%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWB028+2 : TPTP v9.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 : Fri Oct 3 08:03:29 PM UTC 2025 % Result : Theorem 14.84s 14.99s % Output : Proof 15.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SWB028+2 : TPTP v9.2.0. Released v5.2.0. % 0.04/0.15 % Command : duper %s % 0.16/0.36 % Computer : n026.cluster.edu % 0.16/0.36 % Model : x86_64 x86_64 % 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.36 % Memory : 8042.1875MB % 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 300 % 0.16/0.36 % DateTime : Thu Oct 2 11:55:23 EDT 2025 % 0.16/0.36 % CPUTime : % 14.84/14.99 SZS status Theorem for theBenchmark.p % 14.84/14.99 SZS output start Proof for theBenchmark.p % 14.84/14.99 Clause #0 (by assumption #[]): Eq (ic uri_owl_InverseFunctionalProperty) True % 14.84/14.99 Clause #1 (by assumption #[]): Eq (∀ (X Y : Iota), iext uri_owl_inverseOf X Y → And (ip X) (ip Y)) True % 14.84/14.99 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), iext uri_owl_equivalentClass X Y → And (ic X) (ic Y)) True % 14.84/14.99 Clause #3 (by assumption #[]): Eq % 14.84/14.99 (∀ (P : Iota), % 14.84/14.99 Iff (icext uri_owl_FunctionalProperty P) % 14.84/14.99 (And (ip P) (∀ (X Y1 Y2 : Iota), And (iext P X Y1) (iext P X Y2) → Eq Y1 Y2))) % 14.84/14.99 True % 14.84/14.99 Clause #4 (by assumption #[]): Eq % 14.84/14.99 (∀ (P : Iota), % 14.84/14.99 Iff (icext uri_owl_InverseFunctionalProperty P) % 14.84/14.99 (And (ip P) (∀ (X1 X2 Y : Iota), And (iext P X1 Y) (iext P X2 Y) → Eq X1 X2))) % 14.84/14.99 True % 14.84/14.99 Clause #5 (by assumption #[]): Eq % 14.84/14.99 (∀ (C1 C2 : Iota), % 14.84/14.99 Iff (iext uri_rdfs_subClassOf C1 C2) (And (And (ic C1) (ic C2)) (∀ (X : Iota), icext C1 X → icext C2 X))) % 14.84/14.99 True % 14.84/14.99 Clause #6 (by assumption #[]): Eq % 14.84/14.99 (∀ (C1 C2 : Iota), % 14.84/14.99 Iff (iext uri_owl_equivalentClass C1 C2) (And (And (ic C1) (ic C2)) (∀ (X : Iota), Iff (icext C1 X) (icext C2 X)))) % 14.84/14.99 True % 14.84/14.99 Clause #7 (by assumption #[]): Eq % 14.84/14.99 (∀ (Z P C : Iota), % 14.84/14.99 And (iext uri_owl_someValuesFrom Z C) (iext uri_owl_onProperty Z P) → % 14.84/14.99 ∀ (X : Iota), Iff (icext Z X) (Exists fun Y => And (iext P X Y) (icext C Y))) % 14.84/14.99 True % 14.84/14.99 Clause #8 (by assumption #[]): Eq % 14.84/14.99 (∀ (P1 P2 : Iota), % 14.84/14.99 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)))) % 14.84/14.99 True % 14.84/14.99 Clause #9 (by assumption #[]): Eq (Not (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty)) True % 14.84/14.99 Clause #10 (by assumption #[]): Eq % 14.84/14.99 (Exists fun BNODE_z => % 14.84/14.99 And % 14.84/14.99 (And % 14.84/14.99 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties BNODE_z) % 14.84/14.99 (iext uri_rdf_type BNODE_z uri_owl_Restriction)) % 14.84/14.99 (iext uri_owl_onProperty BNODE_z uri_owl_inverseOf)) % 14.84/14.99 (iext uri_owl_someValuesFrom BNODE_z uri_owl_FunctionalProperty)) % 14.84/15.00 True % 14.84/15.00 Clause #11 (by clausification #[9]): Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) False % 14.84/15.00 Clause #12 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), iext uri_owl_equivalentClass a Y → And (ic a) (ic Y)) True % 14.84/15.00 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (iext uri_owl_equivalentClass a a_1 → And (ic a) (ic a_1)) True % 14.84/15.00 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) % 14.84/15.00 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (ic a) True) % 14.84/15.00 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y : Iota), iext uri_owl_inverseOf a Y → And (ip a) (ip Y)) True % 14.84/15.00 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (iext uri_owl_inverseOf a a_1 → And (ip a) (ip a_1)) True % 14.84/15.00 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) % 14.84/15.00 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (iext uri_owl_inverseOf a a_1) False) (Eq (ip a) True) % 14.84/15.00 Clause #22 (by clausification #[3]): ∀ (a : Iota), % 14.84/15.00 Eq % 14.84/15.00 (Iff (icext uri_owl_FunctionalProperty a) % 14.84/15.00 (And (ip a) (∀ (X Y1 Y2 : Iota), And (iext a X Y1) (iext a X Y2) → Eq Y1 Y2))) % 14.84/15.00 True % 14.84/15.00 Clause #24 (by clausification #[22]): ∀ (a : Iota), % 14.84/15.00 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.00 (Eq (And (ip a) (∀ (X Y1 Y2 : Iota), And (iext a X Y1) (iext a X Y2) → Eq Y1 Y2)) True) % 14.84/15.00 Clause #36 (by clausification #[24]): ∀ (a : Iota), % 14.84/15.00 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.00 (Eq (∀ (X Y1 Y2 : Iota), And (iext a X Y1) (iext a X Y2) → Eq Y1 Y2) True) % 14.84/15.00 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), % 14.84/15.00 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.00 (Eq (∀ (Y1 Y2 : Iota), And (iext a a_1 Y1) (iext a a_1 Y2) → Eq Y1 Y2) True) % 14.84/15.00 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 14.84/15.00 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.02 (Eq (∀ (Y2 : Iota), And (iext a a_1 a_2) (iext a a_1 Y2) → Eq a_2 Y2) True) % 14.84/15.02 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 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) % 14.84/15.02 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.02 (Or (Eq (And (iext a a_1 a_2) (iext a a_1 a_3)) False) (Eq (Eq a_2 a_3) True)) % 14.84/15.02 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.02 (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))) % 14.84/15.02 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_FunctionalProperty a) False) % 14.84/15.02 (Or (Eq (iext a a_1 a_2) False) (Or (Eq (iext a a_1 a_3) False) (Eq a_2 a_3))) % 14.84/15.02 Clause #44 (by clausification #[4]): ∀ (a : Iota), % 14.84/15.02 Eq % 14.84/15.02 (Iff (icext uri_owl_InverseFunctionalProperty a) % 14.84/15.02 (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2))) % 14.84/15.02 True % 14.84/15.02 Clause #45 (by clausification #[44]): ∀ (a : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Eq (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2)) False) % 14.84/15.02 Clause #47 (by clausification #[45]): ∀ (a : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) (Eq (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2) False)) % 14.84/15.02 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (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)) % 14.84/15.02 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (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)) % 14.84/15.02 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (Eq % 14.84/15.02 (Not % 14.84/15.02 (∀ (Y : Iota), % 14.84/15.02 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))) % 14.84/15.02 True)) % 14.84/15.02 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (Eq % 14.84/15.02 (∀ (Y : Iota), % 14.84/15.02 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)) % 14.84/15.02 False)) % 14.84/15.02 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (Eq % 14.84/15.02 (Not % 14.84/15.02 (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)) → % 14.84/15.02 Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 14.84/15.02 True)) % 14.84/15.02 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (Eq % 14.84/15.02 (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)) → % 14.84/15.02 Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 14.84/15.02 False)) % 14.84/15.02 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) % 14.84/15.02 (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))) % 14.84/15.02 True)) % 14.84/15.02 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (Or (Eq (ip a) False) (Eq (Eq (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)) % 14.84/15.02 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 14.84/15.02 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.84/15.02 (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)) % 14.89/15.05 Clause #57 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 14.89/15.05 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.89/15.05 (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)) % 14.89/15.05 Clause #66 (by clausification #[5]): ∀ (a : Iota), % 14.89/15.05 Eq % 14.89/15.05 (∀ (C2 : Iota), % 14.89/15.05 Iff (iext uri_rdfs_subClassOf a C2) (And (And (ic a) (ic C2)) (∀ (X : Iota), icext a X → icext C2 X))) % 14.89/15.05 True % 14.89/15.05 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 14.89/15.05 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 % 14.89/15.05 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), icext a X → icext a_1 X)) False) % 14.89/15.05 Clause #70 (by clausification #[68]): ∀ (a a_1 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Or (Eq (And (ic a) (ic a_1)) False) (Eq (∀ (X : Iota), icext a X → icext a_1 X) False)) % 14.89/15.05 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Or (Eq (∀ (X : Iota), icext a X → icext a_1 X) False) (Or (Eq (ic a) False) (Eq (ic a_1) False))) % 14.89/15.05 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Or (Eq (ic a) False) % 14.89/15.05 (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))) % 14.89/15.05 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Or (Eq (ic a) False) % 14.89/15.05 (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))) % 14.89/15.05 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Or (Eq (ic a) False) (Or (Eq (ic a_1) False) (Eq (icext a (skS.0 6 a a_1 a_2)) True))) % 14.89/15.05 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Or (Eq (iext uri_rdfs_subClassOf a a_1) True) % 14.89/15.05 (Or (Eq (ic a) False) (Or (Eq (ic a_1) False) (Eq (icext a_1 (skS.0 6 a a_1 a_2)) False))) % 14.89/15.05 Clause #83 (by clausification #[7]): ∀ (a : Iota), % 14.89/15.05 Eq % 14.89/15.05 (∀ (P C : Iota), % 14.89/15.05 And (iext uri_owl_someValuesFrom a C) (iext uri_owl_onProperty a P) → % 14.89/15.05 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext P X Y) (icext C Y))) % 14.89/15.05 True % 14.89/15.05 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), % 14.89/15.05 Eq % 14.89/15.05 (∀ (C : Iota), % 14.89/15.05 And (iext uri_owl_someValuesFrom a C) (iext uri_owl_onProperty a a_1) → % 14.89/15.05 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_1 X Y) (icext C Y))) % 14.89/15.05 True % 14.89/15.05 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Eq % 14.89/15.05 (And (iext uri_owl_someValuesFrom a a_1) (iext uri_owl_onProperty a a_2) → % 14.89/15.05 ∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_2 X Y) (icext a_1 Y))) % 14.89/15.05 True % 14.89/15.05 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Or (Eq (And (iext uri_owl_someValuesFrom a a_1) (iext uri_owl_onProperty a a_2)) False) % 14.89/15.05 (Eq (∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_2 X Y) (icext a_1 Y))) True) % 14.89/15.05 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 14.89/15.05 Or (Eq (∀ (X : Iota), Iff (icext a X) (Exists fun Y => And (iext a_1 X Y) (icext a_2 Y))) True) % 14.89/15.05 (Or (Eq (iext uri_owl_someValuesFrom a a_2) False) (Eq (iext uri_owl_onProperty a a_1) False)) % 14.89/15.05 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), % 14.89/15.05 Or (Eq (iext uri_owl_someValuesFrom a a_1) False) % 14.89/15.05 (Or (Eq (iext uri_owl_onProperty a a_2) False) % 14.89/15.05 (Eq (Iff (icext a a_3) (Exists fun Y => And (iext a_2 a_3 Y) (icext a_1 Y))) True)) % 14.89/15.05 Clause #90 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), % 14.89/15.05 Or (Eq (iext uri_owl_someValuesFrom a a_1) False) % 14.89/15.05 (Or (Eq (iext uri_owl_onProperty a a_2) False) % 14.89/15.05 (Or (Eq (icext a a_3) False) (Eq (Exists fun Y => And (iext a_2 a_3 Y) (icext a_1 Y)) True))) % 14.89/15.05 Clause #93 (by clausification #[6]): ∀ (a : Iota), % 14.89/15.05 Eq % 14.89/15.05 (∀ (C2 : Iota), % 14.89/15.05 Iff (iext uri_owl_equivalentClass a C2) (And (And (ic a) (ic C2)) (∀ (X : Iota), Iff (icext a X) (icext C2 X)))) % 14.91/15.08 True % 14.91/15.08 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), % 14.91/15.08 Eq % 14.91/15.08 (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)))) % 14.91/15.08 True % 14.91/15.08 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_equivalentClass a a_1) False) % 14.91/15.08 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (icext a_1 X))) True) % 14.91/15.08 Clause #104 (by clausification #[96]): ∀ (a a_1 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Eq (∀ (X : Iota), Iff (icext a X) (icext a_1 X)) True) % 14.91/15.08 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) % 14.91/15.08 Clause #107 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_equivalentClass a a_1) False) (Or (Eq (icext a a_2) False) (Eq (icext a_1 a_2) True)) % 14.91/15.08 Clause #116 (by clausification #[8]): ∀ (a : Iota), % 14.91/15.08 Eq % 14.91/15.08 (∀ (P2 : Iota), % 14.91/15.08 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)))) % 14.91/15.08 True % 14.91/15.08 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota), % 14.91/15.08 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)))) % 14.91/15.08 True % 14.91/15.08 Clause #119 (by clausification #[117]): ∀ (a a_1 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_inverseOf a a_1) False) % 14.91/15.08 (Eq (And (And (ip a) (ip a_1)) (∀ (X Y : Iota), Iff (iext a X Y) (iext a_1 Y X))) True) % 14.91/15.08 Clause #129 (by clausification #[119]): ∀ (a a_1 : Iota), % 14.91/15.08 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) % 14.91/15.08 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota), % 14.91/15.08 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) % 14.91/15.08 Clause #131 (by clausification #[130]): ∀ (a a_1 a_2 a_3 : Iota), % 14.91/15.08 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) % 14.91/15.08 Clause #133 (by clausification #[131]): ∀ (a a_1 a_2 a_3 : Iota), % 14.91/15.08 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)) % 14.91/15.08 Clause #134 (by clausification #[10]): ∀ (a : Iota), % 14.91/15.08 Eq % 14.91/15.08 (And % 14.91/15.08 (And % 14.91/15.08 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a)) % 14.91/15.08 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction)) % 14.91/15.08 (iext uri_owl_onProperty (skS.0 10 a) uri_owl_inverseOf)) % 14.91/15.08 (iext uri_owl_someValuesFrom (skS.0 10 a) uri_owl_FunctionalProperty)) % 14.91/15.08 True % 14.91/15.08 Clause #135 (by clausification #[134]): ∀ (a : Iota), Eq (iext uri_owl_someValuesFrom (skS.0 10 a) uri_owl_FunctionalProperty) True % 14.91/15.08 Clause #136 (by clausification #[134]): ∀ (a : Iota), % 14.91/15.08 Eq % 14.91/15.08 (And % 14.91/15.08 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a)) % 14.91/15.08 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction)) % 14.91/15.08 (iext uri_owl_onProperty (skS.0 10 a) uri_owl_inverseOf)) % 14.91/15.08 True % 14.91/15.08 Clause #153 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_someValuesFrom a a_1) False) % 14.91/15.08 (Or (Eq (iext uri_owl_onProperty a a_2) False) % 14.91/15.08 (Or (Eq (icext a a_3) False) % 14.91/15.08 (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))) % 14.91/15.08 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_someValuesFrom a a_1) False) % 14.91/15.08 (Or (Eq (iext uri_owl_onProperty a a_2) False) % 14.91/15.08 (Or (Eq (icext a a_3) False) (Eq (icext a_1 (skS.0 11 a_2 a_3 a_1 a_4)) True))) % 14.91/15.08 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_someValuesFrom a a_1) False) % 14.91/15.08 (Or (Eq (iext uri_owl_onProperty a a_2) False) % 14.91/15.08 (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))) % 14.91/15.08 Clause #156 (by superposition #[154, 135]): ∀ (a a_1 a_2 a_3 : Iota), % 14.91/15.08 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False) % 14.91/15.08 (Or (Eq (icext (skS.0 10 a) a_2) False) % 14.91/15.08 (Or (Eq (icext uri_owl_FunctionalProperty (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True) % 14.91/15.10 (Eq False True))) % 14.91/15.10 Clause #157 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 14.91/15.10 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 14.91/15.10 (Or (Eq (ip a) False) (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 14.91/15.10 Clause #159 (by superposition #[155, 135]): ∀ (a a_1 a_2 a_3 : Iota), % 14.91/15.10 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False) % 14.91/15.10 (Or (Eq (icext (skS.0 10 a) a_2) False) % 14.91/15.10 (Or (Eq (iext a_1 a_2 (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True) (Eq False True))) % 14.91/15.10 Clause #161 (by clausification #[136]): ∀ (a : Iota), Eq (iext uri_owl_onProperty (skS.0 10 a) uri_owl_inverseOf) True % 14.91/15.10 Clause #162 (by clausification #[136]): ∀ (a : Iota), % 14.91/15.10 Eq % 14.91/15.10 (And (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a)) % 14.91/15.10 (iext uri_rdf_type (skS.0 10 a) uri_owl_Restriction)) % 14.91/15.10 True % 14.91/15.10 Clause #166 (by clausification #[162]): ∀ (a : Iota), Eq (iext uri_owl_equivalentClass uri_ex_InversesOfFunctionalProperties (skS.0 10 a)) True % 14.91/15.10 Clause #170 (by superposition #[166, 16]): Or (Eq True False) (Eq (ic uri_ex_InversesOfFunctionalProperties) True) % 14.91/15.10 Clause #172 (by superposition #[166, 107]): ∀ (a a_1 : Iota), % 14.91/15.10 Or (Eq True False) (Or (Eq (icext uri_ex_InversesOfFunctionalProperties a) False) (Eq (icext (skS.0 10 a_1) a) True)) % 14.91/15.10 Clause #173 (by clausification #[170]): Eq (ic uri_ex_InversesOfFunctionalProperties) True % 14.91/15.10 Clause #174 (by superposition #[173, 74]): ∀ (a a_1 : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True) % 14.91/15.10 (Or (Eq True False) % 14.91/15.10 (Or (Eq (ic a) False) % 14.91/15.10 (Eq (icext uri_ex_InversesOfFunctionalProperties (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) True))) % 14.91/15.10 Clause #177 (by superposition #[173, 75]): ∀ (a a_1 : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True) % 14.91/15.10 (Or (Eq True False) % 14.91/15.10 (Or (Eq (ic a) False) (Eq (icext a (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) False))) % 14.91/15.10 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) % 14.91/15.10 Clause #205 (by clausification #[177]): ∀ (a a_1 : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True) % 14.91/15.10 (Or (Eq (ic a) False) (Eq (icext a (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) False)) % 14.91/15.10 Clause #206 (by superposition #[205, 0]): ∀ (a : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True) % 14.91/15.10 (Or % 14.91/15.10 (Eq % 14.91/15.10 (icext uri_owl_InverseFunctionalProperty % 14.91/15.10 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.91/15.10 False) % 14.91/15.10 (Eq False True)) % 14.91/15.10 Clause #212 (by clausification #[206]): ∀ (a : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True) % 14.91/15.10 (Eq % 14.91/15.10 (icext uri_owl_InverseFunctionalProperty % 14.91/15.10 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.91/15.10 False) % 14.91/15.10 Clause #213 (by forward demodulation #[212, 11]): ∀ (a : Iota), % 14.91/15.10 Or (Eq False True) % 14.91/15.10 (Eq % 14.91/15.10 (icext uri_owl_InverseFunctionalProperty % 14.91/15.10 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.91/15.10 False) % 14.91/15.10 Clause #214 (by clausification #[213]): ∀ (a : Iota), % 14.91/15.10 Eq % 14.91/15.10 (icext uri_owl_InverseFunctionalProperty % 14.91/15.10 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.91/15.10 False % 14.91/15.10 Clause #215 (by clausification #[174]): ∀ (a a_1 : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties a) True) % 14.91/15.10 (Or (Eq (ic a) False) % 14.91/15.10 (Eq (icext uri_ex_InversesOfFunctionalProperties (skS.0 6 uri_ex_InversesOfFunctionalProperties a a_1)) True)) % 14.91/15.10 Clause #216 (by superposition #[215, 0]): ∀ (a : Iota), % 14.91/15.10 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True) % 14.91/15.10 (Or % 14.91/15.10 (Eq % 14.91/15.10 (icext uri_ex_InversesOfFunctionalProperties % 14.97/15.12 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.12 True) % 14.97/15.12 (Eq False True)) % 14.97/15.12 Clause #230 (by clausification #[216]): ∀ (a : Iota), % 14.97/15.12 Or (Eq (iext uri_rdfs_subClassOf uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty) True) % 14.97/15.12 (Eq % 14.97/15.12 (icext uri_ex_InversesOfFunctionalProperties % 14.97/15.12 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.12 True) % 14.97/15.12 Clause #231 (by forward demodulation #[230, 11]): ∀ (a : Iota), % 14.97/15.12 Or (Eq False True) % 14.97/15.12 (Eq % 14.97/15.12 (icext uri_ex_InversesOfFunctionalProperties % 14.97/15.12 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.12 True) % 14.97/15.12 Clause #232 (by clausification #[231]): ∀ (a : Iota), % 14.97/15.12 Eq % 14.97/15.12 (icext uri_ex_InversesOfFunctionalProperties % 14.97/15.12 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.12 True % 14.97/15.12 Clause #233 (by superposition #[232, 189]): ∀ (a a_1 : Iota), % 14.97/15.12 Or (Eq True False) % 14.97/15.12 (Eq (icext (skS.0 10 a) (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a_1)) True) % 14.97/15.12 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota), % 14.97/15.12 Eq (icext (skS.0 10 a) (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a_1)) True % 14.97/15.12 Clause #275 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.12 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False) % 14.97/15.12 (Or (Eq (icext (skS.0 10 a) a_2) False) % 14.97/15.12 (Eq (icext uri_owl_FunctionalProperty (skS.0 11 a_1 a_2 uri_owl_FunctionalProperty a_3)) True)) % 14.97/15.12 Clause #276 (by superposition #[275, 161]): ∀ (a a_1 a_2 : Iota), % 14.97/15.12 Or (Eq (icext (skS.0 10 a) a_1) False) % 14.97/15.12 (Or (Eq (icext uri_owl_FunctionalProperty (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True) % 14.97/15.12 (Eq False True)) % 14.97/15.12 Clause #277 (by clausification #[276]): ∀ (a a_1 a_2 : Iota), % 14.97/15.12 Or (Eq (icext (skS.0 10 a) a_1) False) % 14.97/15.12 (Eq (icext uri_owl_FunctionalProperty (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True) % 14.97/15.12 Clause #278 (by superposition #[277, 234]): ∀ (a a_1 : Iota), % 14.97/15.12 Or % 14.97/15.12 (Eq % 14.97/15.12 (icext uri_owl_FunctionalProperty % 14.97/15.12 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.12 uri_owl_FunctionalProperty a_1)) % 14.97/15.12 True) % 14.97/15.12 (Eq False True) % 14.97/15.12 Clause #279 (by clausification #[278]): ∀ (a a_1 : Iota), % 14.97/15.12 Eq % 14.97/15.12 (icext uri_owl_FunctionalProperty % 14.97/15.12 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.12 uri_owl_FunctionalProperty a_1)) % 14.97/15.12 True % 14.97/15.12 Clause #280 (by superposition #[279, 43]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.97/15.12 Or (Eq True False) % 14.97/15.12 (Or % 14.97/15.12 (Eq % 14.97/15.12 (iext % 14.97/15.12 (skS.0 11 uri_owl_inverseOf % 14.97/15.12 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.12 uri_owl_FunctionalProperty a_1) % 14.97/15.12 a_2 a_3) % 14.97/15.12 False) % 14.97/15.12 (Or % 14.97/15.12 (Eq % 14.97/15.12 (iext % 14.97/15.12 (skS.0 11 uri_owl_inverseOf % 14.97/15.12 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.12 uri_owl_FunctionalProperty a_1) % 14.97/15.12 a_2 a_4) % 14.97/15.12 False) % 14.97/15.12 (Eq a_3 a_4))) % 14.97/15.12 Clause #309 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.12 Or (Eq (iext uri_owl_onProperty (skS.0 10 a) a_1) False) % 14.97/15.12 (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)) % 14.97/15.12 Clause #310 (by superposition #[309, 161]): ∀ (a a_1 a_2 : Iota), % 14.97/15.12 Or (Eq (icext (skS.0 10 a) a_1) False) % 14.97/15.12 (Or (Eq (iext uri_owl_inverseOf a_1 (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True) % 14.97/15.12 (Eq False True)) % 14.97/15.12 Clause #313 (by clausification #[310]): ∀ (a a_1 a_2 : Iota), % 14.97/15.12 Or (Eq (icext (skS.0 10 a) a_1) False) % 14.97/15.12 (Eq (iext uri_owl_inverseOf a_1 (skS.0 11 uri_owl_inverseOf a_1 uri_owl_FunctionalProperty a_2)) True) % 14.97/15.12 Clause #314 (by superposition #[313, 234]): ∀ (a a_1 : Iota), % 14.97/15.12 Or % 14.97/15.12 (Eq % 14.97/15.12 (iext uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 uri_owl_FunctionalProperty a_1)) % 14.97/15.13 True) % 14.97/15.13 (Eq False True) % 14.97/15.13 Clause #315 (by clausification #[314]): ∀ (a a_1 : Iota), % 14.97/15.13 Eq % 14.97/15.13 (iext uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 uri_owl_FunctionalProperty a_1)) % 14.97/15.13 True % 14.97/15.13 Clause #316 (by superposition #[315, 21]): ∀ (a : Iota), % 14.97/15.13 Or (Eq True False) (Eq (ip (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) True) % 14.97/15.13 Clause #318 (by superposition #[315, 133]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.13 Or (Eq True False) % 14.97/15.13 (Or (Eq (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) False) % 14.97/15.13 (Eq % 14.97/15.13 (iext % 14.97/15.13 (skS.0 11 uri_owl_inverseOf % 14.97/15.13 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 uri_owl_FunctionalProperty a_3) % 14.97/15.13 a_2 a_1) % 14.97/15.13 True)) % 14.97/15.13 Clause #320 (by clausification #[316]): ∀ (a : Iota), Eq (ip (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) True % 14.97/15.13 Clause #322 (by superposition #[320, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.13 Or % 14.97/15.13 (Eq % 14.97/15.13 (icext uri_owl_InverseFunctionalProperty % 14.97/15.13 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.13 True) % 14.97/15.13 (Or (Eq True False) % 14.97/15.13 (Eq % 14.97/15.13 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) % 14.97/15.13 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 14.97/15.13 True)) % 14.97/15.13 Clause #326 (by superposition #[320, 157]): ∀ (a a_1 a_2 : Iota), % 14.97/15.13 Or % 14.97/15.13 (Eq % 14.97/15.13 (icext uri_owl_InverseFunctionalProperty % 14.97/15.13 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.13 True) % 14.97/15.13 (Or (Eq True False) % 14.97/15.13 (Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.13 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2))) % 14.97/15.13 Clause #327 (by superposition #[320, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.13 Or % 14.97/15.13 (Eq % 14.97/15.13 (icext uri_owl_InverseFunctionalProperty % 14.97/15.13 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.13 True) % 14.97/15.13 (Or (Eq True False) % 14.97/15.13 (Eq % 14.97/15.13 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.13 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 14.97/15.13 True)) % 14.97/15.13 Clause #406 (by clausification #[318]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.13 Or (Eq (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) False) % 14.97/15.13 (Eq % 14.97/15.13 (iext % 14.97/15.13 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.13 uri_owl_FunctionalProperty a_3) % 14.97/15.13 a_2 a_1) % 14.97/15.13 True) % 14.97/15.13 Clause #490 (by clausification #[326]): ∀ (a a_1 a_2 : Iota), % 14.97/15.13 Or % 14.97/15.13 (Eq % 14.97/15.13 (icext uri_owl_InverseFunctionalProperty % 14.97/15.13 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.13 True) % 14.97/15.13 (Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.13 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)) % 14.97/15.13 Clause #491 (by forward demodulation #[490, 214]): ∀ (a a_1 a_2 : Iota), % 14.97/15.13 Or (Eq False True) % 14.97/15.13 (Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.15 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)) % 14.97/15.15 Clause #492 (by clausification #[491]): ∀ (a a_1 a_2 : Iota), % 14.97/15.15 Ne (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.15 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) % 14.97/15.15 Clause #613 (by clausification #[280]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.97/15.15 Or % 14.97/15.15 (Eq % 14.97/15.15 (iext % 14.97/15.15 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 uri_owl_FunctionalProperty a_1) % 14.97/15.15 a_2 a_3) % 14.97/15.15 False) % 14.97/15.15 (Or % 14.97/15.15 (Eq % 14.97/15.15 (iext % 14.97/15.15 (skS.0 11 uri_owl_inverseOf % 14.97/15.15 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 uri_owl_FunctionalProperty a_1) % 14.97/15.15 a_2 a_4) % 14.97/15.15 False) % 14.97/15.15 (Eq a_3 a_4)) % 14.97/15.15 Clause #705 (by clausification #[327]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.15 Or % 14.97/15.15 (Eq % 14.97/15.15 (icext uri_owl_InverseFunctionalProperty % 14.97/15.15 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 14.97/15.15 True) % 14.97/15.15 (Eq % 14.97/15.15 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.15 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 14.97/15.15 True) % 14.97/15.15 Clause #706 (by forward demodulation #[705, 214]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.15 Or (Eq False True) % 14.97/15.15 (Eq % 14.97/15.15 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.15 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 14.97/15.15 True) % 14.97/15.15 Clause #707 (by clausification #[706]): ∀ (a a_1 a_2 a_3 : Iota), % 14.97/15.15 Eq % 14.97/15.15 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 14.97/15.15 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 14.97/15.15 True % 14.97/15.15 Clause #708 (by superposition #[707, 406]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.97/15.15 Or (Eq True False) % 14.97/15.15 (Eq % 14.97/15.15 (iext % 14.97/15.15 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 uri_owl_FunctionalProperty a_1) % 14.97/15.15 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) % 14.97/15.15 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2)) % 14.97/15.15 True) % 14.97/15.15 Clause #722 (by clausification #[708]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 14.97/15.15 Eq % 14.97/15.15 (iext % 14.97/15.15 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 uri_owl_FunctionalProperty a_1) % 14.97/15.15 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) % 14.97/15.15 (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2)) % 14.97/15.15 True % 14.97/15.15 Clause #724 (by superposition #[722, 613]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 14.97/15.15 Or (Eq True False) % 14.97/15.15 (Or % 14.97/15.15 (Eq % 14.97/15.15 (iext % 14.97/15.15 (skS.0 11 uri_owl_inverseOf % 14.97/15.15 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 14.97/15.15 uri_owl_FunctionalProperty a_1) % 14.97/15.15 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) a_5) % 14.97/15.15 False) % 14.97/15.15 (Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2) a_5)) % 14.97/15.15 Clause #725 (by clausification #[724]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 14.97/15.15 Or % 14.97/15.15 (Eq % 14.97/15.15 (iext % 14.97/15.15 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 15.02/15.16 uri_owl_FunctionalProperty a_1) % 15.02/15.16 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) a_5) % 15.02/15.16 False) % 15.02/15.16 (Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2) a_5) % 15.02/15.16 Clause #732 (by clausification #[322]): ∀ (a a_1 a_2 a_3 : Iota), % 15.02/15.16 Or % 15.02/15.16 (Eq % 15.02/15.16 (icext uri_owl_InverseFunctionalProperty % 15.02/15.16 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a)) % 15.02/15.16 True) % 15.02/15.16 (Eq % 15.02/15.16 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) % 15.02/15.16 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 15.02/15.16 True) % 15.02/15.16 Clause #733 (by forward demodulation #[732, 214]): ∀ (a a_1 a_2 a_3 : Iota), % 15.02/15.16 Or (Eq False True) % 15.02/15.16 (Eq % 15.02/15.16 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) % 15.02/15.16 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 15.02/15.16 True) % 15.02/15.16 Clause #734 (by clausification #[733]): ∀ (a a_1 a_2 a_3 : Iota), % 15.02/15.16 Eq % 15.02/15.16 (iext (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) % 15.02/15.16 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2 a_3)) % 15.02/15.16 True % 15.02/15.16 Clause #735 (by superposition #[734, 406]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 15.02/15.16 Or (Eq True False) % 15.02/15.16 (Eq % 15.02/15.16 (iext % 15.02/15.16 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 15.02/15.16 uri_owl_FunctionalProperty a_1) % 15.02/15.16 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3)) % 15.02/15.16 True) % 15.02/15.16 Clause #736 (by clausification #[735]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 15.02/15.16 Eq % 15.02/15.16 (iext % 15.02/15.16 (skS.0 11 uri_owl_inverseOf (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) % 15.02/15.16 uri_owl_FunctionalProperty a_1) % 15.02/15.16 (skS.0 5 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3 a_4) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_2 a_3)) % 15.02/15.16 True % 15.02/15.16 Clause #737 (by superposition #[736, 725]): ∀ (a a_1 a_2 : Iota), % 15.02/15.16 Or (Eq True False) % 15.02/15.16 (Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2)) % 15.02/15.16 Clause #740 (by clausification #[737]): ∀ (a a_1 a_2 : Iota), % 15.02/15.16 Eq (skS.0 3 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1) % 15.02/15.16 (skS.0 4 (skS.0 6 uri_ex_InversesOfFunctionalProperties uri_owl_InverseFunctionalProperty a) a_1 a_2) % 15.02/15.16 Clause #741 (by forward contextual literal cutting #[740, 492]): False % 15.02/15.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------