TSTP Solution File: SWB013+2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWB013+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 20:03:58 EDT 2023
% Result : Theorem 66.44s 66.62s
% Output : Proof 66.56s
% 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 : duper %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 07:44:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 66.44/66.62 SZS status Theorem for theBenchmark.p
% 66.44/66.62 SZS output start Proof for theBenchmark.p
% 66.44/66.62 Clause #0 (by assumption #[]): Eq (∀ (X C : Iota), Iff (iext uri_rdf_type X C) (icext C X)) True
% 66.44/66.62 Clause #1 (by assumption #[]): Eq
% 66.44/66.62 (∀ (Z P C : Iota),
% 66.44/66.62 And (iext uri_owl_someValuesFrom Z C) (iext uri_owl_onProperty Z P) →
% 66.44/66.62 ∀ (X : Iota), Iff (icext Z X) (Exists fun Y => And (iext P X Y) (icext C Y)))
% 66.44/66.62 True
% 66.44/66.62 Clause #2 (by assumption #[]): Eq
% 66.44/66.62 (∀ (C1 C2 : Iota),
% 66.44/66.62 Iff (iext uri_rdfs_subClassOf C1 C2) (And (And (ic C1) (ic C2)) (∀ (X : Iota), icext C1 X → icext C2 X)))
% 66.44/66.62 True
% 66.44/66.62 Clause #3 (by assumption #[]): Eq
% 66.44/66.62 (∀ (P1 P2 : Iota),
% 66.44/66.62 Iff (iext uri_rdfs_subPropertyOf P1 P2) (And (And (ip P1) (ip P2)) (∀ (X Y : Iota), iext P1 X Y → iext P2 X Y)))
% 66.44/66.62 True
% 66.44/66.62 Clause #4 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (iext uri_owl_sameAs X Y) (Eq X Y)) True
% 66.44/66.62 Clause #5 (by assumption #[]): Eq
% 66.44/66.62 (∀ (P S1 P1 S2 P2 S3 P3 : Iota),
% 66.44/66.62 And
% 66.44/66.62 (And
% 66.44/66.62 (And (And (And (iext uri_rdf_first S1 P1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 P2))
% 66.44/66.62 (iext uri_rdf_rest S2 S3))
% 66.44/66.62 (iext uri_rdf_first S3 P3))
% 66.44/66.62 (iext uri_rdf_rest S3 uri_rdf_nil) →
% 66.44/66.62 Iff (iext uri_owl_propertyChainAxiom P S1)
% 66.44/66.62 (And (And (And (And (ip P) (ip P1)) (ip P2)) (ip P3))
% 66.44/66.62 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext P1 Y0 Y1) (iext P2 Y1 Y2)) (iext P3 Y2 Y3) → iext P Y0 Y3)))
% 66.44/66.62 True
% 66.44/66.62 Clause #6 (by assumption #[]): Eq
% 66.44/66.62 (∀ (P1 P2 : Iota),
% 66.44/66.62 Iff (iext uri_owl_inverseOf P1 P2) (And (And (ip P1) (ip P2)) (∀ (X Y : Iota), Iff (iext P1 X Y) (iext P2 Y X))))
% 66.44/66.62 True
% 66.44/66.62 Clause #7 (by assumption #[]): Eq (Not (iext uri_foaf_knows uri_ex_alice uri_ex_bob)) True
% 66.44/66.62 Clause #8 (by assumption #[]): Eq
% 66.44/66.62 (Exists fun BNODE_r =>
% 66.44/66.62 Exists fun BNODE_i =>
% 66.44/66.62 Exists fun BNODE_l1 =>
% 66.44/66.62 Exists fun BNODE_l2 =>
% 66.44/66.62 Exists fun BNODE_l3 =>
% 66.44/66.62 And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And
% 66.44/66.62 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.44/66.62 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.44/66.62 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.44/66.62 (iext uri_rdfs_subClassOf uri_ex_Clique BNODE_r))
% 66.44/66.62 (iext uri_rdf_type BNODE_r uri_owl_Restriction))
% 66.44/66.62 (iext uri_owl_onProperty BNODE_r uri_ex_sameCliqueAs))
% 66.44/66.62 (iext uri_owl_someValuesFrom BNODE_r uri_ex_Clique))
% 66.44/66.62 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.44/66.62 (iext uri_owl_propertyChainAxiom uri_foaf_knows BNODE_l1))
% 66.44/66.62 (iext uri_rdf_first BNODE_l1 uri_rdf_type))
% 66.44/66.62 (iext uri_rdf_rest BNODE_l1 BNODE_l2))
% 66.44/66.62 (iext uri_rdf_first BNODE_l2 uri_ex_sameCliqueAs))
% 66.44/66.62 (iext uri_rdf_rest BNODE_l2 BNODE_l3))
% 66.44/66.62 (iext uri_rdf_first BNODE_l3 BNODE_i))
% 66.44/66.62 (iext uri_rdf_rest BNODE_l3 uri_rdf_nil))
% 66.44/66.62 (iext uri_owl_inverseOf BNODE_i uri_rdf_type))
% 66.44/66.62 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.44/66.62 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.44/66.62 (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang))
% 66.44/66.62 True
% 66.44/66.62 Clause #9 (by clausification #[7]): Eq (iext uri_foaf_knows uri_ex_alice uri_ex_bob) False
% 66.44/66.62 Clause #10 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (iext uri_rdf_type a C) (icext C a)) True
% 66.49/66.65 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Iff (iext uri_rdf_type a a_1) (icext a_1 a)) True
% 66.49/66.65 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (iext uri_rdf_type a a_1) False) (Eq (icext a_1 a) True)
% 66.49/66.65 Clause #14 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (iext uri_owl_sameAs a Y) (Eq a Y)) True
% 66.49/66.65 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Iff (iext uri_owl_sameAs a a_1) (Eq a a_1)) True
% 66.49/66.65 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_sameAs a a_1) False) (Eq (Eq a a_1) True)
% 66.49/66.65 Clause #20 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_sameAs a a_1) False) (Eq a a_1)
% 66.49/66.65 Clause #22 (by clausification #[1]): ∀ (a : Iota),
% 66.49/66.65 Eq
% 66.49/66.65 (∀ (P C : Iota),
% 66.49/66.65 And (iext uri_owl_someValuesFrom a C) (iext uri_owl_onProperty a P) →
% 66.49/66.65 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext P X Y) (icext C Y)))
% 66.49/66.65 True
% 66.49/66.65 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 66.49/66.65 Eq
% 66.49/66.65 (∀ (C : Iota),
% 66.49/66.65 And (iext uri_owl_someValuesFrom a C) (iext uri_owl_onProperty a a_1) →
% 66.49/66.65 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_1 X Y) (icext C Y)))
% 66.49/66.65 True
% 66.49/66.65 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.65 Eq
% 66.49/66.65 (And (iext uri_owl_someValuesFrom a a_1) (iext uri_owl_onProperty a a_2) →
% 66.49/66.65 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_2 X Y) (icext a_1 Y)))
% 66.49/66.65 True
% 66.49/66.65 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.65 Or (Eq (And (iext uri_owl_someValuesFrom a a_1) (iext uri_owl_onProperty a a_2)) False)
% 66.49/66.65 (Eq (∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_2 X Y) (icext a_1 Y))) True)
% 66.49/66.65 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.65 Or (Eq (∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_1 X Y) (icext a_2 Y))) True)
% 66.49/66.65 (Or (Eq (iext uri_owl_someValuesFrom a a_2) False) (Eq (iext uri_owl_onProperty a a_1) False))
% 66.49/66.65 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.65 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 66.49/66.65 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 66.49/66.65 (Eq (Iff (icext a a_3) (Exists fun Y => And (iext a_2 a_3 Y) (icext a_1 Y))) True))
% 66.49/66.65 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.65 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 66.49/66.65 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 66.49/66.65 (Or (Eq (icext a a_3) False) (Eq (Exists fun Y => And (iext a_2 a_3 Y) (icext a_1 Y)) True)))
% 66.49/66.65 Clause #33 (by clausification #[2]): ∀ (a : Iota),
% 66.49/66.65 Eq
% 66.49/66.65 (∀ (C2 : Iota),
% 66.49/66.65 Iff (iext uri_rdfs_subClassOf a C2) (And (And (ic a) (ic C2)) (∀ (X : Iota), icext a X → icext C2 X)))
% 66.49/66.65 True
% 66.49/66.65 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota),
% 66.49/66.65 Eq (Iff (iext uri_rdfs_subClassOf a a_1) (And (And (ic a) (ic a_1)) (∀ (X : Iota), icext a X → icext a_1 X))) True
% 66.49/66.65 Clause #36 (by clausification #[34]): ∀ (a a_1 : Iota),
% 66.49/66.65 Or (Eq (iext uri_rdfs_subClassOf a a_1) False)
% 66.49/66.65 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), icext a X → icext a_1 X)) True)
% 66.49/66.65 Clause #43 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (iext uri_rdfs_subClassOf a a_1) False) (Eq (∀ (X : Iota), icext a X → icext a_1 X) True)
% 66.49/66.65 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (iext uri_rdfs_subClassOf a a_1) False) (Eq (icext a a_2 → icext a_1 a_2) True)
% 66.49/66.65 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.65 Or (Eq (iext uri_rdfs_subClassOf a a_1) False) (Or (Eq (icext a a_2) False) (Eq (icext a_1 a_2) True))
% 66.49/66.65 Clause #49 (by clausification #[3]): ∀ (a : Iota),
% 66.49/66.65 Eq
% 66.49/66.65 (∀ (P2 : Iota),
% 66.49/66.65 Iff (iext uri_rdfs_subPropertyOf a P2) (And (And (ip a) (ip P2)) (∀ (X Y : Iota), iext a X Y → iext P2 X Y)))
% 66.49/66.65 True
% 66.49/66.65 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 66.49/66.65 Eq (Iff (iext uri_rdfs_subPropertyOf a a_1) (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), iext a X Y → iext a_1 X Y)))
% 66.49/66.65 True
% 66.49/66.65 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota),
% 66.49/66.67 Or (Eq (iext uri_rdfs_subPropertyOf a a_1) False)
% 66.49/66.67 (Eq (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), iext a X Y → iext a_1 X Y)) True)
% 66.49/66.67 Clause #61 (by clausification #[52]): ∀ (a a_1 : Iota),
% 66.49/66.67 Or (Eq (iext uri_rdfs_subPropertyOf a a_1) False) (Eq (∀ (X Y : Iota), iext a X Y → iext a_1 X Y) True)
% 66.49/66.67 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.67 Or (Eq (iext uri_rdfs_subPropertyOf a a_1) False) (Eq (∀ (Y : Iota), iext a a_2 Y → iext a_1 a_2 Y) True)
% 66.49/66.67 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.67 Or (Eq (iext uri_rdfs_subPropertyOf a a_1) False) (Eq (iext a a_2 a_3 → iext a_1 a_2 a_3) True)
% 66.49/66.67 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.67 Or (Eq (iext uri_rdfs_subPropertyOf a a_1) False) (Or (Eq (iext a a_2 a_3) False) (Eq (iext a_1 a_2 a_3) True))
% 66.49/66.67 Clause #68 (by clausification #[6]): ∀ (a : Iota),
% 66.49/66.67 Eq
% 66.49/66.67 (∀ (P2 : Iota),
% 66.49/66.67 Iff (iext uri_owl_inverseOf a P2) (And (And (ip a) (ip P2)) (∀ (X Y : Iota), Iff (iext a X Y) (iext P2 Y X))))
% 66.49/66.67 True
% 66.49/66.67 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota),
% 66.49/66.67 Eq (Iff (iext uri_owl_inverseOf a a_1) (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), Iff (iext a X Y) (iext a_1 Y X))))
% 66.49/66.67 True
% 66.49/66.67 Clause #71 (by clausification #[69]): ∀ (a a_1 : Iota),
% 66.49/66.67 Or (Eq (iext uri_owl_inverseOf a a_1) False)
% 66.49/66.67 (Eq (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), Iff (iext a X Y) (iext a_1 Y X))) True)
% 66.49/66.67 Clause #80 (by clausification #[5]): ∀ (a : Iota),
% 66.49/66.67 Eq
% 66.49/66.67 (∀ (S1 P1 S2 P2 S3 P3 : Iota),
% 66.49/66.67 And
% 66.49/66.67 (And
% 66.49/66.67 (And (And (And (iext uri_rdf_first S1 P1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 P2))
% 66.49/66.67 (iext uri_rdf_rest S2 S3))
% 66.49/66.67 (iext uri_rdf_first S3 P3))
% 66.49/66.67 (iext uri_rdf_rest S3 uri_rdf_nil) →
% 66.49/66.67 Iff (iext uri_owl_propertyChainAxiom a S1)
% 66.49/66.67 (And (And (And (And (ip a) (ip P1)) (ip P2)) (ip P3))
% 66.49/66.67 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext P1 Y0 Y1) (iext P2 Y1 Y2)) (iext P3 Y2 Y3) → iext a Y0 Y3)))
% 66.49/66.67 True
% 66.49/66.67 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota),
% 66.49/66.67 Eq
% 66.49/66.67 (∀ (P1 S2 P2 S3 P3 : Iota),
% 66.49/66.67 And
% 66.49/66.67 (And
% 66.49/66.67 (And (And (And (iext uri_rdf_first a P1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 P2))
% 66.49/66.67 (iext uri_rdf_rest S2 S3))
% 66.49/66.67 (iext uri_rdf_first S3 P3))
% 66.49/66.67 (iext uri_rdf_rest S3 uri_rdf_nil) →
% 66.49/66.67 Iff (iext uri_owl_propertyChainAxiom a_1 a)
% 66.49/66.67 (And (And (And (And (ip a_1) (ip P1)) (ip P2)) (ip P3))
% 66.49/66.67 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext P1 Y0 Y1) (iext P2 Y1 Y2)) (iext P3 Y2 Y3) → iext a_1 Y0 Y3)))
% 66.49/66.67 True
% 66.49/66.67 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.67 Eq
% 66.49/66.67 (∀ (S2 P2 S3 P3 : Iota),
% 66.49/66.67 And
% 66.49/66.67 (And
% 66.49/66.67 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 P2))
% 66.49/66.67 (iext uri_rdf_rest S2 S3))
% 66.49/66.67 (iext uri_rdf_first S3 P3))
% 66.49/66.67 (iext uri_rdf_rest S3 uri_rdf_nil) →
% 66.49/66.67 Iff (iext uri_owl_propertyChainAxiom a_2 a)
% 66.49/66.67 (And (And (And (And (ip a_2) (ip a_1)) (ip P2)) (ip P3))
% 66.49/66.67 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext P2 Y1 Y2)) (iext P3 Y2 Y3) → iext a_2 Y0 Y3)))
% 66.49/66.67 True
% 66.49/66.67 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.67 Eq
% 66.49/66.67 (∀ (P2 S3 P3 : Iota),
% 66.49/66.67 And
% 66.49/66.67 (And
% 66.49/66.67 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 P2))
% 66.49/66.67 (iext uri_rdf_rest a_2 S3))
% 66.49/66.67 (iext uri_rdf_first S3 P3))
% 66.49/66.67 (iext uri_rdf_rest S3 uri_rdf_nil) →
% 66.49/66.67 Iff (iext uri_owl_propertyChainAxiom a_3 a)
% 66.49/66.67 (And (And (And (And (ip a_3) (ip a_1)) (ip P2)) (ip P3))
% 66.49/66.67 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext P2 Y1 Y2)) (iext P3 Y2 Y3) → iext a_3 Y0 Y3)))
% 66.49/66.67 True
% 66.49/66.67 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.49/66.67 Eq
% 66.49/66.67 (∀ (S3 P3 : Iota),
% 66.49/66.67 And
% 66.49/66.67 (And
% 66.49/66.67 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 66.49/66.69 (iext uri_rdf_rest a_2 S3))
% 66.49/66.69 (iext uri_rdf_first S3 P3))
% 66.49/66.69 (iext uri_rdf_rest S3 uri_rdf_nil) →
% 66.49/66.69 Iff (iext uri_owl_propertyChainAxiom a_4 a)
% 66.49/66.69 (And (And (And (And (ip a_4) (ip a_1)) (ip a_3)) (ip P3))
% 66.49/66.69 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2)) (iext P3 Y2 Y3) → iext a_4 Y0 Y3)))
% 66.49/66.69 True
% 66.49/66.69 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 66.49/66.69 Eq
% 66.49/66.69 (∀ (P3 : Iota),
% 66.49/66.69 And
% 66.49/66.69 (And
% 66.49/66.69 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 66.49/66.69 (iext uri_rdf_rest a_2 a_4))
% 66.49/66.69 (iext uri_rdf_first a_4 P3))
% 66.49/66.69 (iext uri_rdf_rest a_4 uri_rdf_nil) →
% 66.49/66.69 Iff (iext uri_owl_propertyChainAxiom a_5 a)
% 66.49/66.69 (And (And (And (And (ip a_5) (ip a_1)) (ip a_3)) (ip P3))
% 66.49/66.69 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2)) (iext P3 Y2 Y3) → iext a_5 Y0 Y3)))
% 66.49/66.69 True
% 66.49/66.69 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.49/66.69 Eq
% 66.49/66.69 (And
% 66.49/66.69 (And
% 66.49/66.69 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 66.49/66.69 (iext uri_rdf_rest a_2 a_4))
% 66.49/66.69 (iext uri_rdf_first a_4 a_5))
% 66.49/66.69 (iext uri_rdf_rest a_4 uri_rdf_nil) →
% 66.49/66.69 Iff (iext uri_owl_propertyChainAxiom a_6 a)
% 66.49/66.69 (And (And (And (And (ip a_6) (ip a_1)) (ip a_3)) (ip a_5))
% 66.49/66.69 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2)) (iext a_5 Y2 Y3) → iext a_6 Y0 Y3)))
% 66.49/66.69 True
% 66.49/66.69 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.49/66.69 Or
% 66.49/66.69 (Eq
% 66.49/66.69 (And
% 66.49/66.69 (And
% 66.49/66.69 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 66.49/66.69 (iext uri_rdf_rest a_2 a_4))
% 66.49/66.69 (iext uri_rdf_first a_4 a_5))
% 66.49/66.69 (iext uri_rdf_rest a_4 uri_rdf_nil))
% 66.49/66.69 False)
% 66.49/66.69 (Eq
% 66.49/66.69 (Iff (iext uri_owl_propertyChainAxiom a_6 a)
% 66.49/66.69 (And (And (And (And (ip a_6) (ip a_1)) (ip a_3)) (ip a_5))
% 66.49/66.69 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2)) (iext a_5 Y2 Y3) → iext a_6 Y0 Y3)))
% 66.49/66.69 True)
% 66.49/66.69 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.49/66.69 Or
% 66.49/66.69 (Eq
% 66.49/66.69 (Iff (iext uri_owl_propertyChainAxiom a a_1)
% 66.49/66.69 (And (And (And (And (ip a) (ip a_2)) (ip a_3)) (ip a_4))
% 66.49/66.69 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_2 Y0 Y1) (iext a_3 Y1 Y2)) (iext a_4 Y2 Y3) → iext a Y0 Y3)))
% 66.49/66.69 True)
% 66.49/66.69 (Or
% 66.49/66.69 (Eq
% 66.49/66.69 (And
% 66.49/66.69 (And (And (And (iext uri_rdf_first a_1 a_2) (iext uri_rdf_rest a_1 a_5)) (iext uri_rdf_first a_5 a_3))
% 66.49/66.69 (iext uri_rdf_rest a_5 a_6))
% 66.49/66.69 (iext uri_rdf_first a_6 a_4))
% 66.49/66.69 False)
% 66.49/66.69 (Eq (iext uri_rdf_rest a_6 uri_rdf_nil) False))
% 66.49/66.69 Clause #90 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.49/66.69 Or
% 66.49/66.69 (Eq
% 66.49/66.69 (And
% 66.49/66.69 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3))
% 66.49/66.69 (iext uri_rdf_rest a_2 a_4))
% 66.49/66.69 (iext uri_rdf_first a_4 a_5))
% 66.49/66.69 False)
% 66.49/66.69 (Or (Eq (iext uri_rdf_rest a_4 uri_rdf_nil) False)
% 66.49/66.69 (Or (Eq (iext uri_owl_propertyChainAxiom a_6 a) False)
% 66.49/66.69 (Eq
% 66.49/66.69 (And (And (And (And (ip a_6) (ip a_1)) (ip a_3)) (ip a_5))
% 66.49/66.69 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2)) (iext a_5 Y2 Y3) → iext a_6 Y0 Y3))
% 66.49/66.69 True)))
% 66.49/66.69 Clause #111 (by clausification #[71]): ∀ (a a_1 : Iota),
% 66.49/66.69 Or (Eq (iext uri_owl_inverseOf a a_1) False) (Eq (∀ (X Y : Iota), Iff (iext a X Y) (iext a_1 Y X)) True)
% 66.49/66.69 Clause #113 (by clausification #[111]): ∀ (a a_1 a_2 : Iota),
% 66.49/66.69 Or (Eq (iext uri_owl_inverseOf a a_1) False) (Eq (∀ (Y : Iota), Iff (iext a a_2 Y) (iext a_1 Y a_2)) True)
% 66.49/66.69 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.69 Or (Eq (iext uri_owl_inverseOf a a_1) False) (Eq (Iff (iext a a_2 a_3) (iext a_1 a_3 a_2)) True)
% 66.49/66.69 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.49/66.69 Or (Eq (iext uri_owl_inverseOf a a_1) False) (Or (Eq (iext a a_2 a_3) True) (Eq (iext a_1 a_3 a_2) False))
% 66.49/66.70 Clause #119 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.49/66.70 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 66.49/66.70 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 66.49/66.70 (Or (Eq (icext a a_3) False)
% 66.49/66.70 (Eq (And (iext a_2 a_3 (skS.0 9 a_2 a_3 a_1 a_4)) (icext a_1 (skS.0 9 a_2 a_3 a_1 a_4))) True)))
% 66.49/66.70 Clause #121 (by clausification #[119]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.49/66.70 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 66.49/66.70 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 66.49/66.70 (Or (Eq (icext a a_3) False) (Eq (iext a_2 a_3 (skS.0 9 a_2 a_3 a_1 a_4)) True)))
% 66.49/66.70 Clause #122 (by clausification #[8]): ∀ (a : Iota),
% 66.49/66.70 Eq
% 66.49/66.70 (Exists fun BNODE_i =>
% 66.49/66.70 Exists fun BNODE_l1 =>
% 66.49/66.70 Exists fun BNODE_l2 =>
% 66.49/66.70 Exists fun BNODE_l3 =>
% 66.49/66.70 And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.49/66.70 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.49/66.70 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.49/66.70 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.49/66.70 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.49/66.70 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.49/66.70 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.49/66.70 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.49/66.70 (iext uri_owl_propertyChainAxiom uri_foaf_knows BNODE_l1))
% 66.49/66.70 (iext uri_rdf_first BNODE_l1 uri_rdf_type))
% 66.49/66.70 (iext uri_rdf_rest BNODE_l1 BNODE_l2))
% 66.49/66.70 (iext uri_rdf_first BNODE_l2 uri_ex_sameCliqueAs))
% 66.49/66.70 (iext uri_rdf_rest BNODE_l2 BNODE_l3))
% 66.49/66.70 (iext uri_rdf_first BNODE_l3 BNODE_i))
% 66.49/66.70 (iext uri_rdf_rest BNODE_l3 uri_rdf_nil))
% 66.49/66.70 (iext uri_owl_inverseOf BNODE_i uri_rdf_type))
% 66.49/66.70 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.49/66.70 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.49/66.70 (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang))
% 66.49/66.70 True
% 66.49/66.70 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota),
% 66.49/66.70 Eq
% 66.49/66.70 (Exists fun BNODE_l1 =>
% 66.49/66.70 Exists fun BNODE_l2 =>
% 66.49/66.70 Exists fun BNODE_l3 =>
% 66.49/66.70 And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And
% 66.49/66.70 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.49/66.70 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.49/66.70 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.49/66.70 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.49/66.70 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.71 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.71 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.71 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.71 (iext uri_owl_propertyChainAxiom uri_foaf_knows BNODE_l1))
% 66.56/66.71 (iext uri_rdf_first BNODE_l1 uri_rdf_type))
% 66.56/66.71 (iext uri_rdf_rest BNODE_l1 BNODE_l2))
% 66.56/66.71 (iext uri_rdf_first BNODE_l2 uri_ex_sameCliqueAs))
% 66.56/66.71 (iext uri_rdf_rest BNODE_l2 BNODE_l3))
% 66.56/66.71 (iext uri_rdf_first BNODE_l3 (skS.0 11 a a_1)))
% 66.56/66.71 (iext uri_rdf_rest BNODE_l3 uri_rdf_nil))
% 66.56/66.71 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.71 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.56/66.71 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.56/66.71 (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang))
% 66.56/66.71 True
% 66.56/66.71 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota),
% 66.56/66.71 Eq
% 66.56/66.71 (Exists fun BNODE_l2 =>
% 66.56/66.71 Exists fun BNODE_l3 =>
% 66.56/66.71 And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.71 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.71 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.71 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.71 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.71 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.71 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.71 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.71 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.71 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.71 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) BNODE_l2))
% 66.56/66.71 (iext uri_rdf_first BNODE_l2 uri_ex_sameCliqueAs))
% 66.56/66.71 (iext uri_rdf_rest BNODE_l2 BNODE_l3))
% 66.56/66.71 (iext uri_rdf_first BNODE_l3 (skS.0 11 a a_1)))
% 66.56/66.71 (iext uri_rdf_rest BNODE_l3 uri_rdf_nil))
% 66.56/66.71 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.71 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.56/66.71 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.56/66.71 (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang))
% 66.56/66.71 True
% 66.56/66.71 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.56/66.71 Eq
% 66.56/66.71 (Exists fun BNODE_l3 =>
% 66.56/66.71 And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And
% 66.56/66.71 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.71 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.71 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.72 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.72 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.72 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.72 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.72 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.72 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.72 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.72 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.72 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.72 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) BNODE_l3))
% 66.56/66.72 (iext uri_rdf_first BNODE_l3 (skS.0 11 a a_1)))
% 66.56/66.72 (iext uri_rdf_rest BNODE_l3 uri_rdf_nil))
% 66.56/66.72 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.72 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.56/66.72 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.56/66.72 (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang))
% 66.56/66.72 True
% 66.56/66.72 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.72 Eq
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.72 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.72 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.72 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.72 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.72 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.72 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.72 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.72 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.72 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.72 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.72 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.72 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.72 (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)))
% 66.56/66.72 (iext uri_rdf_rest (skS.0 14 a a_1 a_2 a_3 a_4) uri_rdf_nil))
% 66.56/66.72 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.72 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.56/66.72 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.56/66.72 (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang))
% 66.56/66.72 True
% 66.56/66.72 Clause #127 (by clausification #[126]): Eq (iext uri_rdf_type uri_ex_bob uri_ex_JoesGang) True
% 66.56/66.72 Clause #128 (by clausification #[126]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.72 Eq
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And
% 66.56/66.72 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.72 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.74 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.74 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.74 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.74 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.74 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.74 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.74 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.74 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.74 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.74 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.74 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.74 (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)))
% 66.56/66.74 (iext uri_rdf_rest (skS.0 14 a a_1 a_2 a_3 a_4) uri_rdf_nil))
% 66.56/66.74 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.74 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.56/66.74 (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang))
% 66.56/66.74 True
% 66.56/66.74 Clause #132 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.56/66.74 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.74 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.74 (Or
% 66.56/66.74 (Eq
% 66.56/66.74 (And (And (And (And (ip a_1) (ip a_3)) (ip a_4)) (ip a_5))
% 66.56/66.74 (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_3 Y0 Y1) (iext a_4 Y1 Y2)) (iext a_5 Y2 Y3) → iext a_1 Y0 Y3))
% 66.56/66.74 True)
% 66.56/66.74 (Or
% 66.56/66.74 (Eq
% 66.56/66.74 (And (And (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a_6)) (iext uri_rdf_first a_6 a_4))
% 66.56/66.74 (iext uri_rdf_rest a_6 a))
% 66.56/66.74 False)
% 66.56/66.74 (Eq (iext uri_rdf_first a a_5) False))))
% 66.56/66.74 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.56/66.74 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.74 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.74 (Or
% 66.56/66.74 (Eq
% 66.56/66.74 (And (And (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a_4)) (iext uri_rdf_first a_4 a_5))
% 66.56/66.74 (iext uri_rdf_rest a_4 a))
% 66.56/66.74 False)
% 66.56/66.74 (Or (Eq (iext uri_rdf_first a a_6) False)
% 66.56/66.74 (Eq (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_3 Y0 Y1) (iext a_5 Y1 Y2)) (iext a_6 Y2 Y3) → iext a_1 Y0 Y3)
% 66.56/66.74 True))))
% 66.56/66.74 Clause #135 (by clausification #[133]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 66.56/66.74 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.74 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.74 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.74 (Or
% 66.56/66.74 (Eq (∀ (Y0 Y1 Y2 Y3 : Iota), And (And (iext a_4 Y0 Y1) (iext a_5 Y1 Y2)) (iext a_3 Y2 Y3) → iext a_1 Y0 Y3)
% 66.56/66.74 True)
% 66.56/66.74 (Or
% 66.56/66.74 (Eq (And (And (iext uri_rdf_first a_2 a_4) (iext uri_rdf_rest a_2 a_6)) (iext uri_rdf_first a_6 a_5)) False)
% 66.56/66.74 (Eq (iext uri_rdf_rest a_6 a) False)))))
% 66.56/66.74 Clause #136 (by clausification #[135]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 66.56/66.74 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.74 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.74 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.74 (Or (Eq (And (And (iext uri_rdf_first a_2 a_4) (iext uri_rdf_rest a_2 a_5)) (iext uri_rdf_first a_5 a_6)) False)
% 66.56/66.74 (Or (Eq (iext uri_rdf_rest a_5 a) False)
% 66.56/66.74 (Eq (∀ (Y1 Y2 Y3 : Iota), And (And (iext a_4 a_7 Y1) (iext a_6 Y1 Y2)) (iext a_3 Y2 Y3) → iext a_1 a_7 Y3)
% 66.56/66.74 True)))))
% 66.56/66.74 Clause #137 (by clausification #[136]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 66.56/66.74 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.74 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.74 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.74 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.74 (Or
% 66.56/66.76 (Eq (∀ (Y1 Y2 Y3 : Iota), And (And (iext a_5 a_6 Y1) (iext a_7 Y1 Y2)) (iext a_3 Y2 Y3) → iext a_1 a_6 Y3)
% 66.56/66.76 True)
% 66.56/66.76 (Or (Eq (And (iext uri_rdf_first a_2 a_5) (iext uri_rdf_rest a_2 a_4)) False)
% 66.56/66.76 (Eq (iext uri_rdf_first a_4 a_7) False))))))
% 66.56/66.76 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 66.56/66.76 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.76 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.76 (Or (Eq (And (iext uri_rdf_first a_2 a_5) (iext uri_rdf_rest a_2 a_4)) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_4 a_6) False)
% 66.56/66.76 (Eq (∀ (Y2 Y3 : Iota), And (And (iext a_5 a_7 a_8) (iext a_6 a_8 Y2)) (iext a_3 Y2 Y3) → iext a_1 a_7 Y3)
% 66.56/66.76 True))))))
% 66.56/66.76 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 66.56/66.76 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.76 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_4 a_5) False)
% 66.56/66.76 (Or
% 66.56/66.76 (Eq (∀ (Y2 Y3 : Iota), And (And (iext a_6 a_7 a_8) (iext a_5 a_8 Y2)) (iext a_3 Y2 Y3) → iext a_1 a_7 Y3)
% 66.56/66.76 True)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_2 a_6) False) (Eq (iext uri_rdf_rest a_2 a_4) False)))))))
% 66.56/66.76 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota),
% 66.56/66.76 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.76 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_4 a_5) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_2 a_6) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_2 a_4) False)
% 66.56/66.76 (Eq (∀ (Y3 : Iota), And (And (iext a_6 a_7 a_8) (iext a_5 a_8 a_9)) (iext a_3 a_9 Y3) → iext a_1 a_7 Y3)
% 66.56/66.76 True)))))))
% 66.56/66.76 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 66.56/66.76 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.76 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_4 a_5) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_2 a_6) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_2 a_4) False)
% 66.56/66.76 (Eq (And (And (iext a_6 a_7 a_8) (iext a_5 a_8 a_9)) (iext a_3 a_9 a_10) → iext a_1 a_7 a_10)
% 66.56/66.76 True)))))))
% 66.56/66.76 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 66.56/66.76 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.76 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_4 a_5) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_2 a_6) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_2 a_4) False)
% 66.56/66.76 (Or (Eq (And (And (iext a_6 a_7 a_8) (iext a_5 a_8 a_9)) (iext a_3 a_9 a_10)) False)
% 66.56/66.76 (Eq (iext a_1 a_7 a_10) True))))))))
% 66.56/66.76 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 66.56/66.76 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.76 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_4 a_5) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_first a_2 a_6) False)
% 66.56/66.76 (Or (Eq (iext uri_rdf_rest a_2 a_4) False)
% 66.56/66.76 (Or (Eq (iext a_1 a_7 a_8) True)
% 66.56/66.76 (Or (Eq (And (iext a_6 a_7 a_9) (iext a_5 a_9 a_10)) False) (Eq (iext a_3 a_10 a_8) False)))))))))
% 66.56/66.76 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 66.56/66.77 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 66.56/66.77 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 66.56/66.77 (Or (Eq (iext uri_rdf_first a a_3) False)
% 66.56/66.77 (Or (Eq (iext uri_rdf_rest a_4 a) False)
% 66.56/66.77 (Or (Eq (iext uri_rdf_first a_4 a_5) False)
% 66.56/66.77 (Or (Eq (iext uri_rdf_first a_2 a_6) False)
% 66.56/66.77 (Or (Eq (iext uri_rdf_rest a_2 a_4) False)
% 66.56/66.77 (Or (Eq (iext a_1 a_7 a_8) True)
% 66.56/66.77 (Or (Eq (iext a_3 a_9 a_8) False)
% 66.56/66.77 (Or (Eq (iext a_6 a_7 a_10) False) (Eq (iext a_5 a_10 a_9) False))))))))))
% 66.56/66.77 Clause #159 (by clausification #[128]): Eq (iext uri_rdf_type uri_ex_alice uri_ex_JoesGang) True
% 66.56/66.77 Clause #160 (by clausification #[128]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.77 Eq
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.77 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.77 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.77 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.77 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.77 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.77 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.77 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.77 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.77 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.77 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.77 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.77 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.77 (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)))
% 66.56/66.77 (iext uri_rdf_rest (skS.0 14 a a_1 a_2 a_3 a_4) uri_rdf_nil))
% 66.56/66.77 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.77 (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique))
% 66.56/66.77 True
% 66.56/66.77 Clause #164 (by clausification #[160]): Eq (iext uri_rdf_type uri_ex_JoesGang uri_ex_Clique) True
% 66.56/66.77 Clause #165 (by clausification #[160]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.77 Eq
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And
% 66.56/66.77 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.77 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.77 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.77 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.77 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.77 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.77 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.77 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.77 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.77 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.77 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.77 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.77 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.78 (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)))
% 66.56/66.78 (iext uri_rdf_rest (skS.0 14 a a_1 a_2 a_3 a_4) uri_rdf_nil))
% 66.56/66.78 (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type))
% 66.56/66.78 True
% 66.56/66.78 Clause #166 (by superposition #[164, 13]): Or (Eq True False) (Eq (icext uri_ex_Clique uri_ex_JoesGang) True)
% 66.56/66.78 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Eq (iext uri_owl_inverseOf (skS.0 11 a a_1) uri_rdf_type) True
% 66.56/66.78 Clause #168 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.78 Eq
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.78 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.78 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.78 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.78 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.78 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.78 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.78 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.78 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.78 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.78 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.78 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.78 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.78 (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)))
% 66.56/66.78 (iext uri_rdf_rest (skS.0 14 a a_1 a_2 a_3 a_4) uri_rdf_nil))
% 66.56/66.78 True
% 66.56/66.78 Clause #169 (by superposition #[167, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.56/66.78 Or (Eq True False) (Or (Eq (iext (skS.0 11 a a_1) a_2 a_3) True) (Eq (iext uri_rdf_type a_3 a_2) False))
% 66.56/66.78 Clause #178 (by clausification #[166]): Eq (icext uri_ex_Clique uri_ex_JoesGang) True
% 66.56/66.78 Clause #185 (by clausification #[169]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (iext (skS.0 11 a a_1) a_2 a_3) True) (Eq (iext uri_rdf_type a_3 a_2) False)
% 66.56/66.78 Clause #186 (by superposition #[185, 127]): ∀ (a a_1 : Iota), Or (Eq (iext (skS.0 11 a a_1) uri_ex_JoesGang uri_ex_bob) True) (Eq False True)
% 66.56/66.78 Clause #189 (by clausification #[168]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (iext uri_rdf_rest (skS.0 14 a a_1 a_2 a_3 a_4) uri_rdf_nil) True
% 66.56/66.78 Clause #190 (by clausification #[168]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.78 Eq
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And
% 66.56/66.78 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.78 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.78 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.78 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.78 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.78 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.78 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.78 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.78 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.78 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.78 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.78 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.78 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.80 (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)))
% 66.56/66.80 True
% 66.56/66.80 Clause #192 (by superposition #[189, 144]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 a_13 a_14 : Iota),
% 66.56/66.80 Or (Eq True False)
% 66.56/66.80 (Or (Eq (iext uri_owl_propertyChainAxiom a a_1) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_first (skS.0 14 a_2 a_3 a_4 a_5 a_6) a_7) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_rest a_8 (skS.0 14 a_2 a_3 a_4 a_5 a_6)) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_first a_8 a_9) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_first a_1 a_10) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_rest a_1 a_8) False)
% 66.56/66.80 (Or (Eq (iext a a_11 a_12) True)
% 66.56/66.80 (Or (Eq (iext a_7 a_13 a_12) False)
% 66.56/66.80 (Or (Eq (iext a_10 a_11 a_14) False) (Eq (iext a_9 a_14 a_13) False))))))))))
% 66.56/66.80 Clause #202 (by clausification #[186]): ∀ (a a_1 : Iota), Eq (iext (skS.0 11 a a_1) uri_ex_JoesGang uri_ex_bob) True
% 66.56/66.80 Clause #274 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) (skS.0 11 a a_1)) True
% 66.56/66.80 Clause #275 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 66.56/66.80 Eq
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.80 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.80 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.80 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.80 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.80 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.80 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.80 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.80 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.80 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.80 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.80 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.80 (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)))
% 66.56/66.80 True
% 66.56/66.80 Clause #289 (by clausification #[192]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 a_13 a_14 : Iota),
% 66.56/66.80 Or (Eq (iext uri_owl_propertyChainAxiom a a_1) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_first (skS.0 14 a_2 a_3 a_4 a_5 a_6) a_7) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_rest a_8 (skS.0 14 a_2 a_3 a_4 a_5 a_6)) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_first a_8 a_9) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_first a_1 a_10) False)
% 66.56/66.80 (Or (Eq (iext uri_rdf_rest a_1 a_8) False)
% 66.56/66.80 (Or (Eq (iext a a_11 a_12) True)
% 66.56/66.80 (Or (Eq (iext a_7 a_13 a_12) False)
% 66.56/66.80 (Or (Eq (iext a_10 a_11 a_14) False) (Eq (iext a_9 a_14 a_13) False)))))))))
% 66.56/66.80 Clause #384 (by clausification #[275]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (iext uri_rdf_rest (skS.0 13 a a_1 a_2 a_3) (skS.0 14 a a_1 a_2 a_3 a_4)) True
% 66.56/66.80 Clause #385 (by clausification #[275]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.56/66.80 Eq
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And
% 66.56/66.80 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.80 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.80 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.80 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.80 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.80 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.80 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.80 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.82 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.82 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.82 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.82 (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs))
% 66.56/66.82 True
% 66.56/66.82 Clause #401 (by clausification #[385]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) uri_ex_sameCliqueAs) True
% 66.56/66.82 Clause #402 (by clausification #[385]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.56/66.82 Eq
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.82 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.82 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.82 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.82 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.82 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.82 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.82 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.82 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.82 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.82 (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)))
% 66.56/66.82 True
% 66.56/66.82 Clause #414 (by clausification #[402]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a a_1 a_2 a_3)) True
% 66.56/66.82 Clause #415 (by clausification #[402]): ∀ (a a_1 a_2 : Iota),
% 66.56/66.82 Eq
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.82 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.82 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.82 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.82 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.82 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.82 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.82 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.82 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.82 (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type))
% 66.56/66.82 True
% 66.56/66.82 Clause #416 (by clausification #[415]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_rdf_first (skS.0 12 a a_1 a_2) uri_rdf_type) True
% 66.56/66.82 Clause #417 (by clausification #[415]): ∀ (a a_1 a_2 : Iota),
% 66.56/66.82 Eq
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.82 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.82 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.82 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.82 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.82 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.82 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.82 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.82 (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)))
% 66.56/66.82 True
% 66.56/66.82 Clause #418 (by clausification #[417]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_owl_propertyChainAxiom uri_foaf_knows (skS.0 12 a a_1 a_2)) True
% 66.56/66.82 Clause #419 (by clausification #[417]): ∀ (a : Iota),
% 66.56/66.82 Eq
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And
% 66.56/66.82 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.82 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.82 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.83 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.83 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.83 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.83 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.83 (iext uri_rdf_type uri_foaf_knows uri_owl_ObjectProperty))
% 66.56/66.83 True
% 66.56/66.83 Clause #424 (by superposition #[418, 289]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 a_13 a_14 a_15 : Iota),
% 66.56/66.83 Or (Eq True False)
% 66.56/66.83 (Or (Eq (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) a_5) False)
% 66.56/66.83 (Or (Eq (iext uri_rdf_rest a_6 (skS.0 14 a a_1 a_2 a_3 a_4)) False)
% 66.56/66.83 (Or (Eq (iext uri_rdf_first a_6 a_7) False)
% 66.56/66.83 (Or (Eq (iext uri_rdf_first (skS.0 12 a_8 a_9 a_10) a_11) False)
% 66.56/66.83 (Or (Eq (iext uri_rdf_rest (skS.0 12 a_8 a_9 a_10) a_6) False)
% 66.56/66.83 (Or (Eq (iext uri_foaf_knows a_12 a_13) True)
% 66.56/66.83 (Or (Eq (iext a_5 a_14 a_13) False)
% 66.56/66.83 (Or (Eq (iext a_11 a_12 a_15) False) (Eq (iext a_7 a_15 a_14) False)))))))))
% 66.56/66.83 Clause #429 (by clausification #[419]): ∀ (a : Iota),
% 66.56/66.83 Eq
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.83 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.83 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.83 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.83 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.83 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.83 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique))
% 66.56/66.83 True
% 66.56/66.83 Clause #439 (by clausification #[429]): ∀ (a : Iota), Eq (iext uri_owl_someValuesFrom (skS.0 10 a) uri_ex_Clique) True
% 66.56/66.83 Clause #440 (by clausification #[429]): ∀ (a : Iota),
% 66.56/66.83 Eq
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.83 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.83 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.83 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.83 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.83 (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs))
% 66.56/66.83 True
% 66.56/66.83 Clause #443 (by superposition #[439, 121]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.56/66.83 Or (Eq True False)
% 66.56/66.83 (Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False)
% 66.56/66.83 (Or (Eq (icext (skS.0 10 a) a_2) False) (Eq (iext a_1 a_2 (skS.0 9 a_1 a_2 uri_ex_Clique a_3)) True)))
% 66.56/66.83 Clause #446 (by clausification #[443]): ∀ (a a_1 a_2 a_3 : Iota),
% 66.56/66.83 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False)
% 66.56/66.83 (Or (Eq (icext (skS.0 10 a) a_2) False) (Eq (iext a_1 a_2 (skS.0 9 a_1 a_2 uri_ex_Clique a_3)) True))
% 66.56/66.83 Clause #449 (by clausification #[440]): ∀ (a : Iota), Eq (iext uri_owl_onProperty (skS.0 10 a) uri_ex_sameCliqueAs) True
% 66.56/66.83 Clause #450 (by clausification #[440]): ∀ (a : Iota),
% 66.56/66.83 Eq
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.83 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.83 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.83 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.83 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 66.56/66.83 True
% 66.56/66.83 Clause #453 (by superposition #[449, 446]): ∀ (a a_1 a_2 : Iota),
% 66.56/66.83 Or (Eq True False)
% 66.56/66.83 (Or (Eq (icext (skS.0 10 a) a_1) False)
% 66.56/66.83 (Eq (iext uri_ex_sameCliqueAs a_1 (skS.0 9 uri_ex_sameCliqueAs a_1 uri_ex_Clique a_2)) True))
% 66.56/66.83 Clause #456 (by clausification #[453]): ∀ (a a_1 a_2 : Iota),
% 66.56/66.83 Or (Eq (icext (skS.0 10 a) a_1) False)
% 66.56/66.83 (Eq (iext uri_ex_sameCliqueAs a_1 (skS.0 9 uri_ex_sameCliqueAs a_1 uri_ex_Clique a_2)) True)
% 66.56/66.83 Clause #458 (by clausification #[450]): ∀ (a : Iota),
% 66.56/66.83 Eq
% 66.56/66.83 (And
% 66.56/66.83 (And
% 66.56/66.83 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.83 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.83 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.83 (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)))
% 66.56/66.85 True
% 66.56/66.85 Clause #467 (by clausification #[458]): ∀ (a : Iota), Eq (iext uri_rdfs_subClassOf uri_ex_Clique (skS.0 10 a)) True
% 66.56/66.85 Clause #468 (by clausification #[458]): Eq
% 66.56/66.85 (And
% 66.56/66.85 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class)
% 66.56/66.85 (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.85 (iext uri_rdfs_range uri_ex_sameCliqueAs uri_ex_Clique))
% 66.56/66.85 True
% 66.56/66.85 Clause #469 (by superposition #[467, 46]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (icext uri_ex_Clique a) False) (Eq (icext (skS.0 10 a_1) a) True))
% 66.56/66.85 Clause #478 (by clausification #[469]): ∀ (a a_1 : Iota), Or (Eq (icext uri_ex_Clique a) False) (Eq (icext (skS.0 10 a_1) a) True)
% 66.56/66.85 Clause #479 (by superposition #[478, 178]): ∀ (a : Iota), Or (Eq (icext (skS.0 10 a) uri_ex_JoesGang) True) (Eq False True)
% 66.56/66.85 Clause #480 (by clausification #[479]): ∀ (a : Iota), Eq (icext (skS.0 10 a) uri_ex_JoesGang) True
% 66.56/66.85 Clause #482 (by superposition #[480, 456]): ∀ (a : Iota),
% 66.56/66.85 Or (Eq True False)
% 66.56/66.85 (Eq (iext uri_ex_sameCliqueAs uri_ex_JoesGang (skS.0 9 uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_Clique a)) True)
% 66.56/66.85 Clause #491 (by clausification #[468]): Eq
% 66.56/66.85 (And (iext uri_rdf_type uri_ex_Clique uri_owl_Class) (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs))
% 66.56/66.85 True
% 66.56/66.85 Clause #492 (by clausification #[491]): Eq (iext uri_rdfs_subPropertyOf uri_ex_sameCliqueAs uri_owl_sameAs) True
% 66.56/66.85 Clause #494 (by superposition #[492, 65]): ∀ (a a_1 : Iota),
% 66.56/66.85 Or (Eq True False) (Or (Eq (iext uri_ex_sameCliqueAs a a_1) False) (Eq (iext uri_owl_sameAs a a_1) True))
% 66.56/66.85 Clause #532 (by clausification #[494]): ∀ (a a_1 : Iota), Or (Eq (iext uri_ex_sameCliqueAs a a_1) False) (Eq (iext uri_owl_sameAs a a_1) True)
% 66.56/66.85 Clause #540 (by clausification #[482]): ∀ (a : Iota),
% 66.56/66.85 Eq (iext uri_ex_sameCliqueAs uri_ex_JoesGang (skS.0 9 uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_Clique a)) True
% 66.56/66.85 Clause #542 (by superposition #[540, 532]): ∀ (a : Iota),
% 66.56/66.85 Or (Eq True False)
% 66.56/66.85 (Eq (iext uri_owl_sameAs uri_ex_JoesGang (skS.0 9 uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_Clique a)) True)
% 66.56/66.85 Clause #544 (by clausification #[542]): ∀ (a : Iota),
% 66.56/66.85 Eq (iext uri_owl_sameAs uri_ex_JoesGang (skS.0 9 uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_Clique a)) True
% 66.56/66.85 Clause #545 (by superposition #[544, 20]): ∀ (a : Iota), Or (Eq True False) (Eq uri_ex_JoesGang (skS.0 9 uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_Clique a))
% 66.56/66.85 Clause #546 (by clausification #[545]): ∀ (a : Iota), Eq uri_ex_JoesGang (skS.0 9 uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_Clique a)
% 66.56/66.85 Clause #547 (by backward demodulation #[546, 540]): Eq (iext uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_JoesGang) True
% 66.56/66.85 Clause #592 (by clausification #[424]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 a_13 a_14 a_15 : Iota),
% 66.56/66.85 Or (Eq (iext uri_rdf_first (skS.0 14 a a_1 a_2 a_3 a_4) a_5) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_rest a_6 (skS.0 14 a a_1 a_2 a_3 a_4)) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_first a_6 a_7) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_first (skS.0 12 a_8 a_9 a_10) a_11) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_rest (skS.0 12 a_8 a_9 a_10) a_6) False)
% 66.56/66.85 (Or (Eq (iext uri_foaf_knows a_12 a_13) True)
% 66.56/66.85 (Or (Eq (iext a_5 a_14 a_13) False)
% 66.56/66.85 (Or (Eq (iext a_11 a_12 a_15) False) (Eq (iext a_7 a_15 a_14) False))))))))
% 66.56/66.85 Clause #593 (by superposition #[592, 274]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 a_13 a_14 : Iota),
% 66.56/66.85 Or (Eq (iext uri_rdf_rest a (skS.0 14 a_1 a_2 a_3 a_4 a_5)) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_first a a_6) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_first (skS.0 12 a_7 a_8 a_9) a_10) False)
% 66.56/66.85 (Or (Eq (iext uri_rdf_rest (skS.0 12 a_7 a_8 a_9) a) False)
% 66.56/66.85 (Or (Eq (iext uri_foaf_knows a_11 a_12) True)
% 66.56/66.85 (Or (Eq (iext (skS.0 11 a_1 a_2) a_13 a_12) False)
% 66.56/66.85 (Or (Eq (iext a_10 a_11 a_14) False) (Or (Eq (iext a_6 a_14 a_13) False) (Eq False True))))))))
% 66.56/66.85 Clause #931 (by clausification #[593]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 a_13 a_14 : Iota),
% 66.56/66.85 Or (Eq (iext uri_rdf_rest a (skS.0 14 a_1 a_2 a_3 a_4 a_5)) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_first a a_6) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_first (skS.0 12 a_7 a_8 a_9) a_10) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_rest (skS.0 12 a_7 a_8 a_9) a) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_11 a_12) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_1 a_2) a_13 a_12) False)
% 66.56/66.88 (Or (Eq (iext a_10 a_11 a_14) False) (Eq (iext a_6 a_14 a_13) False)))))))
% 66.56/66.88 Clause #932 (by superposition #[931, 384]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 : Iota),
% 66.56/66.88 Or (Eq (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) a_4) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_first (skS.0 12 a_5 a_6 a_7) a_8) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_rest (skS.0 12 a_5 a_6 a_7) (skS.0 13 a a_1 a_2 a_3)) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_9 a_10) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a a_1) a_11 a_10) False)
% 66.56/66.88 (Or (Eq (iext a_8 a_9 a_12) False) (Or (Eq (iext a_4 a_12 a_11) False) (Eq False True)))))))
% 66.56/66.88 Clause #1400 (by clausification #[932]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 a_12 : Iota),
% 66.56/66.88 Or (Eq (iext uri_rdf_first (skS.0 13 a a_1 a_2 a_3) a_4) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_first (skS.0 12 a_5 a_6 a_7) a_8) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_rest (skS.0 12 a_5 a_6 a_7) (skS.0 13 a a_1 a_2 a_3)) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_9 a_10) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a a_1) a_11 a_10) False)
% 66.56/66.88 (Or (Eq (iext a_8 a_9 a_12) False) (Eq (iext a_4 a_12 a_11) False))))))
% 66.56/66.88 Clause #1401 (by superposition #[1400, 401]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 : Iota),
% 66.56/66.88 Or (Eq (iext uri_rdf_first (skS.0 12 a a_1 a_2) a_3) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a_4 a_5 a_6 a_7)) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_8 a_9) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_4 a_5) a_10 a_9) False)
% 66.56/66.88 (Or (Eq (iext a_3 a_8 a_11) False) (Or (Eq (iext uri_ex_sameCliqueAs a_11 a_10) False) (Eq False True))))))
% 66.56/66.88 Clause #1685 (by clausification #[1401]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 : Iota),
% 66.56/66.88 Or (Eq (iext uri_rdf_first (skS.0 12 a a_1 a_2) a_3) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a_4 a_5 a_6 a_7)) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_8 a_9) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_4 a_5) a_10 a_9) False)
% 66.56/66.88 (Or (Eq (iext a_3 a_8 a_11) False) (Eq (iext uri_ex_sameCliqueAs a_11 a_10) False)))))
% 66.56/66.88 Clause #1686 (by superposition #[1685, 416]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 66.56/66.88 Or (Eq (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a_3 a_4 a_5 a_6)) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_7 a_8) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_3 a_4) a_9 a_8) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_type a_7 a_10) False)
% 66.56/66.88 (Or (Eq (iext uri_ex_sameCliqueAs a_10 a_9) False) (Eq False True)))))
% 66.56/66.88 Clause #1690 (by clausification #[1686]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 66.56/66.88 Or (Eq (iext uri_rdf_rest (skS.0 12 a a_1 a_2) (skS.0 13 a_3 a_4 a_5 a_6)) False)
% 66.56/66.88 (Or (Eq (iext uri_foaf_knows a_7 a_8) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_3 a_4) a_9 a_8) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_type a_7 a_10) False) (Eq (iext uri_ex_sameCliqueAs a_10 a_9) False))))
% 66.56/66.88 Clause #1691 (by superposition #[1690, 414]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 66.56/66.88 Or (Eq (iext uri_foaf_knows a a_1) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_2 a_3) a_4 a_1) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_type a a_5) False) (Or (Eq (iext uri_ex_sameCliqueAs a_5 a_4) False) (Eq False True))))
% 66.56/66.88 Clause #1692 (by clausification #[1691]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 66.56/66.88 Or (Eq (iext uri_foaf_knows a a_1) True)
% 66.56/66.88 (Or (Eq (iext (skS.0 11 a_2 a_3) a_4 a_1) False)
% 66.56/66.88 (Or (Eq (iext uri_rdf_type a a_5) False) (Eq (iext uri_ex_sameCliqueAs a_5 a_4) False)))
% 66.56/66.88 Clause #1695 (by superposition #[1692, 202]): ∀ (a a_1 : Iota),
% 66.56/66.88 Or (Eq (iext uri_foaf_knows a uri_ex_bob) True)
% 66.56/66.88 (Or (Eq (iext uri_rdf_type a a_1) False)
% 66.56/66.88 (Or (Eq (iext uri_ex_sameCliqueAs a_1 uri_ex_JoesGang) False) (Eq False True)))
% 66.56/66.88 Clause #1759 (by clausification #[1695]): ∀ (a a_1 : Iota),
% 66.56/66.89 Or (Eq (iext uri_foaf_knows a uri_ex_bob) True)
% 66.56/66.89 (Or (Eq (iext uri_rdf_type a a_1) False) (Eq (iext uri_ex_sameCliqueAs a_1 uri_ex_JoesGang) False))
% 66.56/66.89 Clause #1761 (by superposition #[1759, 159]): Or (Eq (iext uri_foaf_knows uri_ex_alice uri_ex_bob) True)
% 66.56/66.89 (Or (Eq (iext uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_JoesGang) False) (Eq False True))
% 66.56/66.89 Clause #1790 (by clausification #[1761]): Or (Eq (iext uri_foaf_knows uri_ex_alice uri_ex_bob) True)
% 66.56/66.89 (Eq (iext uri_ex_sameCliqueAs uri_ex_JoesGang uri_ex_JoesGang) False)
% 66.56/66.89 Clause #1791 (by forward demodulation #[1790, 547]): Or (Eq (iext uri_foaf_knows uri_ex_alice uri_ex_bob) True) (Eq True False)
% 66.56/66.89 Clause #1792 (by clausification #[1791]): Eq (iext uri_foaf_knows uri_ex_alice uri_ex_bob) True
% 66.56/66.89 Clause #1793 (by superposition #[1792, 9]): Eq True False
% 66.56/66.89 Clause #1794 (by clausification #[1793]): False
% 66.56/66.89 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------