%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWB026+2 : TPTP v9.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:03:28 PM UTC 2025 % Result : Theorem 6.86s 7.05s % Output : Proof 6.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWB026+2 : TPTP v9.2.0. Released v5.2.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n007.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 11:51:23 EDT 2025 % 0.12/0.34 % CPUTime : % 6.86/7.05 SZS status Theorem for theBenchmark.p % 6.86/7.05 SZS output start Proof for theBenchmark.p % 6.86/7.05 Clause #0 (by assumption #[]): Eq (∀ (P : Iota), Iff (iext uri_rdf_type P uri_rdf_Property) (ip P)) True % 6.86/7.05 Clause #1 (by assumption #[]): Eq (∀ (X C : Iota), Iff (iext uri_rdf_type X C) (icext C X)) True % 6.86/7.05 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 % 6.86/7.05 Clause #3 (by assumption #[]): Eq (iext uri_rdfs_domain uri_rdfs_domain uri_rdf_Property) True % 6.86/7.05 Clause #4 (by assumption #[]): Eq % 6.86/7.05 (∀ (Z S1 A1 : Iota), % 6.86/7.05 And (iext uri_rdf_first S1 A1) (iext uri_rdf_rest S1 uri_rdf_nil) → % 6.86/7.05 Iff (iext uri_owl_oneOf Z S1) (And (ic Z) (∀ (X : Iota), Iff (icext Z X) (Eq X A1)))) % 6.86/7.05 True % 6.86/7.05 Clause #5 (by assumption #[]): Eq % 6.86/7.05 (∀ (P : Iota), % 6.86/7.05 Iff (icext uri_owl_InverseFunctionalProperty P) % 6.86/7.05 (And (ip P) (∀ (X1 X2 Y : Iota), And (iext P X1 Y) (iext P X2 Y) → Eq X1 X2))) % 6.86/7.05 True % 6.86/7.05 Clause #6 (by assumption #[]): Eq (Not (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty)) True % 6.86/7.05 Clause #7 (by assumption #[]): Eq % 6.86/7.05 (Exists fun BNODE_x1 => % 6.86/7.05 Exists fun BNODE_x2 => % 6.86/7.05 Exists fun BNODE_l1 => % 6.86/7.05 Exists fun BNODE_l2 => % 6.86/7.05 And % 6.86/7.05 (And % 6.86/7.05 (And % 6.86/7.05 (And % 6.86/7.05 (And % 6.86/7.05 (And (And (iext uri_rdfs_domain uri_ex_p BNODE_x1) (iext uri_owl_oneOf BNODE_x1 BNODE_l1)) % 6.86/7.05 (iext uri_rdf_first BNODE_l1 uri_ex_w)) % 6.86/7.05 (iext uri_rdf_rest BNODE_l1 uri_rdf_nil)) % 6.86/7.05 (iext uri_rdfs_range uri_ex_p BNODE_x2)) % 6.86/7.05 (iext uri_owl_oneOf BNODE_x2 BNODE_l2)) % 6.86/7.05 (iext uri_rdf_first BNODE_l2 uri_ex_u)) % 6.86/7.05 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 6.86/7.05 True % 6.86/7.05 Clause #8 (by clausification #[6]): Eq (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty) False % 6.86/7.05 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 % 6.86/7.05 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 % 6.86/7.05 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 % 6.86/7.05 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 % 6.86/7.05 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) % 6.86/7.05 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.05 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)) % 6.86/7.05 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)) % 6.86/7.05 Clause #16 (by clausification #[0]): ∀ (a : Iota), Eq (Iff (iext uri_rdf_type a uri_rdf_Property) (ip a)) True % 6.86/7.05 Clause #18 (by clausification #[16]): ∀ (a : Iota), Or (Eq (iext uri_rdf_type a uri_rdf_Property) False) (Eq (ip a) True) % 6.86/7.05 Clause #19 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (iext uri_rdf_type a C) (icext C a)) True % 6.86/7.05 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Iff (iext uri_rdf_type a a_1) (icext a_1 a)) True % 6.86/7.05 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) % 6.86/7.05 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) % 6.86/7.05 Clause #31 (by clausification #[4]): ∀ (a : Iota), % 6.86/7.05 Eq % 6.86/7.05 (∀ (S1 A1 : Iota), % 6.86/7.05 And (iext uri_rdf_first S1 A1) (iext uri_rdf_rest S1 uri_rdf_nil) → % 6.86/7.05 Iff (iext uri_owl_oneOf a S1) (And (ic a) (∀ (X : Iota), Iff (icext a X) (Eq X A1)))) % 6.86/7.05 True % 6.86/7.05 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 6.86/7.05 Eq % 6.86/7.05 (∀ (A1 : Iota), % 6.86/7.05 And (iext uri_rdf_first a A1) (iext uri_rdf_rest a uri_rdf_nil) → % 6.86/7.05 Iff (iext uri_owl_oneOf a_1 a) (And (ic a_1) (∀ (X : Iota), Iff (icext a_1 X) (Eq X A1)))) % 6.86/7.08 True % 6.86/7.08 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Eq % 6.86/7.08 (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a uri_rdf_nil) → % 6.86/7.08 Iff (iext uri_owl_oneOf a_2 a) (And (ic a_2) (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)))) % 6.86/7.08 True % 6.86/7.08 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Or (Eq (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a uri_rdf_nil)) False) % 6.86/7.08 (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) % 6.86/7.08 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Or (Eq (Iff (iext uri_owl_oneOf a a_1) (And (ic a) (∀ (X : Iota), Iff (icext a X) (Eq X a_2)))) True) % 6.86/7.08 (Or (Eq (iext uri_rdf_first a_1 a_2) False) (Eq (iext uri_rdf_rest a_1 uri_rdf_nil) False)) % 6.86/7.08 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Or (Eq (iext uri_rdf_first a a_1) False) % 6.86/7.08 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 6.86/7.08 (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))) % 6.86/7.08 Clause #44 (by clausification #[5]): ∀ (a : Iota), % 6.86/7.08 Eq % 6.86/7.08 (Iff (icext uri_owl_InverseFunctionalProperty a) % 6.86/7.08 (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2))) % 6.86/7.08 True % 6.86/7.08 Clause #45 (by clausification #[44]): ∀ (a : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Eq (And (ip a) (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2)) False) % 6.86/7.08 Clause #47 (by clausification #[45]): ∀ (a : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) (Eq (∀ (X1 X2 Y : Iota), And (iext a X1 Y) (iext a X2 Y) → Eq X1 X2) False)) % 6.86/7.08 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (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)) % 6.86/7.08 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (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)) % 6.86/7.08 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (Eq % 6.86/7.08 (Not % 6.86/7.08 (∀ (Y : Iota), % 6.86/7.08 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))) % 6.86/7.08 True)) % 6.86/7.08 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (Eq % 6.86/7.08 (∀ (Y : Iota), % 6.86/7.08 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)) % 6.86/7.08 False)) % 6.86/7.08 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (Eq % 6.86/7.08 (Not % 6.86/7.08 (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)) → % 6.86/7.08 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 6.86/7.08 True)) % 6.86/7.08 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (Eq % 6.86/7.08 (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)) → % 6.86/7.08 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 6.86/7.08 False)) % 6.86/7.08 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) % 6.86/7.08 (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))) % 6.86/7.08 True)) % 6.86/7.08 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 6.86/7.08 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.08 (Or (Eq (ip a) False) (Eq (Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False)) % 6.86/7.10 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.10 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.10 (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)) % 6.86/7.10 Clause #57 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.10 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.10 (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)) % 6.86/7.10 Clause #67 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 6.86/7.10 Or (Eq (iext uri_rdf_first a a_1) False) % 6.86/7.10 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 6.86/7.10 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (∀ (X : Iota), Iff (icext a_2 X) (Eq X a_1)) True))) % 6.86/7.10 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.10 Or (Eq (iext uri_rdf_first a a_1) False) % 6.86/7.10 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 6.86/7.10 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Eq (Iff (icext a_2 a_3) (Eq a_3 a_1)) True))) % 6.86/7.10 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.10 Or (Eq (iext uri_rdf_first a a_1) False) % 6.86/7.10 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 6.86/7.10 (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)))) % 6.86/7.10 Clause #74 (by clausification #[7]): ∀ (a : Iota), % 6.86/7.10 Eq % 6.86/7.10 (Exists fun BNODE_x2 => % 6.86/7.10 Exists fun BNODE_l1 => % 6.86/7.10 Exists fun BNODE_l2 => % 6.86/7.10 And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) BNODE_l1)) % 6.86/7.10 (iext uri_rdf_first BNODE_l1 uri_ex_w)) % 6.86/7.10 (iext uri_rdf_rest BNODE_l1 uri_rdf_nil)) % 6.86/7.10 (iext uri_rdfs_range uri_ex_p BNODE_x2)) % 6.86/7.10 (iext uri_owl_oneOf BNODE_x2 BNODE_l2)) % 6.86/7.10 (iext uri_rdf_first BNODE_l2 uri_ex_u)) % 6.86/7.10 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 6.86/7.10 True % 6.86/7.10 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 6.86/7.10 Eq % 6.86/7.10 (Exists fun BNODE_l1 => % 6.86/7.10 Exists fun BNODE_l2 => % 6.86/7.10 And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And (And (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) (iext uri_owl_oneOf (skS.0 4 a) BNODE_l1)) % 6.86/7.10 (iext uri_rdf_first BNODE_l1 uri_ex_w)) % 6.86/7.10 (iext uri_rdf_rest BNODE_l1 uri_rdf_nil)) % 6.86/7.10 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1))) % 6.86/7.10 (iext uri_owl_oneOf (skS.0 5 a a_1) BNODE_l2)) % 6.86/7.10 (iext uri_rdf_first BNODE_l2 uri_ex_u)) % 6.86/7.10 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 6.86/7.10 True % 6.86/7.10 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 6.86/7.10 Eq % 6.86/7.10 (Exists fun BNODE_l2 => % 6.86/7.10 And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (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))) % 6.86/7.10 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.10 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil)) % 6.86/7.10 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1))) % 6.86/7.10 (iext uri_owl_oneOf (skS.0 5 a a_1) BNODE_l2)) % 6.86/7.10 (iext uri_rdf_first BNODE_l2 uri_ex_u)) % 6.86/7.10 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 6.86/7.10 True % 6.86/7.10 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.10 Eq % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (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))) % 6.86/7.10 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.10 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil)) % 6.86/7.10 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1))) % 6.86/7.10 (iext uri_owl_oneOf (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3))) % 6.86/7.10 (iext uri_rdf_first (skS.0 7 a a_1 a_2 a_3) uri_ex_u)) % 6.86/7.10 (iext uri_rdf_rest (skS.0 7 a a_1 a_2 a_3) uri_rdf_nil)) % 6.86/7.10 True % 6.86/7.10 Clause #79 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.10 Eq % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.10 (And % 6.86/7.12 (And % 6.86/7.12 (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))) % 6.86/7.12 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.12 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil)) % 6.86/7.12 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1))) % 6.86/7.12 (iext uri_owl_oneOf (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3))) % 6.86/7.12 (iext uri_rdf_first (skS.0 7 a a_1 a_2 a_3) uri_ex_u)) % 6.86/7.12 True % 6.86/7.12 Clause #80 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.12 Or (Eq (iext uri_rdf_first a a_1) False) % 6.86/7.12 (Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 6.86/7.12 (Or (Eq (iext uri_owl_oneOf a_2 a) False) (Or (Eq (icext a_2 a_3) False) (Eq a_3 a_1)))) % 6.86/7.12 Clause #81 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 6.86/7.12 Or (Eq (icext uri_owl_InverseFunctionalProperty a) True) % 6.86/7.12 (Or (Eq (ip a) False) (Ne (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 6.86/7.12 Clause #112 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 6.86/7.12 Eq % 6.86/7.12 (And % 6.86/7.12 (And % 6.86/7.12 (And % 6.86/7.12 (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))) % 6.86/7.12 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.12 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil)) % 6.86/7.12 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1))) % 6.86/7.12 (iext uri_owl_oneOf (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3))) % 6.86/7.12 True % 6.86/7.12 Clause #162 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), % 6.86/7.12 Eq % 6.86/7.12 (And % 6.86/7.12 (And % 6.86/7.12 (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))) % 6.86/7.12 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.12 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil)) % 6.86/7.12 (iext uri_rdfs_range uri_ex_p (skS.0 5 a a_1))) % 6.86/7.12 True % 6.86/7.12 Clause #179 (by clausification #[162]): ∀ (a a_1 a_2 : Iota), % 6.86/7.12 Eq % 6.86/7.12 (And % 6.86/7.12 (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))) % 6.86/7.12 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.12 (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil)) % 6.86/7.12 True % 6.86/7.12 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 % 6.86/7.12 Clause #181 (by clausification #[179]): ∀ (a a_1 a_2 : Iota), % 6.86/7.12 Eq % 6.86/7.12 (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))) % 6.86/7.12 (iext uri_rdf_first (skS.0 6 a a_1 a_2) uri_ex_w)) % 6.86/7.12 True % 6.86/7.12 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 % 6.86/7.12 Clause #183 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 6.86/7.12 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 % 6.86/7.12 Clause #187 (by superposition #[182, 80]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.86/7.12 Or (Eq True False) % 6.86/7.12 (Or (Eq (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil) False) % 6.86/7.12 (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)))) % 6.86/7.12 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 % 6.86/7.12 Clause #190 (by clausification #[183]): ∀ (a : Iota), Eq (iext uri_rdfs_domain uri_ex_p (skS.0 4 a)) True % 6.86/7.12 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)) % 6.86/7.12 Clause #192 (by superposition #[190, 23]): Or (Eq (icext uri_rdf_Property uri_ex_p) True) (Eq True False) % 6.86/7.12 Clause #199 (by clausification #[192]): Eq (icext uri_rdf_Property uri_ex_p) True % 6.86/7.12 Clause #200 (by superposition #[199, 21]): Or (Eq (iext uri_rdf_type uri_ex_p uri_rdf_Property) True) (Eq True False) % 6.86/7.12 Clause #201 (by clausification #[200]): Eq (iext uri_rdf_type uri_ex_p uri_rdf_Property) True % 6.86/7.12 Clause #202 (by superposition #[201, 18]): Or (Eq True False) (Eq (ip uri_ex_p) True) % 6.86/7.12 Clause #204 (by clausification #[202]): Eq (ip uri_ex_p) True % 6.86/7.12 Clause #205 (by superposition #[204, 56]): ∀ (a a_1 a_2 : Iota), % 6.86/7.12 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (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)) % 6.97/7.14 Clause #206 (by superposition #[204, 81]): ∀ (a a_1 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (Or (Eq True False) (Ne (skS.0 1 uri_ex_p a) (skS.0 2 uri_ex_p a a_1))) % 6.97/7.14 Clause #207 (by superposition #[204, 57]): ∀ (a a_1 a_2 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (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)) % 6.97/7.14 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) % 6.97/7.14 Clause #212 (by clausification #[206]): ∀ (a a_1 : Iota), % 6.97/7.14 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)) % 6.97/7.14 Clause #213 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (Eq (iext uri_ex_p (skS.0 1 uri_ex_p a) (skS.0 3 uri_ex_p a a_1 a_2)) True) % 6.97/7.14 Clause #214 (by superposition #[213, 208]): ∀ (a a_1 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (Or (Eq (icext (skS.0 4 a) (skS.0 1 uri_ex_p a_1)) True) (Eq True False)) % 6.97/7.14 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), % 6.97/7.14 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) % 6.97/7.14 Clause #223 (by clausification #[205]): ∀ (a a_1 a_2 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (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) % 6.97/7.14 Clause #224 (by superposition #[223, 208]): ∀ (a a_1 a_2 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (Or (Eq (icext (skS.0 4 a) (skS.0 2 uri_ex_p a_1 a_2)) True) (Eq True False)) % 6.97/7.14 Clause #225 (by clausification #[224]): ∀ (a a_1 a_2 : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (Eq (icext (skS.0 4 a) (skS.0 2 uri_ex_p a_1 a_2)) True) % 6.97/7.14 Clause #245 (by clausification #[187]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.97/7.14 Or (Eq (iext uri_rdf_rest (skS.0 6 a a_1 a_2) uri_rdf_nil) False) % 6.97/7.14 (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))) % 6.97/7.14 Clause #246 (by forward demodulation #[245, 180]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.97/7.14 Or (Eq True False) % 6.97/7.14 (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))) % 6.97/7.14 Clause #247 (by clausification #[246]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.97/7.14 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)) % 6.97/7.14 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)) % 6.97/7.14 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) % 6.97/7.14 Clause #255 (by superposition #[254, 215]): ∀ (a : Iota), % 6.97/7.14 Or (Eq (skS.0 1 uri_ex_p a) uri_ex_w) % 6.97/7.14 (Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Eq False True)) % 6.97/7.14 Clause #256 (by superposition #[254, 225]): ∀ (a a_1 : Iota), % 6.97/7.14 Or (Eq (skS.0 2 uri_ex_p a a_1) uri_ex_w) % 6.97/7.14 (Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Eq False True)) % 6.97/7.14 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) % 6.97/7.14 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) % 6.97/7.14 Clause #264 (by superposition #[263, 212]): ∀ (a : Iota), % 6.97/7.14 Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) % 6.97/7.14 (Or (Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True) (Ne (skS.0 1 uri_ex_p a) uri_ex_w)) % 6.97/7.14 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) % 6.97/7.14 Clause #266 (by forward contextual literal cutting #[265, 259]): Eq (icext uri_owl_InverseFunctionalProperty uri_ex_p) True % 6.97/7.14 Clause #277 (by superposition #[266, 21]): Or (Eq (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty) True) (Eq True False) % 6.97/7.14 Clause #280 (by clausification #[277]): Eq (iext uri_rdf_type uri_ex_p uri_owl_InverseFunctionalProperty) True % 6.97/7.14 Clause #281 (by superposition #[280, 8]): Eq True False % 6.97/7.14 Clause #283 (by clausification #[281]): False % 6.97/7.14 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------