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P4)) => ![X2]: (icext(Z, X2) <=> ?[Y4]: (iext(P4, X2, Y4) & icext(C, Y4))))).
% 16.97/2.63 fof(rdfs_cext_def, axiom, ![X2, C3]: (iext(uri_rdf_type, X2, C3) <=> icext(C3, X2))).
% 16.97/2.63 fof(testcase_conclusion_fullish_013_Cliques, conjecture, iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)).
% 16.97/2.63 fof(testcase_premise_fullish_013_Cliques, axiom, ?[BNODE_r, BNODE_i, BNODE_l1, BNODE_l2, BNODE_l3]: (iext(uri_rdf_type, uri_ex_Clique, uri_owl_Class) & (iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) & (iext(uri_rdfs_range, uri_ex_sameCliqueAs, uri_ex_Clique) & (iext(uri_rdfs_subClassOf, uri_ex_Clique, BNODE_r) & (iext(uri_rdf_type, BNODE_r, uri_owl_Restriction) & (iext(uri_owl_onProperty, BNODE_r, uri_ex_sameCliqueAs) & (iext(uri_owl_someValuesFrom, BNODE_r, uri_ex_Clique) & (iext(uri_rdf_type, uri_foaf_knows, uri_owl_ObjectProperty) & (iext(uri_owl_propertyChainAxiom, uri_foaf_knows, BNODE_l1) & (iext(uri_rdf_first, BNODE_l1, uri_rdf_type) & (iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & (iext(uri_rdf_first, BNODE_l2, uri_ex_sameCliqueAs) & (iext(uri_rdf_rest, BNODE_l2, BNODE_l3) & (iext(uri_rdf_first, BNODE_l3, BNODE_i) & (iext(uri_rdf_rest, BNODE_l3, uri_rdf_nil) & (iext(uri_owl_inverseOf, BNODE_i, uri_rdf_type) & (iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) & (iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) & iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang)))))))))))))))))))).
% 16.97/2.63
% 16.97/2.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.97/2.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.97/2.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.97/2.63 fresh(y, y, x1...xn) = u
% 16.97/2.63 C => fresh(s, t, x1...xn) = v
% 16.97/2.63 where fresh is a fresh function symbol and x1..xn are the free
% 16.97/2.63 variables of u and v.
% 16.97/2.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.97/2.63 input problem has no model of domain size 1).
% 16.97/2.63
% 16.97/2.63 The encoding turns the above axioms into the following unit equations and goals:
% 16.97/2.63
% 16.97/2.63 Axiom 1 (testcase_premise_fullish_013_Cliques_10): iext(uri_rdf_first, bnode_l3, bnode_i) = true.
% 16.97/2.63 Axiom 2 (testcase_premise_fullish_013_Cliques_11): iext(uri_rdf_first, bnode_l2, uri_ex_sameCliqueAs) = true.
% 16.97/2.63 Axiom 3 (testcase_premise_fullish_013_Cliques_12): iext(uri_rdf_first, bnode_l1, uri_rdf_type) = true.
% 16.97/2.63 Axiom 4 (testcase_premise_fullish_013_Cliques_13): iext(uri_rdf_rest, bnode_l3, uri_rdf_nil) = true.
% 16.97/2.63 Axiom 5 (testcase_premise_fullish_013_Cliques_14): iext(uri_rdf_rest, bnode_l2, bnode_l3) = true.
% 16.97/2.63 Axiom 6 (testcase_premise_fullish_013_Cliques_15): iext(uri_rdf_rest, bnode_l1, bnode_l2) = true.
% 16.97/2.63 Axiom 7 (testcase_premise_fullish_013_Cliques_1): iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang) = true.
% 16.97/2.63 Axiom 8 (testcase_premise_fullish_013_Cliques_2): iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang) = true.
% 16.97/2.63 Axiom 9 (testcase_premise_fullish_013_Cliques_4): iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique) = true.
% 16.97/2.63 Axiom 10 (testcase_premise_fullish_013_Cliques_16): iext(uri_owl_propertyChainAxiom, uri_foaf_knows, bnode_l1) = true.
% 16.97/2.63 Axiom 11 (testcase_premise_fullish_013_Cliques_17): iext(uri_owl_inverseOf, bnode_i, uri_rdf_type) = true.
% 16.97/2.63 Axiom 12 (testcase_premise_fullish_013_Cliques_8): iext(uri_rdfs_subClassOf, uri_ex_Clique, bnode_r) = true.
% 16.97/2.63 Axiom 13 (testcase_premise_fullish_013_Cliques_9): iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs) = true.
% 16.97/2.63 Axiom 14 (testcase_premise_fullish_013_Cliques_6): iext(uri_owl_someValuesFrom, bnode_r, uri_ex_Clique) = true.
% 16.97/2.63 Axiom 15 (testcase_premise_fullish_013_Cliques_7): iext(uri_owl_onProperty, bnode_r, uri_ex_sameCliqueAs) = true.
% 16.97/2.63 Axiom 16 (owl_eqdis_sameas_1): fresh(X, X, Y, Z) = Z.
% 16.97/2.63 Axiom 17 (owl_rdfsext_subclassof_2): fresh12(X, X, Y, Z) = true.
% 16.97/2.63 Axiom 18 (rdfs_cext_def): fresh3(X, X, Y, Z) = true.
% 16.97/2.63 Axiom 19 (owl_restrict_somevaluesfrom_1): fresh84(X, X, Y, Z, W) = true.
% 16.97/2.63 Axiom 20 (owl_chain_003_1): fresh46(X, X, Y, Z, W) = true.
% 16.97/2.63 Axiom 21 (owl_inv_2): fresh18(X, X, Y, Z, W) = true.
% 16.97/2.63 Axiom 22 (owl_rdfsext_subclassof_2): fresh13(X, X, Y, Z, W) = icext(Z, W).
% 16.97/2.63 Axiom 23 (owl_rdfsext_subpropertyof): fresh9(X, X, Y, Z, W) = true.
% 16.97/2.63 Axiom 24 (owl_inv_2): fresh19(X, X, Y, Z, W, V) = iext(Y, W, V).
% 16.97/2.64 Axiom 25 (owl_rdfsext_subpropertyof): fresh10(X, X, Y, Z, W, V) = iext(Z, W, V).
% 16.97/2.64 Axiom 26 (owl_restrict_somevaluesfrom_1): fresh5(X, X, Y, Z, W, V) = iext(Z, V, y5(Z, W, V)).
% 16.97/2.64 Axiom 27 (owl_eqdis_sameas_1): fresh(iext(uri_owl_sameAs, X, Y), true, X, Y) = X.
% 16.97/2.64 Axiom 28 (owl_chain_003_1): fresh44(X, X, Y, Z, W, V, U) = iext(Y, W, U).
% 16.97/2.64 Axiom 29 (owl_rdfsext_subclassof_2): fresh13(icext(X, Y), true, X, Z, Y) = fresh12(iext(uri_rdfs_subClassOf, X, Z), true, Z, Y).
% 16.97/2.64 Axiom 30 (rdfs_cext_def): fresh3(iext(uri_rdf_type, X, Y), true, X, Y) = icext(Y, X).
% 16.97/2.64 Axiom 31 (owl_restrict_somevaluesfrom_1): fresh83(X, X, Y, Z, W, V) = fresh84(iext(uri_owl_someValuesFrom, Y, W), true, Z, W, V).
% 16.97/2.64 Axiom 32 (owl_chain_003_1): fresh45(X, X, Y, Z, W, V, U, T, S) = fresh46(iext(Z, V, U), true, Y, V, S).
% 16.97/2.64 Axiom 33 (owl_inv_2): fresh19(iext(uri_owl_inverseOf, X, Y), true, X, Y, Z, W) = fresh18(iext(Y, W, Z), true, X, Z, W).
% 16.97/2.64 Axiom 34 (owl_rdfsext_subpropertyof): fresh10(iext(uri_rdfs_subPropertyOf, X, Y), true, X, Y, Z, W) = fresh9(iext(X, Z, W), true, Y, Z, W).
% 16.97/2.64 Axiom 35 (owl_restrict_somevaluesfrom_1): fresh83(icext(X, Y), true, X, Z, W, Y) = fresh5(iext(uri_owl_onProperty, X, Z), true, X, Z, W, Y).
% 16.97/2.64 Axiom 36 (owl_chain_003_1): fresh43(X, X, Y, Z, W, V, U, T, S, X2) = fresh44(iext(W, T, S), true, Y, Z, U, T, X2).
% 16.97/2.64 Axiom 37 (owl_chain_003_1): fresh42(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh45(iext(U, X2, Y2), true, Y, W, V, T, S, X2, Y2).
% 16.97/2.64 Axiom 38 (owl_chain_003_1): fresh41(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh43(iext(uri_rdf_first, Z, W), true, Y, W, U, T, S, X2, Y2, Z2).
% 16.97/2.64 Axiom 39 (owl_chain_003_1): fresh40(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh42(iext(uri_rdf_first, V, U), true, Y, Z, W, U, S, X2, Y2, Z2, W2).
% 16.97/2.64 Axiom 40 (owl_chain_003_1): fresh39(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh41(iext(uri_rdf_first, T, S), true, Y, Z, W, V, U, S, X2, Y2, Z2, W2).
% 16.97/2.64 Axiom 41 (owl_chain_003_1): fresh38(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh40(iext(uri_rdf_rest, Z, V), true, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2).
% 16.97/2.64 Axiom 42 (owl_chain_003_1): fresh37(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = fresh39(iext(uri_rdf_rest, V, T), true, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2).
% 16.97/2.64 Axiom 43 (owl_chain_003_1): fresh37(iext(uri_owl_propertyChainAxiom, X, Y), true, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh38(iext(uri_rdf_rest, U, uri_rdf_nil), true, X, Y, Z, W, V, U, T, S, X2, Y2, Z2).
% 16.97/2.64
% 16.97/2.64 Lemma 44: iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)) = true.
% 16.97/2.64 Proof:
% 16.97/2.64 iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))
% 16.97/2.64 = { by axiom 26 (owl_restrict_somevaluesfrom_1) R->L }
% 16.97/2.64 fresh5(true, true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 15 (testcase_premise_fullish_013_Cliques_7) R->L }
% 16.97/2.64 fresh5(iext(uri_owl_onProperty, bnode_r, uri_ex_sameCliqueAs), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 35 (owl_restrict_somevaluesfrom_1) R->L }
% 16.97/2.64 fresh83(icext(bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 22 (owl_rdfsext_subclassof_2) R->L }
% 16.97/2.64 fresh83(fresh13(true, true, uri_ex_Clique, bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 18 (rdfs_cext_def) R->L }
% 16.97/2.64 fresh83(fresh13(fresh3(true, true, uri_ex_JoesGang, uri_ex_Clique), true, uri_ex_Clique, bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 9 (testcase_premise_fullish_013_Cliques_4) R->L }
% 16.97/2.64 fresh83(fresh13(fresh3(iext(uri_rdf_type, uri_ex_JoesGang, uri_ex_Clique), true, uri_ex_JoesGang, uri_ex_Clique), true, uri_ex_Clique, bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 30 (rdfs_cext_def) }
% 16.97/2.64 fresh83(fresh13(icext(uri_ex_Clique, uri_ex_JoesGang), true, uri_ex_Clique, bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 29 (owl_rdfsext_subclassof_2) }
% 16.97/2.64 fresh83(fresh12(iext(uri_rdfs_subClassOf, uri_ex_Clique, bnode_r), true, bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 12 (testcase_premise_fullish_013_Cliques_8) }
% 16.97/2.64 fresh83(fresh12(true, true, bnode_r, uri_ex_JoesGang), true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 17 (owl_rdfsext_subclassof_2) }
% 16.97/2.64 fresh83(true, true, bnode_r, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 31 (owl_restrict_somevaluesfrom_1) }
% 16.97/2.64 fresh84(iext(uri_owl_someValuesFrom, bnode_r, uri_ex_Clique), true, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 14 (testcase_premise_fullish_013_Cliques_6) }
% 16.97/2.64 fresh84(true, true, uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)
% 16.97/2.64 = { by axiom 19 (owl_restrict_somevaluesfrom_1) }
% 16.97/2.64 true
% 16.97/2.64
% 16.97/2.64 Goal 1 (testcase_conclusion_fullish_013_Cliques): iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob) = true.
% 16.97/2.64 Proof:
% 16.97/2.64 iext(uri_foaf_knows, uri_ex_alice, uri_ex_bob)
% 16.97/2.64 = { by axiom 28 (owl_chain_003_1) R->L }
% 16.97/2.64 fresh44(true, true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by lemma 44 R->L }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 16 (owl_eqdis_sameas_1) R->L }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(true, true, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 23 (owl_rdfsext_subpropertyof) R->L }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh9(true, true, uri_owl_sameAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by lemma 44 R->L }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh9(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_owl_sameAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 34 (owl_rdfsext_subpropertyof) R->L }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh10(iext(uri_rdfs_subPropertyOf, uri_ex_sameCliqueAs, uri_owl_sameAs), true, uri_ex_sameCliqueAs, uri_owl_sameAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 13 (testcase_premise_fullish_013_Cliques_9) }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(fresh10(true, true, uri_ex_sameCliqueAs, uri_owl_sameAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 25 (owl_rdfsext_subpropertyof) }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, fresh(iext(uri_owl_sameAs, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang)), true, uri_ex_JoesGang, y5(uri_ex_sameCliqueAs, uri_ex_Clique, uri_ex_JoesGang))), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 27 (owl_eqdis_sameas_1) }
% 16.97/2.64 fresh44(iext(uri_ex_sameCliqueAs, uri_ex_JoesGang, uri_ex_JoesGang), true, uri_foaf_knows, uri_rdf_type, uri_ex_alice, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 36 (owl_chain_003_1) R->L }
% 16.97/2.64 fresh43(true, true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 3 (testcase_premise_fullish_013_Cliques_12) R->L }
% 16.97/2.64 fresh43(iext(uri_rdf_first, bnode_l1, uri_rdf_type), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 38 (owl_chain_003_1) R->L }
% 16.97/2.64 fresh41(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 1 (testcase_premise_fullish_013_Cliques_10) R->L }
% 16.97/2.64 fresh41(iext(uri_rdf_first, bnode_l3, bnode_i), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 40 (owl_chain_003_1) R->L }
% 16.97/2.64 fresh39(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 5 (testcase_premise_fullish_013_Cliques_14) R->L }
% 16.97/2.64 fresh39(iext(uri_rdf_rest, bnode_l2, bnode_l3), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 42 (owl_chain_003_1) R->L }
% 16.97/2.64 fresh37(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 10 (testcase_premise_fullish_013_Cliques_16) R->L }
% 16.97/2.64 fresh37(iext(uri_owl_propertyChainAxiom, uri_foaf_knows, bnode_l1), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 43 (owl_chain_003_1) }
% 16.97/2.64 fresh38(iext(uri_rdf_rest, bnode_l3, uri_rdf_nil), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 4 (testcase_premise_fullish_013_Cliques_13) }
% 16.97/2.64 fresh38(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 41 (owl_chain_003_1) }
% 16.97/2.64 fresh40(iext(uri_rdf_rest, bnode_l1, bnode_l2), true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 6 (testcase_premise_fullish_013_Cliques_15) }
% 16.97/2.64 fresh40(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, bnode_l2, uri_ex_sameCliqueAs, bnode_l3, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 39 (owl_chain_003_1) }
% 16.97/2.64 fresh42(iext(uri_rdf_first, bnode_l2, uri_ex_sameCliqueAs), true, uri_foaf_knows, bnode_l1, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 2 (testcase_premise_fullish_013_Cliques_11) }
% 16.97/2.64 fresh42(true, true, uri_foaf_knows, bnode_l1, uri_rdf_type, uri_ex_sameCliqueAs, bnode_i, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 37 (owl_chain_003_1) }
% 16.97/2.64 fresh45(iext(bnode_i, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 24 (owl_inv_2) R->L }
% 16.97/2.64 fresh45(fresh19(true, true, bnode_i, uri_rdf_type, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 11 (testcase_premise_fullish_013_Cliques_17) R->L }
% 16.97/2.64 fresh45(fresh19(iext(uri_owl_inverseOf, bnode_i, uri_rdf_type), true, bnode_i, uri_rdf_type, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 33 (owl_inv_2) }
% 16.97/2.64 fresh45(fresh18(iext(uri_rdf_type, uri_ex_bob, uri_ex_JoesGang), true, bnode_i, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 8 (testcase_premise_fullish_013_Cliques_2) }
% 16.97/2.64 fresh45(fresh18(true, true, bnode_i, uri_ex_JoesGang, uri_ex_bob), true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 21 (owl_inv_2) }
% 16.97/2.64 fresh45(true, true, uri_foaf_knows, uri_rdf_type, uri_ex_sameCliqueAs, uri_ex_alice, uri_ex_JoesGang, uri_ex_JoesGang, uri_ex_bob)
% 16.97/2.64 = { by axiom 32 (owl_chain_003_1) }
% 16.97/2.64 fresh46(iext(uri_rdf_type, uri_ex_alice, uri_ex_JoesGang), true, uri_foaf_knows, uri_ex_alice, uri_ex_bob)
% 16.97/2.64 = { by axiom 7 (testcase_premise_fullish_013_Cliques_1) }
% 16.97/2.64 fresh46(true, true, uri_foaf_knows, uri_ex_alice, uri_ex_bob)
% 16.97/2.64 = { by axiom 20 (owl_chain_003_1) }
% 16.97/2.64 true
% 16.97/2.64 % SZS output end Proof
% 16.97/2.64
% 16.97/2.64 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------