TSTP Solution File: SWB028+2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWB028+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n009.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 20:04:09 EDT 2023
% Result : Theorem 12.60s 12.80s
% Output : Proof 12.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWB028+2 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : duper %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 06:27:20 EDT 2023
% 0.12/0.33 % CPUTime :
% 12.60/12.80 SZS status Theorem for theBenchmark.p
% 12.60/12.80 SZS output start Proof for theBenchmark.p
% 12.60/12.80 Clause #0 (by assumption #[]): Eq (ic uri_owl_InverseFunctionalProperty) True
% 12.60/12.80 Clause #1 (by assumption #[]): Eq (∀ (X Y : Iota), iext uri_owl_inverseOf X Y → And (ip X) (ip Y)) True
% 12.60/12.80 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), iext uri_owl_equivalentClass X Y → And (ic X) (ic Y)) True
% 12.60/12.80 Clause #3 (by assumption #[]): Eq
% 12.60/12.80 (∀ (P : Iota),
% 12.60/12.80 Iff (icext uri_owl_FunctionalProperty P)
% 12.60/12.80 (And (ip P) (∀ (X Y1 Y2 : Iota), And (iext P X Y1) (iext P X Y2) → Eq Y1 Y2)))
% 12.60/12.80 True
% 12.60/12.80 Clause #4 (by assumption #[]): Eq
% 12.60/12.80 (∀ (P : Iota),
% 12.60/12.80 Iff (icext uri_owl_InverseFunctionalProperty P)
% 12.60/12.80 (And (ip P) (∀ (X1 X2 Y : Iota), And (iext P X1 Y) (iext P X2 Y) → Eq X1 X2)))
% 12.60/12.80 True
% 12.60/12.80 Clause #5 (by assumption #[]): Eq
% 12.60/12.80 (∀ (C1 C2 : Iota),
% 12.60/12.80 Iff (iext uri_rdfs_subClassOf C1 C2) (And (And (ic C1) (ic C2)) (∀ (X : Iota), icext C1 X → icext C2 X)))
% 12.60/12.80 True
% 12.60/12.80 Clause #6 (by assumption #[]): Eq
% 12.60/12.80 (∀ (C1 C2 : Iota),
% 12.60/12.80 Iff (iext uri_owl_equivalentClass C1 C2) (And (And (ic C1) (ic C2)) (∀ (X : Iota), Iff (icext C1 X) (icext C2 X))))
% 12.60/12.80 True
% 12.60/12.80 Clause #7 (by assumption #[]): Eq
% 12.60/12.80 (∀ (Z P C : Iota),
% 12.60/12.80 And (iext uri_owl_someValuesFrom Z C) (iext uri_owl_onProperty Z P) →
% 12.60/12.80 ∀ (X : Iota), Iff (icext Z X) (Exists fun Y => And (iext P X Y) (icext C Y)))
% 12.60/12.80 True
% 12.60/12.80 Clause #8 (by assumption #[]): Eq
% 12.60/12.80 (∀ (P1 P2 : Iota),
% 12.60/12.80 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))))
% 12.60/12.80 True
% 12.60/12.80 Clause #9 (by assumption #[]): Eq (Not (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty)) True
% 12.60/12.80 Clause #10 (by assumption #[]): Eq
% 12.60/12.80 (Exists fun BNODE_z =>
% 12.60/12.80 And
% 12.60/12.80 (And
% 12.60/12.80 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties BNODE_z)
% 12.60/12.80 (iext uri_rdf_type BNODE_z uri_owl_Restriction))
% 12.60/12.80 (iext uri_owl_onProperty BNODE_z uri_owl_inverseOf))
% 12.60/12.80 (iext uri_owl_someValuesFrom BNODE_z uri_owl_FunctionalProperty))
% 12.60/12.80 True
% 12.60/12.80 Clause #11 (by clausification #[9]): Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) False
% 12.60/12.80 Clause #12 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), iext uri_owl_equivalentClass a Y → And (ic a) (ic Y)) True
% 12.60/12.80 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (iext uri_owl_equivalentClass a a_1 → And (ic a) (ic a_1)) True
% 12.60/12.80 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (And (ic a) (ic a_1)) True)
% 12.60/12.80 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (ic a) True)
% 12.60/12.80 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y : Iota), iext uri_owl_inverseOf a Y → And (ip a) (ip Y)) True
% 12.60/12.80 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (iext uri_owl_inverseOf a a_1 → And (ip a) (ip a_1)) True
% 12.60/12.80 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_inverseOf a a_1) False) (Eq (And (ip a) (ip a_1)) True)
% 12.60/12.80 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_inverseOf a a_1) False) (Eq (ip a) True)
% 12.60/12.80 Clause #22 (by clausification #[3]): ∀ (a : Iota),
% 12.60/12.80 Eq
% 12.60/12.80 (Iff (icext uri_owl_FunctionalProperty a)
% 12.60/12.80 (And (ip a) (∀ (X Y1 Y2 : Iota), And (iext a X Y1) (iext a X Y2) → Eq Y1 Y2)))
% 12.60/12.80 True
% 12.60/12.80 Clause #24 (by clausification #[22]): ∀ (a : Iota),
% 12.60/12.80 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.60/12.80 (Eq (And (ip a) (∀ (X Y1 Y2 : Iota), And (iext a X Y1) (iext a X Y2) → Eq Y1 Y2)) True)
% 12.60/12.80 Clause #36 (by clausification #[24]): ∀ (a : Iota),
% 12.60/12.80 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.60/12.80 (Eq (∀ (X Y1 Y2 : Iota), And (iext a X Y1) (iext a X Y2) → Eq Y1 Y2) True)
% 12.60/12.80 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota),
% 12.60/12.80 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.60/12.80 (Eq (∀ (Y1 Y2 : Iota), And (iext a a_1 Y1) (iext a a_1 Y2) → Eq Y1 Y2) True)
% 12.60/12.80 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 12.60/12.80 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.64/12.82 (Eq (∀ (Y2 : Iota), And (iext a a_1 a_2) (iext a a_1 Y2) → Eq a_2 Y2) True)
% 12.64/12.82 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_FunctionalProperty a) False) (Eq (And (iext a a_1 a_2) (iext a a_1 a_3) → Eq a_2 a_3) True)
% 12.64/12.82 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.64/12.82 (Or (Eq (And (iext a a_1 a_2) (iext a a_1 a_3)) False) (Eq (Eq a_2 a_3) True))
% 12.64/12.82 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.64/12.82 (Or (Eq (Eq a_1 a_2) True) (Or (Eq (iext a a_3 a_1) False) (Eq (iext a a_3 a_2) False)))
% 12.64/12.82 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_FunctionalProperty a) False)
% 12.64/12.82 (Or (Eq (iext a a_1 a_2) False) (Or (Eq (iext a a_1 a_3) False) (Eq a_2 a_3)))
% 12.64/12.82 Clause #44 (by clausification #[4]): ∀ (a : Iota),
% 12.64/12.82 Eq
% 12.64/12.82 (Iff (icext uri_owl_InverseFunctionalProperty a)
% 12.64/12.82 (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2)))
% 12.64/12.82 True
% 12.64/12.82 Clause #45 (by clausification #[44]): ∀ (a : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Eq (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2)) False)
% 12.64/12.82 Clause #47 (by clausification #[45]): ∀ (a : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False) (Eq (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2) False))
% 12.64/12.82 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq (Not (∀ (X2 Y : Iota), And (iext a (skS.0 3 a a_1) Y) (iext a X2 Y) → Eq (skS.0 3 a a_1) X2)) True))
% 12.64/12.82 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq (∀ (X2 Y : Iota), And (iext a (skS.0 3 a a_1) Y) (iext a X2 Y) → Eq (skS.0 3 a a_1) X2) False))
% 12.64/12.82 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq
% 12.64/12.82 (Not
% 12.64/12.82 (∀ (Y : Iota),
% 12.64/12.82 And (iext a (skS.0 3 a a_1) Y) (iext a (skS.0 4 a a_1 a_2) Y) → Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 12.64/12.82 True))
% 12.64/12.82 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq
% 12.64/12.82 (∀ (Y : Iota),
% 12.64/12.82 And (iext a (skS.0 3 a a_1) Y) (iext a (skS.0 4 a a_1 a_2) Y) → Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 12.64/12.82 False))
% 12.64/12.82 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq
% 12.64/12.82 (Not
% 12.64/12.82 (And (iext a (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) (iext a (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 12.64/12.82 Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 12.64/12.82 True))
% 12.64/12.82 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq
% 12.64/12.82 (And (iext a (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) (iext a (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 12.64/12.82 Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 12.64/12.82 False))
% 12.64/12.82 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False)
% 12.64/12.82 (Eq (And (iext a (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) (iext a (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 12.64/12.82 True))
% 12.64/12.82 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False) (Eq (Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))
% 12.64/12.82 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.64/12.82 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.64/12.82 (Or (Eq (ip a) False) (Eq (iext a (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) True))
% 12.69/12.85 Clause #57 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.85 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.69/12.85 (Or (Eq (ip a) False) (Eq (iext a (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True))
% 12.69/12.85 Clause #66 (by clausification #[5]): ∀ (a : Iota),
% 12.69/12.85 Eq
% 12.69/12.85 (∀ (C2 : Iota),
% 12.69/12.85 Iff (iext uri_rdfs_subClassOf a C2) (And (And (ic a) (ic C2)) (∀ (X : Iota), icext a X → icext C2 X)))
% 12.69/12.85 True
% 12.69/12.85 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota),
% 12.69/12.85 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
% 12.69/12.85 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), icext a X → icext a_1 X)) False)
% 12.69/12.85 Clause #70 (by clausification #[68]): ∀ (a a_1 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Or (Eq (And (ic a) (ic a_1)) False) (Eq (∀ (X : Iota), icext a X → icext a_1 X) False))
% 12.69/12.85 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Or (Eq (∀ (X : Iota), icext a X → icext a_1 X) False) (Or (Eq (ic a) False) (Eq (ic a_1) False)))
% 12.69/12.85 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Or (Eq (ic a) False)
% 12.69/12.85 (Or (Eq (ic a_1) False) (Eq (Not (icext a (skS.0 6 a a_1 a_2) → icext a_1 (skS.0 6 a a_1 a_2))) True)))
% 12.69/12.85 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Or (Eq (ic a) False)
% 12.69/12.85 (Or (Eq (ic a_1) False) (Eq (icext a (skS.0 6 a a_1 a_2) → icext a_1 (skS.0 6 a a_1 a_2)) False)))
% 12.69/12.85 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Or (Eq (ic a) False) (Or (Eq (ic a_1) False) (Eq (icext a (skS.0 6 a a_1 a_2)) True)))
% 12.69/12.85 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Or (Eq (iext uri_rdfs_subClassOf a a_1) True)
% 12.69/12.85 (Or (Eq (ic a) False) (Or (Eq (ic a_1) False) (Eq (icext a_1 (skS.0 6 a a_1 a_2)) False)))
% 12.69/12.85 Clause #83 (by clausification #[7]): ∀ (a : Iota),
% 12.69/12.85 Eq
% 12.69/12.85 (∀ (P C : Iota),
% 12.69/12.85 And (iext uri_owl_someValuesFrom a C) (iext uri_owl_onProperty a P) →
% 12.69/12.85 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext P X Y) (icext C Y)))
% 12.69/12.85 True
% 12.69/12.85 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota),
% 12.69/12.85 Eq
% 12.69/12.85 (∀ (C : Iota),
% 12.69/12.85 And (iext uri_owl_someValuesFrom a C) (iext uri_owl_onProperty a a_1) →
% 12.69/12.85 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_1 X Y) (icext C Y)))
% 12.69/12.85 True
% 12.69/12.85 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Eq
% 12.69/12.85 (And (iext uri_owl_someValuesFrom a a_1) (iext uri_owl_onProperty a a_2) →
% 12.69/12.85 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_2 X Y) (icext a_1 Y)))
% 12.69/12.85 True
% 12.69/12.85 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Or (Eq (And (iext uri_owl_someValuesFrom a a_1) (iext uri_owl_onProperty a a_2)) False)
% 12.69/12.85 (Eq (∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_2 X Y) (icext a_1 Y))) True)
% 12.69/12.85 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.85 Or (Eq (∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_1 X Y) (icext a_2 Y))) True)
% 12.69/12.85 (Or (Eq (iext uri_owl_someValuesFrom a a_2) False) (Eq (iext uri_owl_onProperty a a_1) False))
% 12.69/12.85 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.85 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 12.69/12.85 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 12.69/12.85 (Eq (Iff (icext a a_3) (Exists fun Y => And (iext a_2 a_3 Y) (icext a_1 Y))) True))
% 12.69/12.85 Clause #90 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.85 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 12.69/12.85 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 12.69/12.85 (Or (Eq (icext a a_3) False) (Eq (Exists fun Y => And (iext a_2 a_3 Y) (icext a_1 Y)) True)))
% 12.69/12.85 Clause #93 (by clausification #[6]): ∀ (a : Iota),
% 12.69/12.85 Eq
% 12.69/12.85 (∀ (C2 : Iota),
% 12.69/12.85 Iff (iext uri_owl_equivalentClass a C2) (And (And (ic a) (ic C2)) (∀ (X : Iota), Iff (icext a X) (icext C2 X))))
% 12.69/12.87 True
% 12.69/12.87 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota),
% 12.69/12.87 Eq
% 12.69/12.87 (Iff (iext uri_owl_equivalentClass a a_1) (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (icext a_1 X))))
% 12.69/12.87 True
% 12.69/12.87 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_equivalentClass a a_1) False)
% 12.69/12.87 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (icext a_1 X))) True)
% 12.69/12.87 Clause #104 (by clausification #[96]): ∀ (a a_1 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (∀ (X : Iota), Iff (icext a X) (icext a_1 X)) True)
% 12.69/12.87 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (Iff (icext a a_2) (icext a_1 a_2)) True)
% 12.69/12.87 Clause #107 (by clausification #[105]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Or (Eq (icext a a_2) False) (Eq (icext a_1 a_2) True))
% 12.69/12.87 Clause #116 (by clausification #[8]): ∀ (a : Iota),
% 12.69/12.87 Eq
% 12.69/12.87 (∀ (P2 : Iota),
% 12.69/12.87 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))))
% 12.69/12.87 True
% 12.69/12.87 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota),
% 12.69/12.87 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))))
% 12.69/12.87 True
% 12.69/12.87 Clause #119 (by clausification #[117]): ∀ (a a_1 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_inverseOf a a_1) False)
% 12.69/12.87 (Eq (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), Iff (iext a X Y) (iext a_1 Y X))) True)
% 12.69/12.87 Clause #129 (by clausification #[119]): ∀ (a a_1 : Iota),
% 12.69/12.87 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)
% 12.69/12.87 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.87 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)
% 12.69/12.87 Clause #131 (by clausification #[130]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.87 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)
% 12.69/12.87 Clause #133 (by clausification #[131]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_inverseOf a a_1) False) (Or (Eq (iext a a_2 a_3) False) (Eq (iext a_1 a_3 a_2) True))
% 12.69/12.87 Clause #134 (by clausification #[10]): ∀ (a : Iota),
% 12.69/12.87 Eq
% 12.69/12.87 (And
% 12.69/12.87 (And
% 12.69/12.87 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a))
% 12.69/12.87 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 12.69/12.87 (iext uri_owl_onProperty (skS.0 10 a) uri_owl_inverseOf))
% 12.69/12.87 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_owl_FunctionalProperty))
% 12.69/12.87 True
% 12.69/12.87 Clause #135 (by clausification #[134]): ∀ (a : Iota), Eq (iext uri_owl_someValuesFrom (skS.0 10 a) uri_owl_FunctionalProperty) True
% 12.69/12.87 Clause #136 (by clausification #[134]): ∀ (a : Iota),
% 12.69/12.87 Eq
% 12.69/12.87 (And
% 12.69/12.87 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a))
% 12.69/12.87 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 12.69/12.87 (iext uri_owl_onProperty (skS.0 10 a) uri_owl_inverseOf))
% 12.69/12.87 True
% 12.69/12.87 Clause #153 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 12.69/12.87 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 12.69/12.87 (Or (Eq (icext a a_3) False)
% 12.69/12.87 (Eq (And (iext a_2 a_3 (skS.0 11 a_2 a_3 a_1 a_4)) (icext a_1 (skS.0 11 a_2 a_3 a_1 a_4))) True)))
% 12.69/12.87 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 12.69/12.87 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 12.69/12.87 (Or (Eq (icext a a_3) False) (Eq (icext a_1 (skS.0 11 a_2 a_3 a_1 a_4)) True)))
% 12.69/12.87 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_someValuesFrom a a_1) False)
% 12.69/12.87 (Or (Eq (iext uri_owl_onProperty a a_2) False)
% 12.69/12.87 (Or (Eq (icext a a_3) False) (Eq (iext a_2 a_3 (skS.0 11 a_2 a_3 a_1 a_4)) True)))
% 12.69/12.87 Clause #156 (by superposition #[154, 135]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.87 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False)
% 12.69/12.87 (Or (Eq (icext (skS.0 10 a) a_2) False)
% 12.69/12.87 (Or (Eq (icext uri_owl_FunctionalProperty (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True)
% 12.69/12.88 (Eq False True)))
% 12.69/12.88 Clause #157 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.88 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True)
% 12.69/12.88 (Or (Eq (ip a) False) (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 12.69/12.88 Clause #159 (by superposition #[155, 135]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.88 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False)
% 12.69/12.88 (Or (Eq (icext (skS.0 10 a) a_2) False)
% 12.69/12.88 (Or (Eq (iext a_1 a_2 (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True) (Eq False True)))
% 12.69/12.88 Clause #161 (by clausification #[136]): ∀ (a : Iota), Eq (iext uri_owl_onProperty (skS.0 10 a) uri_owl_inverseOf) True
% 12.69/12.88 Clause #162 (by clausification #[136]): ∀ (a : Iota),
% 12.69/12.88 Eq
% 12.69/12.88 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a))
% 12.69/12.88 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction))
% 12.69/12.88 True
% 12.69/12.88 Clause #166 (by clausification #[162]): ∀ (a : Iota), Eq (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a)) True
% 12.69/12.88 Clause #170 (by superposition #[166, 16]): Or (Eq True False) (Eq (ic uri_ex_InversesOfFunctionalProperties) True)
% 12.69/12.88 Clause #172 (by superposition #[166, 107]): ∀ (a a_1 : Iota),
% 12.69/12.88 Or (Eq True False) (Or (Eq (icext uri_ex_InversesOfFunctionalProperties a) False) (Eq (icext (skS.0 10 a_1) a) True))
% 12.69/12.88 Clause #173 (by clausification #[170]): Eq (ic uri_ex_InversesOfFunctionalProperties) True
% 12.69/12.88 Clause #174 (by superposition #[173, 74]): ∀ (a a_1 : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True)
% 12.69/12.88 (Or (Eq True False)
% 12.69/12.88 (Or (Eq (ic a) False)
% 12.69/12.88 (Eq (icext uri_ex_InversesOfFunctionalProperties (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) True)))
% 12.69/12.88 Clause #177 (by superposition #[173, 75]): ∀ (a a_1 : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True)
% 12.69/12.88 (Or (Eq True False)
% 12.69/12.88 (Or (Eq (ic a) False) (Eq (icext a (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) False)))
% 12.69/12.88 Clause #189 (by clausification #[172]): ∀ (a a_1 : Iota), Or (Eq (icext uri_ex_InversesOfFunctionalProperties a) False) (Eq (icext (skS.0 10 a_1) a) True)
% 12.69/12.88 Clause #205 (by clausification #[177]): ∀ (a a_1 : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True)
% 12.69/12.88 (Or (Eq (ic a) False) (Eq (icext a (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) False))
% 12.69/12.88 Clause #206 (by superposition #[205, 0]): ∀ (a : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True)
% 12.69/12.88 (Or
% 12.69/12.88 (Eq
% 12.69/12.88 (icext uri_owl_InverseFunctionalProperty
% 12.69/12.88 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.88 False)
% 12.69/12.88 (Eq False True))
% 12.69/12.88 Clause #212 (by clausification #[206]): ∀ (a : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True)
% 12.69/12.88 (Eq
% 12.69/12.88 (icext uri_owl_InverseFunctionalProperty
% 12.69/12.88 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.88 False)
% 12.69/12.88 Clause #213 (by forward demodulation #[212, 11]): ∀ (a : Iota),
% 12.69/12.88 Or (Eq False True)
% 12.69/12.88 (Eq
% 12.69/12.88 (icext uri_owl_InverseFunctionalProperty
% 12.69/12.88 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.88 False)
% 12.69/12.88 Clause #214 (by clausification #[213]): ∀ (a : Iota),
% 12.69/12.88 Eq
% 12.69/12.88 (icext uri_owl_InverseFunctionalProperty
% 12.69/12.88 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.88 False
% 12.69/12.88 Clause #215 (by clausification #[174]): ∀ (a a_1 : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True)
% 12.69/12.88 (Or (Eq (ic a) False)
% 12.69/12.88 (Eq (icext uri_ex_InversesOfFunctionalProperties (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) True))
% 12.69/12.88 Clause #216 (by superposition #[215, 0]): ∀ (a : Iota),
% 12.69/12.88 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True)
% 12.69/12.88 (Or
% 12.69/12.88 (Eq
% 12.69/12.88 (icext uri_ex_InversesOfFunctionalProperties
% 12.69/12.90 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.90 True)
% 12.69/12.90 (Eq False True))
% 12.69/12.90 Clause #230 (by clausification #[216]): ∀ (a : Iota),
% 12.69/12.90 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True)
% 12.69/12.90 (Eq
% 12.69/12.90 (icext uri_ex_InversesOfFunctionalProperties
% 12.69/12.90 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.90 True)
% 12.69/12.90 Clause #231 (by forward demodulation #[230, 11]): ∀ (a : Iota),
% 12.69/12.90 Or (Eq False True)
% 12.69/12.90 (Eq
% 12.69/12.90 (icext uri_ex_InversesOfFunctionalProperties
% 12.69/12.90 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.90 True)
% 12.69/12.90 Clause #232 (by clausification #[231]): ∀ (a : Iota),
% 12.69/12.90 Eq
% 12.69/12.90 (icext uri_ex_InversesOfFunctionalProperties
% 12.69/12.90 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.69/12.90 True
% 12.69/12.90 Clause #233 (by superposition #[232, 189]): ∀ (a a_1 : Iota),
% 12.69/12.90 Or (Eq True False)
% 12.69/12.90 (Eq (icext (skS.0 10 a) (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a_1)) True)
% 12.69/12.90 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota),
% 12.69/12.90 Eq (icext (skS.0 10 a) (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a_1)) True
% 12.69/12.90 Clause #275 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.69/12.90 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False)
% 12.69/12.90 (Or (Eq (icext (skS.0 10 a) a_2) False)
% 12.69/12.90 (Eq (icext uri_owl_FunctionalProperty (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True))
% 12.69/12.90 Clause #276 (by superposition #[275, 161]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.90 Or (Eq (icext (skS.0 10 a) a_1) False)
% 12.69/12.90 (Or (Eq (icext uri_owl_FunctionalProperty (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True)
% 12.69/12.90 (Eq False True))
% 12.69/12.90 Clause #277 (by clausification #[276]): ∀ (a a_1 a_2 : Iota),
% 12.69/12.90 Or (Eq (icext (skS.0 10 a) a_1) False)
% 12.69/12.90 (Eq (icext uri_owl_FunctionalProperty (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True)
% 12.69/12.90 Clause #278 (by superposition #[277, 234]): ∀ (a a_1 : Iota),
% 12.69/12.90 Or
% 12.69/12.90 (Eq
% 12.69/12.90 (icext uri_owl_FunctionalProperty
% 12.69/12.90 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.69/12.90 uri_owl_FunctionalProperty a_1))
% 12.69/12.90 True)
% 12.69/12.90 (Eq False True)
% 12.69/12.90 Clause #279 (by clausification #[278]): ∀ (a a_1 : Iota),
% 12.69/12.90 Eq
% 12.69/12.90 (icext uri_owl_FunctionalProperty
% 12.69/12.90 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.69/12.90 uri_owl_FunctionalProperty a_1))
% 12.69/12.90 True
% 12.69/12.90 Clause #280 (by superposition #[279, 43]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.69/12.90 Or (Eq True False)
% 12.69/12.90 (Or
% 12.69/12.90 (Eq
% 12.69/12.90 (iext
% 12.69/12.90 (skS.0 11 uri_owl_inverseOf
% 12.69/12.90 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.69/12.90 uri_owl_FunctionalProperty a_1)
% 12.69/12.90 a_2 a_3)
% 12.69/12.90 False)
% 12.69/12.90 (Or
% 12.69/12.90 (Eq
% 12.69/12.90 (iext
% 12.69/12.90 (skS.0 11 uri_owl_inverseOf
% 12.74/12.90 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.90 uri_owl_FunctionalProperty a_1)
% 12.74/12.90 a_2 a_4)
% 12.74/12.90 False)
% 12.74/12.90 (Eq a_3 a_4)))
% 12.74/12.90 Clause #309 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.90 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False)
% 12.74/12.90 (Or (Eq (icext (skS.0 10 a) a_2) False) (Eq (iext a_1 a_2 (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True))
% 12.74/12.90 Clause #310 (by superposition #[309, 161]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.90 Or (Eq (icext (skS.0 10 a) a_1) False)
% 12.74/12.90 (Or (Eq (iext uri_owl_inverseOf a_1 (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True)
% 12.74/12.90 (Eq False True))
% 12.74/12.90 Clause #313 (by clausification #[310]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.90 Or (Eq (icext (skS.0 10 a) a_1) False)
% 12.74/12.90 (Eq (iext uri_owl_inverseOf a_1 (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True)
% 12.74/12.90 Clause #314 (by superposition #[313, 234]): ∀ (a a_1 : Iota),
% 12.74/12.90 Or
% 12.74/12.90 (Eq
% 12.74/12.90 (iext uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 uri_owl_FunctionalProperty a_1))
% 12.74/12.91 True)
% 12.74/12.91 (Eq False True)
% 12.74/12.91 Clause #315 (by clausification #[314]): ∀ (a a_1 : Iota),
% 12.74/12.91 Eq
% 12.74/12.91 (iext uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 uri_owl_FunctionalProperty a_1))
% 12.74/12.91 True
% 12.74/12.91 Clause #316 (by superposition #[315, 21]): ∀ (a : Iota),
% 12.74/12.91 Or (Eq True False) (Eq (ip (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) True)
% 12.74/12.91 Clause #318 (by superposition #[315, 133]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.91 Or (Eq True False)
% 12.74/12.91 (Or (Eq (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) False)
% 12.74/12.91 (Eq
% 12.74/12.91 (iext
% 12.74/12.91 (skS.0 11 uri_owl_inverseOf
% 12.74/12.91 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 uri_owl_FunctionalProperty a_3)
% 12.74/12.91 a_2 a_1)
% 12.74/12.91 True))
% 12.74/12.91 Clause #320 (by clausification #[316]): ∀ (a : Iota), Eq (ip (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) True
% 12.74/12.91 Clause #322 (by superposition #[320, 56]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.91 Or
% 12.74/12.91 (Eq
% 12.74/12.91 (icext uri_owl_InverseFunctionalProperty
% 12.74/12.91 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.74/12.91 True)
% 12.74/12.91 (Or (Eq True False)
% 12.74/12.91 (Eq
% 12.74/12.91 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)
% 12.74/12.91 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.91 True))
% 12.74/12.91 Clause #326 (by superposition #[320, 157]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.91 Or
% 12.74/12.91 (Eq
% 12.74/12.91 (icext uri_owl_InverseFunctionalProperty
% 12.74/12.91 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.74/12.91 True)
% 12.74/12.91 (Or (Eq True False)
% 12.74/12.91 (Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.91 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)))
% 12.74/12.91 Clause #327 (by superposition #[320, 57]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.91 Or
% 12.74/12.91 (Eq
% 12.74/12.91 (icext uri_owl_InverseFunctionalProperty
% 12.74/12.91 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.74/12.91 True)
% 12.74/12.91 (Or (Eq True False)
% 12.74/12.91 (Eq
% 12.74/12.91 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.91 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.91 True))
% 12.74/12.91 Clause #406 (by clausification #[318]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.91 Or (Eq (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) False)
% 12.74/12.91 (Eq
% 12.74/12.91 (iext
% 12.74/12.91 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.91 uri_owl_FunctionalProperty a_3)
% 12.74/12.91 a_2 a_1)
% 12.74/12.91 True)
% 12.74/12.91 Clause #490 (by clausification #[326]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.91 Or
% 12.74/12.91 (Eq
% 12.74/12.91 (icext uri_owl_InverseFunctionalProperty
% 12.74/12.91 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.74/12.91 True)
% 12.74/12.91 (Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.91 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2))
% 12.74/12.91 Clause #491 (by forward demodulation #[490, 214]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.91 Or (Eq False True)
% 12.74/12.91 (Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.93 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2))
% 12.74/12.93 Clause #492 (by clausification #[491]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.93 Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.93 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)
% 12.74/12.93 Clause #613 (by clausification #[280]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.74/12.93 Or
% 12.74/12.93 (Eq
% 12.74/12.93 (iext
% 12.74/12.93 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 uri_owl_FunctionalProperty a_1)
% 12.74/12.93 a_2 a_3)
% 12.74/12.93 False)
% 12.74/12.93 (Or
% 12.74/12.93 (Eq
% 12.74/12.93 (iext
% 12.74/12.93 (skS.0 11 uri_owl_inverseOf
% 12.74/12.93 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 uri_owl_FunctionalProperty a_1)
% 12.74/12.93 a_2 a_4)
% 12.74/12.93 False)
% 12.74/12.93 (Eq a_3 a_4))
% 12.74/12.93 Clause #705 (by clausification #[327]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.93 Or
% 12.74/12.93 (Eq
% 12.74/12.93 (icext uri_owl_InverseFunctionalProperty
% 12.74/12.93 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.74/12.93 True)
% 12.74/12.93 (Eq
% 12.74/12.93 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.93 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.93 True)
% 12.74/12.93 Clause #706 (by forward demodulation #[705, 214]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.93 Or (Eq False True)
% 12.74/12.93 (Eq
% 12.74/12.93 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.93 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.93 True)
% 12.74/12.93 Clause #707 (by clausification #[706]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.93 Eq
% 12.74/12.93 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.93 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.93 True
% 12.74/12.93 Clause #708 (by superposition #[707, 406]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.74/12.93 Or (Eq True False)
% 12.74/12.93 (Eq
% 12.74/12.93 (iext
% 12.74/12.93 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 uri_owl_FunctionalProperty a_1)
% 12.74/12.93 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4)
% 12.74/12.93 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2))
% 12.74/12.93 True)
% 12.74/12.93 Clause #722 (by clausification #[708]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.74/12.93 Eq
% 12.74/12.93 (iext
% 12.74/12.93 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 uri_owl_FunctionalProperty a_1)
% 12.74/12.93 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4)
% 12.74/12.93 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2))
% 12.74/12.93 True
% 12.74/12.93 Clause #724 (by superposition #[722, 613]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.74/12.93 Or (Eq True False)
% 12.74/12.93 (Or
% 12.74/12.93 (Eq
% 12.74/12.93 (iext
% 12.74/12.93 (skS.0 11 uri_owl_inverseOf
% 12.74/12.93 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.93 uri_owl_FunctionalProperty a_1)
% 12.74/12.93 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) a_5)
% 12.74/12.93 False)
% 12.74/12.93 (Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2) a_5))
% 12.74/12.93 Clause #725 (by clausification #[724]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.74/12.93 Or
% 12.74/12.93 (Eq
% 12.74/12.93 (iext
% 12.74/12.93 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.94 uri_owl_FunctionalProperty a_1)
% 12.74/12.94 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) a_5)
% 12.74/12.94 False)
% 12.74/12.94 (Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2) a_5)
% 12.74/12.94 Clause #732 (by clausification #[322]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.94 Or
% 12.74/12.94 (Eq
% 12.74/12.94 (icext uri_owl_InverseFunctionalProperty
% 12.74/12.94 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a))
% 12.74/12.94 True)
% 12.74/12.94 (Eq
% 12.74/12.94 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)
% 12.74/12.94 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.94 True)
% 12.74/12.94 Clause #733 (by forward demodulation #[732, 214]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.94 Or (Eq False True)
% 12.74/12.94 (Eq
% 12.74/12.94 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)
% 12.74/12.94 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.94 True)
% 12.74/12.94 Clause #734 (by clausification #[733]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.74/12.94 Eq
% 12.74/12.94 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)
% 12.74/12.94 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3))
% 12.74/12.94 True
% 12.74/12.94 Clause #735 (by superposition #[734, 406]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.74/12.94 Or (Eq True False)
% 12.74/12.94 (Eq
% 12.74/12.94 (iext
% 12.74/12.94 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.94 uri_owl_FunctionalProperty a_1)
% 12.74/12.94 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3))
% 12.74/12.94 True)
% 12.74/12.94 Clause #736 (by clausification #[735]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.74/12.94 Eq
% 12.74/12.94 (iext
% 12.74/12.94 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)
% 12.74/12.94 uri_owl_FunctionalProperty a_1)
% 12.74/12.94 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3))
% 12.74/12.94 True
% 12.74/12.94 Clause #737 (by superposition #[736, 725]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.94 Or (Eq True False)
% 12.74/12.94 (Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2))
% 12.74/12.94 Clause #740 (by clausification #[737]): ∀ (a a_1 a_2 : Iota),
% 12.74/12.94 Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1)
% 12.74/12.94 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)
% 12.74/12.94 Clause #741 (by forward contextual literal cutting #[740, 492]): False
% 12.74/12.94 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------