TSTP Solution File: SWB025+2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWB025+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 20:04:06 EDT 2023
% Result : Theorem 12.34s 12.57s
% Output : Proof 12.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWB025+2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.07 % Command : duper %s
% 0.06/0.26 % Computer : n023.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Sun Aug 27 07:21:56 EDT 2023
% 0.06/0.26 % CPUTime :
% 12.34/12.57 SZS status Theorem for theBenchmark.p
% 12.34/12.57 SZS output start Proof for theBenchmark.p
% 12.34/12.57 Clause #0 (by assumption #[]): Eq
% 12.34/12.57 (∀ (P S1 P1 S2 P2 : Iota),
% 12.34/12.57 And (And (And (iext uri_rdf_first S1 P1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 P2))
% 12.34/12.57 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 12.34/12.57 Iff (iext uri_owl_propertyChainAxiom P S1)
% 12.34/12.57 (And (And (And (ip P) (ip P1)) (ip P2))
% 12.34/12.57 (∀ (Y0 Y1 Y2 : Iota), And (iext P1 Y0 Y1) (iext P2 Y1 Y2) → iext P Y0 Y2)))
% 12.34/12.57 True
% 12.34/12.57 Clause #1 (by assumption #[]): Eq
% 12.34/12.57 (∀ (P1 P2 : Iota),
% 12.34/12.57 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))))
% 12.34/12.57 True
% 12.34/12.57 Clause #2 (by assumption #[]): Eq (Not (And (iext uri_ex_hasUncle uri_ex_alice uri_ex_charly) (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice))) True
% 12.34/12.57 Clause #3 (by assumption #[]): Eq
% 12.34/12.57 (Exists fun BNODE_l11 =>
% 12.34/12.57 Exists fun BNODE_l12 =>
% 12.34/12.57 Exists fun BNODE_l21 =>
% 12.34/12.57 Exists fun BNODE_l22 =>
% 12.34/12.57 Exists fun BNODE_l3 =>
% 12.34/12.57 And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And
% 12.34/12.57 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle BNODE_l11)
% 12.34/12.57 (iext uri_rdf_first BNODE_l11 uri_ex_hasCousin))
% 12.34/12.57 (iext uri_rdf_rest BNODE_l11 BNODE_l12))
% 12.34/12.57 (iext uri_rdf_first BNODE_l12 uri_ex_hasFather))
% 12.34/12.57 (iext uri_rdf_rest BNODE_l12 uri_rdf_nil))
% 12.34/12.57 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin BNODE_l21))
% 12.34/12.57 (iext uri_rdf_first BNODE_l21 uri_ex_hasUncle))
% 12.34/12.57 (iext uri_rdf_rest BNODE_l21 BNODE_l22))
% 12.34/12.57 (iext uri_rdf_first BNODE_l22 BNODE_l3))
% 12.34/12.57 (iext uri_rdf_rest BNODE_l22 uri_rdf_nil))
% 12.34/12.57 (iext uri_owl_inverseOf BNODE_l3 uri_ex_hasFather))
% 12.34/12.57 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.34/12.57 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.34/12.57 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.34/12.57 (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave))
% 12.34/12.57 True
% 12.34/12.57 Clause #4 (by clausification #[2]): Eq (And (iext uri_ex_hasUncle uri_ex_alice uri_ex_charly) (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice)) False
% 12.34/12.57 Clause #5 (by clausification #[4]): Or (Eq (iext uri_ex_hasUncle uri_ex_alice uri_ex_charly) False)
% 12.34/12.57 (Eq (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice) False)
% 12.34/12.57 Clause #6 (by clausification #[1]): ∀ (a : Iota),
% 12.34/12.57 Eq
% 12.34/12.57 (∀ (P2 : Iota),
% 12.34/12.57 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))))
% 12.34/12.57 True
% 12.34/12.57 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 12.34/12.57 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))))
% 12.34/12.57 True
% 12.34/12.57 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota),
% 12.34/12.57 Or (Eq (iext uri_owl_inverseOf a a_1) False)
% 12.34/12.57 (Eq (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), Iff (iext a X Y) (iext a_1 Y X))) True)
% 12.34/12.57 Clause #18 (by clausification #[9]): ∀ (a a_1 : Iota),
% 12.34/12.57 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)
% 12.34/12.57 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 12.34/12.57 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)
% 12.34/12.57 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.34/12.57 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)
% 12.34/12.57 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.34/12.57 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))
% 12.41/12.59 Clause #26 (by clausification #[0]): ∀ (a : Iota),
% 12.41/12.59 Eq
% 12.41/12.59 (∀ (S1 P1 S2 P2 : Iota),
% 12.41/12.59 And (And (And (iext uri_rdf_first S1 P1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 P2))
% 12.41/12.59 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 12.41/12.59 Iff (iext uri_owl_propertyChainAxiom a S1)
% 12.41/12.59 (And (And (And (ip a) (ip P1)) (ip P2))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext P1 Y0 Y1) (iext P2 Y1 Y2) → iext a Y0 Y2)))
% 12.41/12.59 True
% 12.41/12.59 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota),
% 12.41/12.59 Eq
% 12.41/12.59 (∀ (P1 S2 P2 : Iota),
% 12.41/12.59 And (And (And (iext uri_rdf_first a P1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 P2))
% 12.41/12.59 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 12.41/12.59 Iff (iext uri_owl_propertyChainAxiom a_1 a)
% 12.41/12.59 (And (And (And (ip a_1) (ip P1)) (ip P2))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext P1 Y0 Y1) (iext P2 Y1 Y2) → iext a_1 Y0 Y2)))
% 12.41/12.59 True
% 12.41/12.59 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 12.41/12.59 Eq
% 12.41/12.59 (∀ (S2 P2 : Iota),
% 12.41/12.59 And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 P2))
% 12.41/12.59 (iext uri_rdf_rest S2 uri_rdf_nil) →
% 12.41/12.59 Iff (iext uri_owl_propertyChainAxiom a_2 a)
% 12.41/12.59 (And (And (And (ip a_2) (ip a_1)) (ip P2))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_1 Y0 Y1) (iext P2 Y1 Y2) → iext a_2 Y0 Y2)))
% 12.41/12.59 True
% 12.41/12.59 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.41/12.59 Eq
% 12.41/12.59 (∀ (P2 : Iota),
% 12.41/12.59 And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 P2))
% 12.41/12.59 (iext uri_rdf_rest a_2 uri_rdf_nil) →
% 12.41/12.59 Iff (iext uri_owl_propertyChainAxiom a_3 a)
% 12.41/12.59 (And (And (And (ip a_3) (ip a_1)) (ip P2))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_1 Y0 Y1) (iext P2 Y1 Y2) → iext a_3 Y0 Y2)))
% 12.41/12.59 True
% 12.41/12.59 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.59 Eq
% 12.41/12.59 (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))
% 12.41/12.59 (iext uri_rdf_rest a_2 uri_rdf_nil) →
% 12.41/12.59 Iff (iext uri_owl_propertyChainAxiom a_4 a)
% 12.41/12.59 (And (And (And (ip a_4) (ip a_1)) (ip a_3))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2) → iext a_4 Y0 Y2)))
% 12.41/12.59 True
% 12.41/12.59 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.59 Or
% 12.41/12.59 (Eq
% 12.41/12.59 (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))
% 12.41/12.59 (iext uri_rdf_rest a_2 uri_rdf_nil))
% 12.41/12.59 False)
% 12.41/12.59 (Eq
% 12.41/12.59 (Iff (iext uri_owl_propertyChainAxiom a_4 a)
% 12.41/12.59 (And (And (And (ip a_4) (ip a_1)) (ip a_3))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2) → iext a_4 Y0 Y2)))
% 12.41/12.59 True)
% 12.41/12.59 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.59 Or
% 12.41/12.59 (Eq
% 12.41/12.59 (Iff (iext uri_owl_propertyChainAxiom a a_1)
% 12.41/12.59 (And (And (And (ip a) (ip a_2)) (ip a_3))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_2 Y0 Y1) (iext a_3 Y1 Y2) → iext a Y0 Y2)))
% 12.41/12.59 True)
% 12.41/12.59 (Or (Eq (And (And (iext uri_rdf_first a_1 a_2) (iext uri_rdf_rest a_1 a_4)) (iext uri_rdf_first a_4 a_3)) False)
% 12.41/12.59 (Eq (iext uri_rdf_rest a_4 uri_rdf_nil) False))
% 12.41/12.59 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.59 Or (Eq (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3)) False)
% 12.41/12.59 (Or (Eq (iext uri_rdf_rest a_2 uri_rdf_nil) False)
% 12.41/12.59 (Or (Eq (iext uri_owl_propertyChainAxiom a_4 a) False)
% 12.41/12.59 (Eq
% 12.41/12.59 (And (And (And (ip a_4) (ip a_1)) (ip a_3))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_1 Y0 Y1) (iext a_3 Y1 Y2) → iext a_4 Y0 Y2))
% 12.41/12.59 True)))
% 12.41/12.59 Clause #50 (by clausification #[34]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.59 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.59 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.59 (Or
% 12.41/12.59 (Eq
% 12.41/12.59 (And (And (And (ip a_1) (ip a_3)) (ip a_4))
% 12.41/12.59 (∀ (Y0 Y1 Y2 : Iota), And (iext a_3 Y0 Y1) (iext a_4 Y1 Y2) → iext a_1 Y0 Y2))
% 12.41/12.59 True)
% 12.41/12.59 (Or (Eq (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a)) False)
% 12.41/12.59 (Eq (iext uri_rdf_first a a_4) False))))
% 12.41/12.61 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a)) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_4) False)
% 12.41/12.61 (Eq (∀ (Y0 Y1 Y2 : Iota), And (iext a_3 Y0 Y1) (iext a_4 Y1 Y2) → iext a_1 Y0 Y2) True))))
% 12.41/12.61 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_3) False)
% 12.41/12.61 (Or (Eq (∀ (Y0 Y1 Y2 : Iota), And (iext a_4 Y0 Y1) (iext a_3 Y1 Y2) → iext a_1 Y0 Y2) True)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a_2 a_4) False) (Eq (iext uri_rdf_rest a_2 a) False)))))
% 12.41/12.61 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_3) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 12.41/12.61 (Eq (∀ (Y1 Y2 : Iota), And (iext a_4 a_5 Y1) (iext a_3 Y1 Y2) → iext a_1 a_5 Y2) True)))))
% 12.41/12.61 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_3) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 12.41/12.61 (Eq (∀ (Y2 : Iota), And (iext a_4 a_5 a_6) (iext a_3 a_6 Y2) → iext a_1 a_5 Y2) True)))))
% 12.41/12.61 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_3) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 12.41/12.61 (Eq (And (iext a_4 a_5 a_6) (iext a_3 a_6 a_7) → iext a_1 a_5 a_7) True)))))
% 12.41/12.61 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_3) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 12.41/12.61 (Or (Eq (And (iext a_4 a_5 a_6) (iext a_3 a_6 a_7)) False) (Eq (iext a_1 a_5 a_7) True))))))
% 12.41/12.61 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.41/12.61 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 12.41/12.61 (Or (Eq (iext uri_owl_propertyChainAxiom a_1 a_2) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a a_3) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_first a_2 a_4) False)
% 12.41/12.61 (Or (Eq (iext uri_rdf_rest a_2 a) False)
% 12.41/12.61 (Or (Eq (iext a_1 a_5 a_6) True) (Or (Eq (iext a_4 a_5 a_7) False) (Eq (iext a_3 a_7 a_6) False)))))))
% 12.41/12.61 Clause #64 (by clausification #[3]): ∀ (a : Iota),
% 12.41/12.61 Eq
% 12.41/12.61 (Exists fun BNODE_l12 =>
% 12.41/12.61 Exists fun BNODE_l21 =>
% 12.41/12.61 Exists fun BNODE_l22 =>
% 12.41/12.61 Exists fun BNODE_l3 =>
% 12.41/12.61 And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And
% 12.41/12.61 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.61 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.61 (iext uri_rdf_rest (skS.0 5 a) BNODE_l12))
% 12.41/12.61 (iext uri_rdf_first BNODE_l12 uri_ex_hasFather))
% 12.41/12.61 (iext uri_rdf_rest BNODE_l12 uri_rdf_nil))
% 12.41/12.62 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin BNODE_l21))
% 12.41/12.62 (iext uri_rdf_first BNODE_l21 uri_ex_hasUncle))
% 12.41/12.62 (iext uri_rdf_rest BNODE_l21 BNODE_l22))
% 12.41/12.62 (iext uri_rdf_first BNODE_l22 BNODE_l3))
% 12.41/12.62 (iext uri_rdf_rest BNODE_l22 uri_rdf_nil))
% 12.41/12.62 (iext uri_owl_inverseOf BNODE_l3 uri_ex_hasFather))
% 12.41/12.62 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.62 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.62 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.41/12.62 (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave))
% 12.41/12.62 True
% 12.41/12.62 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota),
% 12.41/12.62 Eq
% 12.41/12.62 (Exists fun BNODE_l21 =>
% 12.41/12.62 Exists fun BNODE_l22 =>
% 12.41/12.62 Exists fun BNODE_l3 =>
% 12.41/12.62 And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.62 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.62 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.62 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.62 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.62 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin BNODE_l21))
% 12.41/12.62 (iext uri_rdf_first BNODE_l21 uri_ex_hasUncle))
% 12.41/12.62 (iext uri_rdf_rest BNODE_l21 BNODE_l22))
% 12.41/12.62 (iext uri_rdf_first BNODE_l22 BNODE_l3))
% 12.41/12.62 (iext uri_rdf_rest BNODE_l22 uri_rdf_nil))
% 12.41/12.62 (iext uri_owl_inverseOf BNODE_l3 uri_ex_hasFather))
% 12.41/12.62 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.62 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.62 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.41/12.62 (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave))
% 12.41/12.62 True
% 12.41/12.62 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 12.41/12.62 Eq
% 12.41/12.62 (Exists fun BNODE_l22 =>
% 12.41/12.62 Exists fun BNODE_l3 =>
% 12.41/12.62 And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And
% 12.41/12.62 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.62 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.62 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.62 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.62 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.62 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.62 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.62 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) BNODE_l22))
% 12.41/12.62 (iext uri_rdf_first BNODE_l22 BNODE_l3))
% 12.41/12.62 (iext uri_rdf_rest BNODE_l22 uri_rdf_nil))
% 12.41/12.62 (iext uri_owl_inverseOf BNODE_l3 uri_ex_hasFather))
% 12.41/12.62 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.62 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.62 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.41/12.62 (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave))
% 12.41/12.62 True
% 12.41/12.62 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.41/12.62 Eq
% 12.41/12.62 (Exists fun BNODE_l3 =>
% 12.41/12.63 And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.63 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.63 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) BNODE_l3))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.41/12.63 (iext uri_owl_inverseOf BNODE_l3 uri_ex_hasFather))
% 12.41/12.63 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.63 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.63 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.41/12.63 (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave))
% 12.41/12.63 True
% 12.41/12.63 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.63 Eq
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.63 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.63 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.41/12.63 (iext uri_owl_inverseOf (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_hasFather))
% 12.41/12.63 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.63 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.63 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.41/12.63 (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave))
% 12.41/12.63 True
% 12.41/12.63 Clause #69 (by clausification #[68]): Eq (iext uri_ex_hasUncle uri_ex_bob uri_ex_dave) True
% 12.41/12.63 Clause #70 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.63 Eq
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And
% 12.41/12.63 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.63 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.63 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.63 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.41/12.63 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.41/12.65 (iext uri_owl_inverseOf (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_hasFather))
% 12.41/12.65 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.65 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.65 (iext uri_ex_hasFather uri_ex_bob uri_ex_charly))
% 12.41/12.65 True
% 12.41/12.65 Clause #71 (by clausification #[70]): Eq (iext uri_ex_hasFather uri_ex_bob uri_ex_charly) True
% 12.41/12.65 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.65 Eq
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.65 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.65 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.41/12.65 (iext uri_owl_inverseOf (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_hasFather))
% 12.41/12.65 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.65 (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob))
% 12.41/12.65 True
% 12.41/12.65 Clause #73 (by clausification #[72]): Eq (iext uri_ex_hasCousin uri_ex_alice uri_ex_bob) True
% 12.41/12.65 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.65 Eq
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.65 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.65 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.41/12.65 (iext uri_owl_inverseOf (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_hasFather))
% 12.41/12.65 (iext uri_ex_hasFather uri_ex_alice uri_ex_dave))
% 12.41/12.65 True
% 12.41/12.65 Clause #75 (by clausification #[74]): Eq (iext uri_ex_hasFather uri_ex_alice uri_ex_dave) True
% 12.41/12.65 Clause #76 (by clausification #[74]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.41/12.65 Eq
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And
% 12.41/12.65 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.41/12.65 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.41/12.65 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.41/12.65 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.41/12.65 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.49/12.67 (iext uri_owl_inverseOf (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_hasFather))
% 12.49/12.67 True
% 12.49/12.67 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (iext uri_owl_inverseOf (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_hasFather) True
% 12.49/12.67 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.49/12.67 Eq
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.67 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.67 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.49/12.67 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.49/12.67 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.49/12.67 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil))
% 12.49/12.67 True
% 12.49/12.67 Clause #79 (by superposition #[77, 22]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.49/12.67 Or (Eq True False)
% 12.49/12.67 (Or (Eq (iext (skS.0 9 a a_1 a_2 a_3 a_4) a_5 a_6) True) (Eq (iext uri_ex_hasFather a_6 a_5) False))
% 12.49/12.67 Clause #89 (by clausification #[79]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.49/12.67 Or (Eq (iext (skS.0 9 a a_1 a_2 a_3 a_4) a_5 a_6) True) (Eq (iext uri_ex_hasFather a_6 a_5) False)
% 12.49/12.67 Clause #91 (by superposition #[89, 75]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (iext (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_dave uri_ex_alice) True) (Eq False True)
% 12.49/12.67 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (iext (skS.0 9 a a_1 a_2 a_3 a_4) uri_ex_dave uri_ex_alice) True
% 12.49/12.67 Clause #93 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 8 a a_1 a_2 a_3) uri_rdf_nil) True
% 12.49/12.67 Clause #94 (by clausification #[78]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.49/12.67 Eq
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.67 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.67 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.49/12.67 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.49/12.67 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.49/12.67 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.49/12.67 (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)))
% 12.49/12.67 True
% 12.49/12.67 Clause #96 (by superposition #[93, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 12.49/12.67 Or (Eq True False)
% 12.49/12.67 (Or (Eq (iext uri_owl_propertyChainAxiom a a_1) False)
% 12.49/12.67 (Or (Eq (iext uri_rdf_first (skS.0 8 a_2 a_3 a_4 a_5) a_6) False)
% 12.49/12.67 (Or (Eq (iext uri_rdf_first a_1 a_7) False)
% 12.49/12.67 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 8 a_2 a_3 a_4 a_5)) False)
% 12.49/12.67 (Or (Eq (iext a a_8 a_9) True) (Or (Eq (iext a_7 a_8 a_10) False) (Eq (iext a_6 a_10 a_9) False)))))))
% 12.49/12.67 Clause #113 (by clausification #[96]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 12.49/12.67 Or (Eq (iext uri_owl_propertyChainAxiom a a_1) False)
% 12.49/12.67 (Or (Eq (iext uri_rdf_first (skS.0 8 a_2 a_3 a_4 a_5) a_6) False)
% 12.49/12.67 (Or (Eq (iext uri_rdf_first a_1 a_7) False)
% 12.49/12.67 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 8 a_2 a_3 a_4 a_5)) False)
% 12.49/12.67 (Or (Eq (iext a a_8 a_9) True) (Or (Eq (iext a_7 a_8 a_10) False) (Eq (iext a_6 a_10 a_9) False))))))
% 12.49/12.67 Clause #139 (by clausification #[94]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2 a_3 a_4)) True
% 12.49/12.67 Clause #140 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.49/12.67 Eq
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.67 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.68 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.49/12.68 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)))
% 12.49/12.68 True
% 12.49/12.68 Clause #152 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3)) True
% 12.49/12.68 Clause #153 (by clausification #[140]): ∀ (a a_1 a_2 : Iota),
% 12.49/12.68 Eq
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.68 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.49/12.68 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle))
% 12.49/12.68 True
% 12.49/12.68 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_rdf_first (skS.0 7 a a_1 a_2) uri_ex_hasUncle) True
% 12.49/12.68 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 : Iota),
% 12.49/12.68 Eq
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.68 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.49/12.68 (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)))
% 12.49/12.68 True
% 12.49/12.68 Clause #160 (by clausification #[155]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_owl_propertyChainAxiom uri_ex_hasCousin (skS.0 7 a a_1 a_2)) True
% 12.49/12.68 Clause #161 (by clausification #[155]): ∀ (a a_1 : Iota),
% 12.49/12.68 Eq
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.68 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil))
% 12.49/12.68 True
% 12.49/12.68 Clause #165 (by superposition #[160, 113]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 : Iota),
% 12.49/12.68 Or (Eq True False)
% 12.49/12.68 (Or (Eq (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) a_4) False)
% 12.49/12.68 (Or (Eq (iext uri_rdf_first (skS.0 7 a_5 a_6 a_7) a_8) False)
% 12.49/12.68 (Or (Eq (iext uri_rdf_rest (skS.0 7 a_5 a_6 a_7) (skS.0 8 a a_1 a_2 a_3)) False)
% 12.49/12.68 (Or (Eq (iext uri_ex_hasCousin a_9 a_10) True)
% 12.49/12.68 (Or (Eq (iext a_8 a_9 a_11) False) (Eq (iext a_4 a_11 a_10) False))))))
% 12.49/12.68 Clause #257 (by clausification #[161]): ∀ (a a_1 : Iota), Eq (iext uri_rdf_rest (skS.0 6 a a_1) uri_rdf_nil) True
% 12.49/12.68 Clause #258 (by clausification #[161]): ∀ (a a_1 : Iota),
% 12.49/12.68 Eq
% 12.49/12.68 (And
% 12.49/12.68 (And
% 12.49/12.68 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.49/12.68 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.49/12.68 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.49/12.68 (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather))
% 12.49/12.68 True
% 12.49/12.68 Clause #260 (by superposition #[257, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 12.49/12.68 Or (Eq True False)
% 12.49/12.68 (Or (Eq (iext uri_owl_propertyChainAxiom a a_1) False)
% 12.49/12.68 (Or (Eq (iext uri_rdf_first (skS.0 6 a_2 a_3) a_4) False)
% 12.49/12.68 (Or (Eq (iext uri_rdf_first a_1 a_5) False)
% 12.49/12.68 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 6 a_2 a_3)) False)
% 12.49/12.68 (Or (Eq (iext a a_6 a_7) True) (Or (Eq (iext a_5 a_6 a_8) False) (Eq (iext a_4 a_8 a_7) False)))))))
% 12.49/12.68 Clause #276 (by clausification #[258]): ∀ (a a_1 : Iota), Eq (iext uri_rdf_first (skS.0 6 a a_1) uri_ex_hasFather) True
% 12.51/12.70 Clause #277 (by clausification #[258]): ∀ (a a_1 : Iota),
% 12.51/12.70 Eq
% 12.51/12.70 (And
% 12.51/12.70 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.51/12.70 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.51/12.70 (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)))
% 12.51/12.70 True
% 12.51/12.70 Clause #281 (by clausification #[277]): ∀ (a a_1 : Iota), Eq (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a a_1)) True
% 12.51/12.70 Clause #282 (by clausification #[277]): ∀ (a : Iota),
% 12.51/12.70 Eq
% 12.51/12.70 (And (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a))
% 12.51/12.70 (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin))
% 12.51/12.70 True
% 12.51/12.70 Clause #283 (by clausification #[282]): ∀ (a : Iota), Eq (iext uri_rdf_first (skS.0 5 a) uri_ex_hasCousin) True
% 12.51/12.70 Clause #284 (by clausification #[282]): ∀ (a : Iota), Eq (iext uri_owl_propertyChainAxiom uri_ex_hasUncle (skS.0 5 a)) True
% 12.51/12.70 Clause #323 (by clausification #[260]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 12.51/12.70 Or (Eq (iext uri_owl_propertyChainAxiom a a_1) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_first (skS.0 6 a_2 a_3) a_4) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_first a_1 a_5) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 6 a_2 a_3)) False)
% 12.51/12.70 (Or (Eq (iext a a_6 a_7) True) (Or (Eq (iext a_5 a_6 a_8) False) (Eq (iext a_4 a_8 a_7) False))))))
% 12.51/12.70 Clause #325 (by superposition #[323, 284]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_first (skS.0 6 a a_1) a_2) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_first (skS.0 5 a_3) a_4) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest (skS.0 5 a_3) (skS.0 6 a a_1)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasUncle a_5 a_6) True)
% 12.51/12.70 (Or (Eq (iext a_4 a_5 a_7) False) (Or (Eq (iext a_2 a_7 a_6) False) (Eq False True))))))
% 12.51/12.70 Clause #326 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_first (skS.0 8 a a_1 a_2 a_3) a_4) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_first (skS.0 7 a_5 a_6 a_7) a_8) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest (skS.0 7 a_5 a_6 a_7) (skS.0 8 a a_1 a_2 a_3)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasCousin a_9 a_10) True)
% 12.51/12.70 (Or (Eq (iext a_8 a_9 a_11) False) (Eq (iext a_4 a_11 a_10) False)))))
% 12.51/12.70 Clause #327 (by superposition #[326, 139]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_first (skS.0 7 a a_1 a_2) a_3) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a_4 a_5 a_6 a_7)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasCousin a_8 a_9) True)
% 12.51/12.70 (Or (Eq (iext a_3 a_8 a_10) False)
% 12.51/12.70 (Or (Eq (iext (skS.0 9 a_4 a_5 a_6 a_7 a_11) a_10 a_9) False) (Eq False True)))))
% 12.51/12.70 Clause #355 (by clausification #[325]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_first (skS.0 6 a a_1) a_2) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_first (skS.0 5 a_3) a_4) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest (skS.0 5 a_3) (skS.0 6 a a_1)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasUncle a_5 a_6) True) (Or (Eq (iext a_4 a_5 a_7) False) (Eq (iext a_2 a_7 a_6) False)))))
% 12.51/12.70 Clause #356 (by superposition #[355, 276]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_first (skS.0 5 a) a_1) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a_2 a_3)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasUncle a_4 a_5) True)
% 12.51/12.70 (Or (Eq (iext a_1 a_4 a_6) False) (Or (Eq (iext uri_ex_hasFather a_6 a_5) False) (Eq False True)))))
% 12.51/12.70 Clause #357 (by clausification #[356]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_first (skS.0 5 a) a_1) False)
% 12.51/12.70 (Or (Eq (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a_2 a_3)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasUncle a_4 a_5) True)
% 12.51/12.70 (Or (Eq (iext a_1 a_4 a_6) False) (Eq (iext uri_ex_hasFather a_6 a_5) False))))
% 12.51/12.70 Clause #358 (by superposition #[357, 283]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.51/12.70 Or (Eq (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a_1 a_2)) False)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasUncle a_3 a_4) True)
% 12.51/12.70 (Or (Eq (iext uri_ex_hasCousin a_3 a_5) False) (Or (Eq (iext uri_ex_hasFather a_5 a_4) False) (Eq False True))))
% 12.51/12.70 Clause #361 (by clausification #[358]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.55/12.72 Or (Eq (iext uri_rdf_rest (skS.0 5 a) (skS.0 6 a_1 a_2)) False)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasUncle a_3 a_4) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasCousin a_3 a_5) False) (Eq (iext uri_ex_hasFather a_5 a_4) False)))
% 12.55/12.72 Clause #362 (by superposition #[361, 281]): ∀ (a a_1 a_2 : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasUncle a a_1) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasCousin a a_2) False) (Or (Eq (iext uri_ex_hasFather a_2 a_1) False) (Eq False True)))
% 12.55/12.72 Clause #363 (by clausification #[362]): ∀ (a a_1 a_2 : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasUncle a a_1) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasCousin a a_2) False) (Eq (iext uri_ex_hasFather a_2 a_1) False))
% 12.55/12.72 Clause #364 (by superposition #[363, 73]): ∀ (a : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasUncle uri_ex_alice a) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasFather uri_ex_bob a) False) (Eq False True))
% 12.55/12.72 Clause #368 (by clausification #[364]): ∀ (a : Iota), Or (Eq (iext uri_ex_hasUncle uri_ex_alice a) True) (Eq (iext uri_ex_hasFather uri_ex_bob a) False)
% 12.55/12.72 Clause #369 (by superposition #[368, 71]): Or (Eq (iext uri_ex_hasUncle uri_ex_alice uri_ex_charly) True) (Eq False True)
% 12.55/12.72 Clause #370 (by clausification #[369]): Eq (iext uri_ex_hasUncle uri_ex_alice uri_ex_charly) True
% 12.55/12.72 Clause #371 (by backward demodulation #[370, 5]): Or (Eq True False) (Eq (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice) False)
% 12.55/12.72 Clause #372 (by clausification #[371]): Eq (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice) False
% 12.55/12.72 Clause #396 (by clausification #[327]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 a_11 : Iota),
% 12.55/12.72 Or (Eq (iext uri_rdf_first (skS.0 7 a a_1 a_2) a_3) False)
% 12.55/12.72 (Or (Eq (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a_4 a_5 a_6 a_7)) False)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasCousin a_8 a_9) True)
% 12.55/12.72 (Or (Eq (iext a_3 a_8 a_10) False) (Eq (iext (skS.0 9 a_4 a_5 a_6 a_7 a_11) a_10 a_9) False))))
% 12.55/12.72 Clause #397 (by superposition #[396, 154]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 12.55/12.72 Or (Eq (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a_3 a_4 a_5 a_6)) False)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasCousin a_7 a_8) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasUncle a_7 a_9) False)
% 12.55/12.72 (Or (Eq (iext (skS.0 9 a_3 a_4 a_5 a_6 a_10) a_9 a_8) False) (Eq False True))))
% 12.55/12.72 Clause #398 (by clausification #[397]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota),
% 12.55/12.72 Or (Eq (iext uri_rdf_rest (skS.0 7 a a_1 a_2) (skS.0 8 a_3 a_4 a_5 a_6)) False)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasCousin a_7 a_8) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasUncle a_7 a_9) False) (Eq (iext (skS.0 9 a_3 a_4 a_5 a_6 a_10) a_9 a_8) False)))
% 12.55/12.72 Clause #399 (by superposition #[398, 152]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasCousin a a_1) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasUncle a a_2) False)
% 12.55/12.72 (Or (Eq (iext (skS.0 9 a_3 a_4 a_5 a_6 a_7) a_2 a_1) False) (Eq False True)))
% 12.55/12.72 Clause #400 (by clausification #[399]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasCousin a a_1) True)
% 12.55/12.72 (Or (Eq (iext uri_ex_hasUncle a a_2) False) (Eq (iext (skS.0 9 a_3 a_4 a_5 a_6 a_7) a_2 a_1) False))
% 12.55/12.72 Clause #401 (by superposition #[400, 69]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasCousin uri_ex_bob a) True)
% 12.55/12.72 (Or (Eq (iext (skS.0 9 a_1 a_2 a_3 a_4 a_5) uri_ex_dave a) False) (Eq False True))
% 12.55/12.72 Clause #409 (by clausification #[401]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.55/12.72 Or (Eq (iext uri_ex_hasCousin uri_ex_bob a) True) (Eq (iext (skS.0 9 a_1 a_2 a_3 a_4 a_5) uri_ex_dave a) False)
% 12.55/12.72 Clause #410 (by superposition #[409, 92]): Or (Eq (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice) True) (Eq False True)
% 12.55/12.72 Clause #411 (by clausification #[410]): Eq (iext uri_ex_hasCousin uri_ex_bob uri_ex_alice) True
% 12.55/12.72 Clause #412 (by superposition #[411, 372]): Eq True False
% 12.55/12.72 Clause #414 (by clausification #[412]): False
% 12.55/12.72 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------