TSTP Solution File: SWB026+2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWB026+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 20:04:07 EDT 2023
% Result : Theorem 11.04s 11.29s
% Output : Proof 11.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB026+2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 06:38:09 EDT 2023
% 0.14/0.34 % CPUTime :
% 11.04/11.29 SZS status Theorem for theBenchmark.p
% 11.04/11.29 SZS output start Proof for theBenchmark.p
% 11.04/11.29 Clause #0 (by assumption #[]): Eq (∀ (P : Iota), Iff (iext uri_rdf_type P uri_rdf_Property) (ip P)) True
% 11.04/11.29 Clause #1 (by assumption #[]): Eq (∀ (X C : Iota), Iff (iext uri_rdf_type X C) (icext C X)) True
% 11.04/11.29 Clause #2 (by assumption #[]): Eq (∀ (P C X Y : Iota), And (iext uri_rdfs_domain P C) (iext P X Y) → icext C X) True
% 11.04/11.29 Clause #3 (by assumption #[]): Eq (iext uri_rdfs_domain uri_rdfs_domain uri_rdf_Property) True
% 11.04/11.29 Clause #4 (by assumption #[]): Eq
% 11.04/11.29 (∀ (Z S1 A1 : Iota),
% 11.04/11.29 And (iext uri_rdf_first S1 A1) (iext uri_rdf_rest S1 uri_rdf_nil) →
% 11.04/11.29 Iff (iext uri_owl_oneOf Z S1) (And (ic Z) (∀ (X : Iota), Iff (icext Z X) (Eq X A1))))
% 11.04/11.29 True
% 11.04/11.29 Clause #5 (by assumption #[]): Eq
% 11.04/11.29 (∀ (P : Iota),
% 11.04/11.29 Iff (icext uri_owl_InverseFunctionalProperty P)
% 11.04/11.29 (And (ip P) (∀ (X1 X2 Y : Iota), And (iext P X1 Y) (iext P X2 Y) → Eq X1 X2)))
% 11.04/11.29 True
% 11.04/11.29 Clause #6 (by assumption #[]): Eq (Not (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty)) True
% 11.04/11.29 Clause #7 (by assumption #[]): Eq
% 11.04/11.29 (Exists fun BNODE_x1 =>
% 11.04/11.29 Exists fun BNODE_x2 =>
% 11.04/11.29 Exists fun BNODE_l1 =>
% 11.04/11.29 Exists fun BNODE_l2 =>
% 11.04/11.29 And
% 11.04/11.29 (And
% 11.04/11.29 (And
% 11.04/11.29 (And
% 11.04/11.29 (And
% 11.04/11.29 (And (And (iext uri_rdfs_domain uri_ex_p BNODE_x1) (iext uri_owl_oneOf BNODE_x1 BNODE_l1))
% 11.04/11.29 (iext uri_rdf_first BNODE_l1 uri_ex_w))
% 11.04/11.29 (iext uri_rdf_rest BNODE_l1 uri_rdf_nil))
% 11.04/11.29 (iext uri_rdfs_range uri_ex_p BNODE_x2))
% 11.04/11.29 (iext uri_owl_oneOf BNODE_x2 BNODE_l2))
% 11.04/11.29 (iext uri_rdf_first BNODE_l2 uri_ex_u))
% 11.04/11.29 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 11.04/11.29 True
% 11.04/11.29 Clause #8 (by clausification #[6]): Eq (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty) False
% 11.04/11.29 Clause #9 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C X Y : Iota), And (iext uri_rdfs_domain a C) (iext a X Y) → icext C X) True
% 11.04/11.29 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (X Y : Iota), And (iext uri_rdfs_domain a a_1) (iext a X Y) → icext a_1 X) True
% 11.04/11.29 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Y : Iota), And (iext uri_rdfs_domain a a_1) (iext a a_2 Y) → icext a_1 a_2) True
% 11.04/11.29 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (iext uri_rdfs_domain a a_1) (iext a a_2 a_3) → icext a_1 a_2) True
% 11.04/11.29 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (And (iext uri_rdfs_domain a a_1) (iext a a_2 a_3)) False) (Eq (icext a_1 a_2) True)
% 11.04/11.29 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.04/11.29 Or (Eq (icext a a_1) True) (Or (Eq (iext uri_rdfs_domain a_2 a) False) (Eq (iext a_2 a_1 a_3) False))
% 11.04/11.29 Clause #15 (by superposition #[14, 3]): ∀ (a a_1 : Iota), Or (Eq (icext uri_rdf_Property a) True) (Or (Eq (iext uri_rdfs_domain a a_1) False) (Eq False True))
% 11.04/11.29 Clause #16 (by clausification #[0]): ∀ (a : Iota), Eq (Iff (iext uri_rdf_type a uri_rdf_Property) (ip a)) True
% 11.04/11.29 Clause #18 (by clausification #[16]): ∀ (a : Iota), Or (Eq (iext uri_rdf_type a uri_rdf_Property) False) (Eq (ip a) True)
% 11.04/11.29 Clause #19 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (iext uri_rdf_type a C) (icext C a)) True
% 11.04/11.29 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Iff (iext uri_rdf_type a a_1) (icext a_1 a)) True
% 11.04/11.29 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (iext uri_rdf_type a a_1) True) (Eq (icext a_1 a) False)
% 11.04/11.29 Clause #23 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (icext uri_rdf_Property a) True) (Eq (iext uri_rdfs_domain a a_1) False)
% 11.04/11.29 Clause #31 (by clausification #[4]): ∀ (a : Iota),
% 11.04/11.29 Eq
% 11.04/11.29 (∀ (S1 A1 : Iota),
% 11.04/11.29 And (iext uri_rdf_first S1 A1) (iext uri_rdf_rest S1 uri_rdf_nil) →
% 11.04/11.29 Iff (iext uri_owl_oneOf a S1) (And (ic a) (∀ (X : Iota), Iff (icext a X) (Eq X A1))))
% 11.04/11.29 True
% 11.04/11.29 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 11.04/11.29 Eq
% 11.04/11.29 (∀ (A1 : Iota),
% 11.04/11.29 And (iext uri_rdf_first a A1) (iext uri_rdf_rest a uri_rdf_nil) →
% 11.04/11.29 Iff (iext uri_owl_oneOf a_1 a) (And (ic a_1) (∀ (X : Iota), Iff (icext a_1 X) (Eq X A1))))
% 11.13/11.32 True
% 11.13/11.32 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Eq
% 11.13/11.32 (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a uri_rdf_nil) →
% 11.13/11.32 Iff (iext uri_owl_oneOf a_2 a) (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1))))
% 11.13/11.32 True
% 11.13/11.32 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Or (Eq (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a uri_rdf_nil)) False)
% 11.13/11.32 (Eq (Iff (iext uri_owl_oneOf a_2 a) (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)))) True)
% 11.13/11.32 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Or (Eq (Iff (iext uri_owl_oneOf a a_1) (And (ic a) (∀ (X : Iota), Iff (icext a X) (Eq X a_2)))) True)
% 11.13/11.32 (Or (Eq (iext uri_rdf_first a_1 a_2) False) (Eq (iext uri_rdf_rest a_1 uri_rdf_nil) False))
% 11.13/11.32 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Or (Eq (iext uri_rdf_first a a_1) False)
% 11.13/11.32 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 11.13/11.32 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1))) True)))
% 11.13/11.32 Clause #44 (by clausification #[5]): ∀ (a : Iota),
% 11.13/11.32 Eq
% 11.13/11.32 (Iff (icext uri_owl_InverseFunctionalProperty a)
% 11.13/11.32 (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2)))
% 11.13/11.32 True
% 11.13/11.32 Clause #45 (by clausification #[44]): ∀ (a : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Eq (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2)) False)
% 11.13/11.32 Clause #47 (by clausification #[45]): ∀ (a : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False) (Eq (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2) False))
% 11.13/11.32 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq (Not (∀ (X2 Y : Iota), And (iext a (skS.0 1 a a_1) Y) (iext a X2 Y) → Eq (skS.0 1 a a_1) X2)) True))
% 11.13/11.32 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq (∀ (X2 Y : Iota), And (iext a (skS.0 1 a a_1) Y) (iext a X2 Y) → Eq (skS.0 1 a a_1) X2) False))
% 11.13/11.32 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq
% 11.13/11.32 (Not
% 11.13/11.32 (∀ (Y : Iota),
% 11.13/11.32 And (iext a (skS.0 1 a a_1) Y) (iext a (skS.0 2 a a_1 a_2) Y) → Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 11.13/11.32 True))
% 11.13/11.32 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq
% 11.13/11.32 (∀ (Y : Iota),
% 11.13/11.32 And (iext a (skS.0 1 a a_1) Y) (iext a (skS.0 2 a a_1 a_2) Y) → Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 11.13/11.32 False))
% 11.13/11.32 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq
% 11.13/11.32 (Not
% 11.13/11.32 (And (iext a (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)) (iext a (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) →
% 11.13/11.32 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 11.13/11.32 True))
% 11.13/11.32 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq
% 11.13/11.32 (And (iext a (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)) (iext a (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) →
% 11.13/11.32 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 11.13/11.32 False))
% 11.13/11.32 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False)
% 11.13/11.32 (Eq (And (iext a (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)) (iext a (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 11.13/11.32 True))
% 11.13/11.32 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.32 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.32 (Or (Eq (ip a) False) (Eq (Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False))
% 11.13/11.35 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.35 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.35 (Or (Eq (ip a) False) (Eq (iext a (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) True))
% 11.13/11.35 Clause #57 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.35 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.13/11.35 (Or (Eq (ip a) False) (Eq (iext a (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)) True))
% 11.13/11.35 Clause #67 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.35 Or (Eq (iext uri_rdf_first a a_1) False)
% 11.13/11.35 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 11.13/11.35 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)) True)))
% 11.13/11.35 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.35 Or (Eq (iext uri_rdf_first a a_1) False)
% 11.13/11.35 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 11.13/11.35 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (Iff (icext a_2 a_3) (Eq a_3 a_1)) True)))
% 11.13/11.35 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.35 Or (Eq (iext uri_rdf_first a a_1) False)
% 11.13/11.35 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 11.13/11.35 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Or (Eq (icext a_2 a_3) False) (Eq (Eq a_3 a_1) True))))
% 11.13/11.35 Clause #74 (by clausification #[7]): ∀ (a : Iota),
% 11.13/11.35 Eq
% 11.13/11.35 (Exists fun BNODE_x2 =>
% 11.13/11.35 Exists fun BNODE_l1 =>
% 11.13/11.35 Exists fun BNODE_l2 =>
% 11.13/11.35 And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) BNODE_l1))
% 11.13/11.35 (iext uri_rdf_first BNODE_l1 uri_ex_w))
% 11.13/11.35 (iext uri_rdf_rest BNODE_l1 uri_rdf_nil))
% 11.13/11.35 (iext uri_rdfs_range uri_ex_p BNODE_x2))
% 11.13/11.35 (iext uri_owl_oneOf BNODE_x2 BNODE_l2))
% 11.13/11.35 (iext uri_rdf_first BNODE_l2 uri_ex_u))
% 11.13/11.35 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 11.13/11.35 True
% 11.13/11.35 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota),
% 11.13/11.35 Eq
% 11.13/11.35 (Exists fun BNODE_l1 =>
% 11.13/11.35 Exists fun BNODE_l2 =>
% 11.13/11.35 And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) BNODE_l1))
% 11.13/11.35 (iext uri_rdf_first BNODE_l1 uri_ex_w))
% 11.13/11.35 (iext uri_rdf_rest BNODE_l1 uri_rdf_nil))
% 11.13/11.35 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1)))
% 11.13/11.35 (iext uri_owl_oneOf (skS.0 5 a a_1) BNODE_l2))
% 11.13/11.35 (iext uri_rdf_first BNODE_l2 uri_ex_u))
% 11.13/11.35 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 11.13/11.35 True
% 11.13/11.35 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 11.13/11.35 Eq
% 11.13/11.35 (Exists fun BNODE_l2 =>
% 11.13/11.35 And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.13/11.35 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.13/11.35 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil))
% 11.13/11.35 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1)))
% 11.13/11.35 (iext uri_owl_oneOf (skS.0 5 a a_1) BNODE_l2))
% 11.13/11.35 (iext uri_rdf_first BNODE_l2 uri_ex_u))
% 11.13/11.35 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil))
% 11.13/11.35 True
% 11.13/11.35 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.35 Eq
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.13/11.35 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.13/11.35 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil))
% 11.13/11.35 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1)))
% 11.13/11.35 (iext uri_owl_oneOf (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3)))
% 11.13/11.35 (iext uri_rdf_first (skS.0 7 a a_1 a_2 a_3) uri_ex_u))
% 11.13/11.35 (iext uri_rdf_rest (skS.0 7 a a_1 a_2 a_3) uri_rdf_nil))
% 11.13/11.35 True
% 11.13/11.35 Clause #79 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.13/11.35 Eq
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.13/11.35 (And
% 11.22/11.40 (And
% 11.22/11.40 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.22/11.40 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.22/11.40 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil))
% 11.22/11.40 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1)))
% 11.22/11.40 (iext uri_owl_oneOf (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3)))
% 11.22/11.40 (iext uri_rdf_first (skS.0 7 a a_1 a_2 a_3) uri_ex_u))
% 11.22/11.40 True
% 11.22/11.40 Clause #80 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.22/11.40 Or (Eq (iext uri_rdf_first a a_1) False)
% 11.22/11.40 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False)
% 11.22/11.40 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Or (Eq (icext a_2 a_3) False) (Eq a_3 a_1))))
% 11.22/11.40 Clause #81 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.40 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 11.22/11.40 (Or (Eq (ip a) False) (Ne (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 11.22/11.40 Clause #112 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 11.22/11.40 Eq
% 11.22/11.40 (And
% 11.22/11.40 (And
% 11.22/11.40 (And
% 11.22/11.40 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.22/11.40 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.22/11.40 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil))
% 11.22/11.40 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1)))
% 11.22/11.40 (iext uri_owl_oneOf (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3)))
% 11.22/11.40 True
% 11.22/11.40 Clause #162 (by clausification #[112]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.40 Eq
% 11.22/11.40 (And
% 11.22/11.40 (And
% 11.22/11.40 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.22/11.40 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.22/11.40 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil))
% 11.22/11.40 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1)))
% 11.22/11.40 True
% 11.22/11.40 Clause #179 (by clausification #[162]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.40 Eq
% 11.22/11.40 (And
% 11.22/11.40 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.22/11.40 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.22/11.40 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil))
% 11.22/11.40 True
% 11.22/11.40 Clause #180 (by clausification #[179]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil) True
% 11.22/11.40 Clause #181 (by clausification #[179]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.40 Eq
% 11.22/11.40 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 11.22/11.40 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w))
% 11.22/11.40 True
% 11.22/11.40 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w) True
% 11.22/11.40 Clause #183 (by clausification #[181]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.40 Eq (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2))) True
% 11.22/11.40 Clause #187 (by superposition #[182, 80]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 11.22/11.40 Or (Eq True False)
% 11.22/11.40 (Or (Eq (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil) False)
% 11.22/11.40 (Or (Eq (iext uri_owl_oneOf a_3 (skS.0 6 a a_1 a_2)) False) (Or (Eq (icext a_3 a_4) False) (Eq a_4 uri_ex_w))))
% 11.22/11.40 Clause #189 (by clausification #[183]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_owl_oneOf (skS.0 4 a) (skS.0 6 a a_1 a_2)) True
% 11.22/11.40 Clause #190 (by clausification #[183]): ∀ (a : Iota), Eq (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) True
% 11.22/11.40 Clause #191 (by superposition #[190, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 4 a) a_1) True) (Or (Eq True False) (Eq (iext uri_ex_p a_1 a_2) False))
% 11.22/11.40 Clause #192 (by superposition #[190, 23]): Or (Eq (icext uri_rdf_Property uri_ex_p) True) (Eq True False)
% 11.22/11.40 Clause #199 (by clausification #[192]): Eq (icext uri_rdf_Property uri_ex_p) True
% 11.22/11.40 Clause #200 (by superposition #[199, 21]): Or (Eq (iext uri_rdf_type uri_ex_p uri_rdf_Property) True) (Eq True False)
% 11.22/11.40 Clause #201 (by clausification #[200]): Eq (iext uri_rdf_type uri_ex_p uri_rdf_Property) True
% 11.22/11.40 Clause #202 (by superposition #[201, 18]): Or (Eq True False) (Eq (ip uri_ex_p) True)
% 11.22/11.40 Clause #204 (by clausification #[202]): Eq (ip uri_ex_p) True
% 11.22/11.40 Clause #205 (by superposition #[204, 56]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.40 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Or (Eq True False) (Eq (iext uri_ex_p (skS.0 2 uri_ex_p a a_1) (skS.0 3 uri_ex_p a a_1 a_2)) True))
% 11.22/11.44 Clause #206 (by superposition #[204, 81]): ∀ (a a_1 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Or (Eq True False) (Ne (skS.0 1 uri_ex_p a) (skS.0 2 uri_ex_p a a_1)))
% 11.22/11.44 Clause #207 (by superposition #[204, 57]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Or (Eq True False) (Eq (iext uri_ex_p (skS.0 1 uri_ex_p a) (skS.0 3 uri_ex_p a a_1 a_2)) True))
% 11.22/11.44 Clause #208 (by clausification #[191]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 4 a) a_1) True) (Eq (iext uri_ex_p a_1 a_2) False)
% 11.22/11.44 Clause #212 (by clausification #[206]): ∀ (a a_1 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Ne (skS.0 1 uri_ex_p a) (skS.0 2 uri_ex_p a a_1))
% 11.22/11.44 Clause #213 (by clausification #[207]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Eq (iext uri_ex_p (skS.0 1 uri_ex_p a) (skS.0 3 uri_ex_p a a_1 a_2)) True)
% 11.22/11.44 Clause #214 (by superposition #[213, 208]): ∀ (a a_1 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Or (Eq (icext (skS.0 4 a) (skS.0 1 uri_ex_p a_1)) True) (Eq True False))
% 11.22/11.44 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Eq (icext (skS.0 4 a) (skS.0 1 uri_ex_p a_1)) True)
% 11.22/11.44 Clause #223 (by clausification #[205]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Eq (iext uri_ex_p (skS.0 2 uri_ex_p a a_1) (skS.0 3 uri_ex_p a a_1 a_2)) True)
% 11.22/11.44 Clause #224 (by superposition #[223, 208]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Or (Eq (icext (skS.0 4 a) (skS.0 2 uri_ex_p a_1 a_2)) True) (Eq True False))
% 11.22/11.44 Clause #225 (by clausification #[224]): ∀ (a a_1 a_2 : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Eq (icext (skS.0 4 a) (skS.0 2 uri_ex_p a_1 a_2)) True)
% 11.22/11.44 Clause #245 (by clausification #[187]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 11.22/11.44 Or (Eq (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil) False)
% 11.22/11.44 (Or (Eq (iext uri_owl_oneOf a_3 (skS.0 6 a a_1 a_2)) False) (Or (Eq (icext a_3 a_4) False) (Eq a_4 uri_ex_w)))
% 11.22/11.44 Clause #246 (by forward demodulation #[245, 180]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 11.22/11.44 Or (Eq True False)
% 11.22/11.44 (Or (Eq (iext uri_owl_oneOf a (skS.0 6 a_1 a_2 a_3)) False) (Or (Eq (icext a a_4) False) (Eq a_4 uri_ex_w)))
% 11.22/11.44 Clause #247 (by clausification #[246]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 11.22/11.44 Or (Eq (iext uri_owl_oneOf a (skS.0 6 a_1 a_2 a_3)) False) (Or (Eq (icext a a_4) False) (Eq a_4 uri_ex_w))
% 11.22/11.44 Clause #248 (by superposition #[247, 189]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 4 a) a_1) False) (Or (Eq a_1 uri_ex_w) (Eq False True))
% 11.22/11.44 Clause #254 (by clausification #[248]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 4 a) a_1) False) (Eq a_1 uri_ex_w)
% 11.22/11.44 Clause #255 (by superposition #[254, 215]): ∀ (a : Iota),
% 11.22/11.44 Or (Eq (skS.0 1 uri_ex_p a) uri_ex_w)
% 11.22/11.44 (Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Eq False True))
% 11.22/11.44 Clause #256 (by superposition #[254, 225]): ∀ (a a_1 : Iota),
% 11.22/11.44 Or (Eq (skS.0 2 uri_ex_p a a_1) uri_ex_w)
% 11.22/11.44 (Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Eq False True))
% 11.22/11.44 Clause #259 (by clausification #[255]): ∀ (a : Iota), Or (Eq (skS.0 1 uri_ex_p a) uri_ex_w) (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 Clause #263 (by clausification #[256]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 uri_ex_p a a_1) uri_ex_w) (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 Clause #264 (by superposition #[263, 212]): ∀ (a : Iota),
% 11.22/11.44 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True)
% 11.22/11.44 (Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Ne (skS.0 1 uri_ex_p a) uri_ex_w))
% 11.22/11.44 Clause #265 (by eliminate duplicate literals #[264]): ∀ (a : Iota), Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Ne (skS.0 1 uri_ex_p a) uri_ex_w)
% 11.22/11.44 Clause #266 (by forward contextual literal cutting #[265, 259]): Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True
% 11.22/11.44 Clause #277 (by superposition #[266, 21]): Or (Eq (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty) True) (Eq True False)
% 11.22/11.44 Clause #280 (by clausification #[277]): Eq (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty) True
% 11.22/11.44 Clause #281 (by superposition #[280, 8]): Eq True False
% 11.22/11.44 Clause #283 (by clausification #[281]): False
% 11.22/11.44 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------