%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWB029+2 : TPTP v9.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 4.81s 4.96s % Output : Proof 4.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWB029+2 : TPTP v9.2.0. Released v5.2.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n006.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 11:52:38 EDT 2025 % 0.14/0.34 % CPUTime : % 4.81/4.96 SZS status Theorem for theBenchmark.p % 4.81/4.96 SZS output start Proof for theBenchmark.p % 4.81/4.96 Clause #0 (by assumption #[]): Eq (∀ (X C : Iota), Iff (iext uri_rdf_type X C) (icext C X)) True % 4.81/4.96 Clause #1 (by assumption #[]): Eq % 4.81/4.96 (∀ (Z C : Iota), % 4.81/4.96 iext uri_owl_complementOf Z C → And (And (ic Z) (ic C)) (∀ (X : Iota), Iff (icext Z X) (Not (icext C X)))) % 4.81/4.96 True % 4.81/4.96 Clause #2 (by assumption #[]): Eq % 4.81/4.96 (∀ (Z S1 C1 S2 C2 : Iota), % 4.81/4.96 And (And (And (iext uri_rdf_first S1 C1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 C2)) % 4.81/4.96 (iext uri_rdf_rest S2 uri_rdf_nil) → % 4.81/4.96 Iff (iext uri_owl_intersectionOf Z S1) % 4.81/4.96 (And (And (And (ic Z) (ic C1)) (ic C2)) (∀ (X : Iota), Iff (icext Z X) (And (icext C1 X) (icext C2 X))))) % 4.81/4.96 True % 4.81/4.96 Clause #4 (by assumption #[]): Eq % 4.81/4.96 (Exists fun BNODE_x => % 4.81/4.96 Exists fun BNODE_y => % 4.81/4.96 Exists fun BNODE_l1 => % 4.81/4.96 Exists fun BNODE_l2 => % 4.81/4.96 And % 4.81/4.96 (And % 4.81/4.96 (And % 4.81/4.96 (And % 4.81/4.96 (And % 4.81/4.96 (And % 4.81/4.96 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.81/4.96 (iext uri_rdf_type uri_ex_w BNODE_x)) % 4.81/4.96 (iext uri_owl_intersectionOf BNODE_x BNODE_l1)) % 4.81/4.96 (iext uri_rdf_first BNODE_l1 uri_ex_A)) % 4.81/4.96 (iext uri_rdf_rest BNODE_l1 BNODE_l2)) % 4.81/4.96 (iext uri_rdf_first BNODE_l2 BNODE_y)) % 4.81/4.96 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 4.81/4.96 (iext uri_owl_complementOf BNODE_y uri_ex_A)) % 4.81/4.96 True % 4.81/4.96 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (iext uri_rdf_type a C) (icext C a)) True % 4.81/4.96 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Iff (iext uri_rdf_type a a_1) (icext a_1 a)) True % 4.81/4.96 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (iext uri_rdf_type a a_1) False) (Eq (icext a_1 a) True) % 4.81/4.96 Clause #10 (by clausification #[1]): ∀ (a : Iota), % 4.81/4.96 Eq % 4.81/4.96 (∀ (C : Iota), % 4.81/4.96 iext uri_owl_complementOf a C → And (And (ic a) (ic C)) (∀ (X : Iota), Iff (icext a X) (Not (icext C X)))) % 4.81/4.96 True % 4.81/4.96 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.81/4.96 Eq (iext uri_owl_complementOf a a_1 → And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (Not (icext a_1 X)))) % 4.81/4.96 True % 4.81/4.96 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 4.81/4.96 Or (Eq (iext uri_owl_complementOf a a_1) False) % 4.81/4.96 (Eq (And (And (ic a) (ic a_1)) (∀ (X : Iota), Iff (icext a X) (Not (icext a_1 X)))) True) % 4.81/4.96 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 4.81/4.96 Or (Eq (iext uri_owl_complementOf a a_1) False) (Eq (∀ (X : Iota), Iff (icext a X) (Not (icext a_1 X))) True) % 4.81/4.96 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.81/4.96 Or (Eq (iext uri_owl_complementOf a a_1) False) (Eq (Iff (icext a a_2) (Not (icext a_1 a_2))) True) % 4.81/4.96 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 4.81/4.96 Or (Eq (iext uri_owl_complementOf a a_1) False) (Or (Eq (icext a a_2) False) (Eq (Not (icext a_1 a_2)) True)) % 4.81/4.96 Clause #21 (by clausification #[2]): ∀ (a : Iota), % 4.81/4.96 Eq % 4.81/4.96 (∀ (S1 C1 S2 C2 : Iota), % 4.81/4.96 And (And (And (iext uri_rdf_first S1 C1) (iext uri_rdf_rest S1 S2)) (iext uri_rdf_first S2 C2)) % 4.81/4.96 (iext uri_rdf_rest S2 uri_rdf_nil) → % 4.81/4.96 Iff (iext uri_owl_intersectionOf a S1) % 4.81/4.96 (And (And (And (ic a) (ic C1)) (ic C2)) (∀ (X : Iota), Iff (icext a X) (And (icext C1 X) (icext C2 X))))) % 4.81/4.96 True % 4.81/4.96 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 4.81/4.96 Eq % 4.81/4.96 (∀ (C1 S2 C2 : Iota), % 4.81/4.96 And (And (And (iext uri_rdf_first a C1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 C2)) % 4.81/4.96 (iext uri_rdf_rest S2 uri_rdf_nil) → % 4.81/4.96 Iff (iext uri_owl_intersectionOf a_1 a) % 4.81/4.96 (And (And (And (ic a_1) (ic C1)) (ic C2)) (∀ (X : Iota), Iff (icext a_1 X) (And (icext C1 X) (icext C2 X))))) % 4.81/4.96 True % 4.81/4.96 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.81/4.96 Eq % 4.81/4.96 (∀ (S2 C2 : Iota), % 4.81/4.96 And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a S2)) (iext uri_rdf_first S2 C2)) % 4.81/4.96 (iext uri_rdf_rest S2 uri_rdf_nil) → % 4.81/4.96 Iff (iext uri_owl_intersectionOf a_2 a) % 4.82/4.98 (And (And (And (ic a_2) (ic a_1)) (ic C2)) % 4.82/4.98 (∀ (X : Iota), Iff (icext a_2 X) (And (icext a_1 X) (icext C2 X))))) % 4.82/4.98 True % 4.82/4.98 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 4.82/4.98 Eq % 4.82/4.98 (∀ (C2 : Iota), % 4.82/4.98 And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 C2)) % 4.82/4.98 (iext uri_rdf_rest a_2 uri_rdf_nil) → % 4.82/4.98 Iff (iext uri_owl_intersectionOf a_3 a) % 4.82/4.98 (And (And (And (ic a_3) (ic a_1)) (ic C2)) % 4.82/4.98 (∀ (X : Iota), Iff (icext a_3 X) (And (icext a_1 X) (icext C2 X))))) % 4.82/4.98 True % 4.82/4.98 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Eq % 4.82/4.98 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3)) % 4.82/4.98 (iext uri_rdf_rest a_2 uri_rdf_nil) → % 4.82/4.98 Iff (iext uri_owl_intersectionOf a_4 a) % 4.82/4.98 (And (And (And (ic a_4) (ic a_1)) (ic a_3)) % 4.82/4.98 (∀ (X : Iota), Iff (icext a_4 X) (And (icext a_1 X) (icext a_3 X))))) % 4.82/4.98 True % 4.82/4.98 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Or % 4.82/4.98 (Eq % 4.82/4.98 (And (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3)) % 4.82/4.98 (iext uri_rdf_rest a_2 uri_rdf_nil)) % 4.82/4.98 False) % 4.82/4.98 (Eq % 4.82/4.98 (Iff (iext uri_owl_intersectionOf a_4 a) % 4.82/4.98 (And (And (And (ic a_4) (ic a_1)) (ic a_3)) % 4.82/4.98 (∀ (X : Iota), Iff (icext a_4 X) (And (icext a_1 X) (icext a_3 X))))) % 4.82/4.98 True) % 4.82/4.98 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Or % 4.82/4.98 (Eq % 4.82/4.98 (Iff (iext uri_owl_intersectionOf a a_1) % 4.82/4.98 (And (And (And (ic a) (ic a_2)) (ic a_3)) (∀ (X : Iota), Iff (icext a X) (And (icext a_2 X) (icext a_3 X))))) % 4.82/4.98 True) % 4.82/4.98 (Or (Eq (And (And (iext uri_rdf_first a_1 a_2) (iext uri_rdf_rest a_1 a_4)) (iext uri_rdf_first a_4 a_3)) False) % 4.82/4.98 (Eq (iext uri_rdf_rest a_4 uri_rdf_nil) False)) % 4.82/4.98 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Or (Eq (And (And (iext uri_rdf_first a a_1) (iext uri_rdf_rest a a_2)) (iext uri_rdf_first a_2 a_3)) False) % 4.82/4.98 (Or (Eq (iext uri_rdf_rest a_2 uri_rdf_nil) False) % 4.82/4.98 (Or (Eq (iext uri_owl_intersectionOf a_4 a) False) % 4.82/4.98 (Eq % 4.82/4.98 (And (And (And (ic a_4) (ic a_1)) (ic a_3)) % 4.82/4.98 (∀ (X : Iota), Iff (icext a_4 X) (And (icext a_1 X) (icext a_3 X)))) % 4.82/4.98 True))) % 4.82/4.98 Clause #40 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 4.82/4.98 Or (Eq (iext uri_owl_complementOf a a_1) False) (Or (Eq (icext a a_2) False) (Eq (icext a_1 a_2) False)) % 4.82/4.98 Clause #41 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.82/4.98 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.82/4.98 (Or % 4.82/4.98 (Eq % 4.82/4.98 (And (And (And (ic a_1) (ic a_3)) (ic a_4)) % 4.82/4.98 (∀ (X : Iota), Iff (icext a_1 X) (And (icext a_3 X) (icext a_4 X)))) % 4.82/4.98 True) % 4.82/4.98 (Or (Eq (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a)) False) % 4.82/4.98 (Eq (iext uri_rdf_first a a_4) False)))) % 4.82/4.98 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.82/4.98 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.82/4.98 (Or (Eq (And (iext uri_rdf_first a_2 a_3) (iext uri_rdf_rest a_2 a)) False) % 4.82/4.98 (Or (Eq (iext uri_rdf_first a a_4) False) % 4.82/4.98 (Eq (∀ (X : Iota), Iff (icext a_1 X) (And (icext a_3 X) (icext a_4 X))) True)))) % 4.82/4.98 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.82/4.98 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.82/4.98 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.82/4.98 (Or (Eq (iext uri_rdf_first a a_3) False) % 4.82/4.98 (Or (Eq (∀ (X : Iota), Iff (icext a_1 X) (And (icext a_4 X) (icext a_3 X))) True) % 4.82/4.98 (Or (Eq (iext uri_rdf_first a_2 a_4) False) (Eq (iext uri_rdf_rest a_2 a) False))))) % 4.82/4.98 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.82/4.98 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.82/4.98 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.82/4.98 (Or (Eq (iext uri_rdf_first a a_3) False) % 4.82/4.98 (Or (Eq (iext uri_rdf_first a_2 a_4) False) % 4.82/5.00 (Or (Eq (iext uri_rdf_rest a_2 a) False) % 4.82/5.00 (Eq (Iff (icext a_1 a_5) (And (icext a_4 a_5) (icext a_3 a_5))) True))))) % 4.82/5.00 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.82/5.00 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.82/5.00 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.82/5.00 (Or (Eq (iext uri_rdf_first a a_3) False) % 4.82/5.00 (Or (Eq (iext uri_rdf_first a_2 a_4) False) % 4.82/5.00 (Or (Eq (iext uri_rdf_rest a_2 a) False) % 4.82/5.00 (Or (Eq (icext a_1 a_5) False) (Eq (And (icext a_4 a_5) (icext a_3 a_5)) True)))))) % 4.82/5.00 Clause #54 (by clausification #[4]): ∀ (a : Iota), % 4.82/5.00 Eq % 4.82/5.00 (Exists fun BNODE_y => % 4.82/5.00 Exists fun BNODE_l1 => % 4.82/5.00 Exists fun BNODE_l2 => % 4.82/5.00 And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.82/5.00 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.82/5.00 (iext uri_owl_intersectionOf (skS.0 1 a) BNODE_l1)) % 4.82/5.00 (iext uri_rdf_first BNODE_l1 uri_ex_A)) % 4.82/5.00 (iext uri_rdf_rest BNODE_l1 BNODE_l2)) % 4.82/5.00 (iext uri_rdf_first BNODE_l2 BNODE_y)) % 4.82/5.00 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 4.82/5.00 (iext uri_owl_complementOf BNODE_y uri_ex_A)) % 4.82/5.00 True % 4.82/5.00 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 4.82/5.00 Eq % 4.82/5.00 (Exists fun BNODE_l1 => % 4.82/5.00 Exists fun BNODE_l2 => % 4.82/5.00 And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.82/5.00 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.82/5.00 (iext uri_owl_intersectionOf (skS.0 1 a) BNODE_l1)) % 4.82/5.00 (iext uri_rdf_first BNODE_l1 uri_ex_A)) % 4.82/5.00 (iext uri_rdf_rest BNODE_l1 BNODE_l2)) % 4.82/5.00 (iext uri_rdf_first BNODE_l2 (skS.0 2 a a_1))) % 4.82/5.00 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 4.82/5.00 (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A)) % 4.82/5.00 True % 4.82/5.00 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 4.82/5.00 Eq % 4.82/5.00 (Exists fun BNODE_l2 => % 4.82/5.00 And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.82/5.00 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.82/5.00 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.82/5.00 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A)) % 4.82/5.00 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) BNODE_l2)) % 4.82/5.00 (iext uri_rdf_first BNODE_l2 (skS.0 2 a a_1))) % 4.82/5.00 (iext uri_rdf_rest BNODE_l2 uri_rdf_nil)) % 4.82/5.00 (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A)) % 4.82/5.00 True % 4.82/5.00 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 4.82/5.00 Eq % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.82/5.00 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.82/5.00 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.82/5.00 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A)) % 4.82/5.00 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3))) % 4.82/5.00 (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1))) % 4.82/5.00 (iext uri_rdf_rest (skS.0 4 a a_1 a_2 a_3) uri_rdf_nil)) % 4.82/5.00 (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A)) % 4.82/5.00 True % 4.82/5.00 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (iext uri_owl_complementOf (skS.0 2 a a_1) uri_ex_A) True % 4.82/5.00 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 4.82/5.00 Eq % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And % 4.82/5.00 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.82/5.00 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.87/5.02 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.87/5.02 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A)) % 4.87/5.02 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3))) % 4.87/5.02 (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1))) % 4.87/5.02 (iext uri_rdf_rest (skS.0 4 a a_1 a_2 a_3) uri_rdf_nil)) % 4.87/5.02 True % 4.87/5.02 Clause #63 (by superposition #[58, 40]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (icext (skS.0 2 a a_1) a_2) False) (Eq (icext uri_ex_A a_2) False)) % 4.87/5.02 Clause #66 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 2 a a_1) a_2) False) (Eq (icext uri_ex_A a_2) False) % 4.87/5.02 Clause #76 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.87/5.02 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.87/5.02 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a a_3) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a_2 a_4) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_rest a_2 a) False) (Or (Eq (icext a_1 a_5) False) (Eq (icext a_3 a_5) True)))))) % 4.87/5.02 Clause #77 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.87/5.02 Or (Eq (iext uri_rdf_rest a uri_rdf_nil) False) % 4.87/5.02 (Or (Eq (iext uri_owl_intersectionOf a_1 a_2) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a a_3) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a_2 a_4) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_rest a_2 a) False) (Or (Eq (icext a_1 a_5) False) (Eq (icext a_4 a_5) True)))))) % 4.87/5.02 Clause #78 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 4 a a_1 a_2 a_3) uri_rdf_nil) True % 4.87/5.02 Clause #79 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 4.87/5.02 Eq % 4.87/5.02 (And % 4.87/5.02 (And % 4.87/5.02 (And % 4.87/5.02 (And % 4.87/5.02 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.87/5.02 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.87/5.02 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.87/5.02 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A)) % 4.87/5.02 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3))) % 4.87/5.02 (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1))) % 4.87/5.02 True % 4.87/5.02 Clause #86 (by superposition #[78, 76]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.87/5.02 Or (Eq True False) % 4.87/5.02 (Or (Eq (iext uri_owl_intersectionOf a a_1) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a_1 a_7) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False) % 4.87/5.02 (Or (Eq (icext a a_8) False) (Eq (icext a_6 a_8) True)))))) % 4.87/5.02 Clause #87 (by superposition #[78, 77]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.87/5.02 Or (Eq True False) % 4.87/5.02 (Or (Eq (iext uri_owl_intersectionOf a a_1) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a_1 a_7) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False) % 4.87/5.02 (Or (Eq (icext a a_8) False) (Eq (icext a_7 a_8) True)))))) % 4.87/5.02 Clause #91 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.87/5.02 Or (Eq (iext uri_owl_intersectionOf a a_1) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a_1 a_7) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False) % 4.87/5.02 (Or (Eq (icext a a_8) False) (Eq (icext a_7 a_8) True))))) % 4.87/5.02 Clause #92 (by clausification #[86]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.87/5.02 Or (Eq (iext uri_owl_intersectionOf a a_1) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first (skS.0 4 a_2 a_3 a_4 a_5) a_6) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_first a_1 a_7) False) % 4.87/5.02 (Or (Eq (iext uri_rdf_rest a_1 (skS.0 4 a_2 a_3 a_4 a_5)) False) % 4.87/5.02 (Or (Eq (icext a a_8) False) (Eq (icext a_6 a_8) True))))) % 4.87/5.02 Clause #98 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) (skS.0 2 a a_1)) True % 4.87/5.02 Clause #99 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 4.87/5.02 Eq % 4.87/5.02 (And % 4.87/5.02 (And % 4.87/5.02 (And % 4.87/5.02 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.89/5.04 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.89/5.04 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.89/5.04 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A)) % 4.89/5.04 (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3))) % 4.89/5.04 True % 4.89/5.04 Clause #103 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota), Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) True % 4.89/5.04 Clause #104 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), % 4.89/5.04 Eq % 4.89/5.04 (And % 4.89/5.04 (And % 4.89/5.04 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.89/5.04 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.89/5.04 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.89/5.04 (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A)) % 4.89/5.04 True % 4.89/5.04 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) uri_ex_A) True % 4.89/5.04 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 4.89/5.04 Eq % 4.89/5.04 (And % 4.89/5.04 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.89/5.04 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.89/5.04 (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 4.89/5.04 True % 4.89/5.04 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Eq (iext uri_owl_intersectionOf (skS.0 1 a) (skS.0 3 a a_1 a_2)) True % 4.89/5.04 Clause #108 (by clausification #[106]): ∀ (a : Iota), % 4.89/5.04 Eq % 4.89/5.04 (And (And (iext uri_rdf_type uri_ex_A uri_owl_Class) (iext uri_rdf_type uri_ex_B uri_owl_Class)) % 4.89/5.04 (iext uri_rdf_type uri_ex_w (skS.0 1 a))) % 4.89/5.04 True % 4.89/5.04 Clause #112 (by superposition #[107, 91]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 4.89/5.04 Or (Eq True False) % 4.89/5.04 (Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False) % 4.89/5.04 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_8 a_9) True))))) % 4.89/5.04 Clause #113 (by superposition #[107, 92]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 4.89/5.04 Or (Eq True False) % 4.89/5.04 (Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False) % 4.89/5.04 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_4 a_9) True))))) % 4.89/5.04 Clause #115 (by clausification #[108]): ∀ (a : Iota), Eq (iext uri_rdf_type uri_ex_w (skS.0 1 a)) True % 4.89/5.04 Clause #117 (by superposition #[115, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (icext (skS.0 1 a) uri_ex_w) True) % 4.89/5.04 Clause #131 (by clausification #[117]): ∀ (a : Iota), Eq (icext (skS.0 1 a) uri_ex_w) True % 4.89/5.04 Clause #160 (by clausification #[112]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 4.89/5.04 Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False) % 4.89/5.04 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_8 a_9) True)))) % 4.89/5.04 Clause #161 (by superposition #[160, 98]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.89/5.04 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False) % 4.89/5.04 (Or (Eq (icext (skS.0 1 a) a_8) False) (Or (Eq (icext a_3 a_8) True) (Eq False True)))) % 4.89/5.04 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.89/5.04 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False) % 4.89/5.04 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False) % 4.89/5.04 (Or (Eq (icext (skS.0 1 a) a_8) False) (Eq (icext a_3 a_8) True))) % 4.89/5.04 Clause #163 (by superposition #[162, 105]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.89/5.04 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False) % 4.89/5.04 (Or (Eq (icext (skS.0 1 a) a_7) False) (Or (Eq (icext uri_ex_A a_7) True) (Eq False True))) % 4.89/5.06 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.89/5.06 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False) % 4.89/5.06 (Or (Eq (icext (skS.0 1 a) a_7) False) (Eq (icext uri_ex_A a_7) True)) % 4.89/5.06 Clause #165 (by superposition #[164, 103]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Or (Eq (icext uri_ex_A a_1) True) (Eq False True)) % 4.89/5.06 Clause #166 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Eq (icext uri_ex_A a_1) True) % 4.89/5.06 Clause #167 (by superposition #[166, 131]): Or (Eq (icext uri_ex_A uri_ex_w) True) (Eq False True) % 4.89/5.06 Clause #168 (by clausification #[167]): Eq (icext uri_ex_A uri_ex_w) True % 4.89/5.06 Clause #172 (by clausification #[113]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 4.89/5.06 Or (Eq (iext uri_rdf_first (skS.0 4 a a_1 a_2 a_3) a_4) False) % 4.89/5.06 (Or (Eq (iext uri_rdf_first (skS.0 3 a_5 a_6 a_7) a_8) False) % 4.89/5.06 (Or (Eq (iext uri_rdf_rest (skS.0 3 a_5 a_6 a_7) (skS.0 4 a a_1 a_2 a_3)) False) % 4.89/5.06 (Or (Eq (icext (skS.0 1 a_5) a_9) False) (Eq (icext a_4 a_9) True)))) % 4.89/5.06 Clause #173 (by superposition #[172, 98]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.89/5.06 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False) % 4.89/5.06 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False) % 4.89/5.06 (Or (Eq (icext (skS.0 1 a) a_8) False) (Or (Eq (icext (skS.0 2 a_4 a_5) a_8) True) (Eq False True)))) % 4.89/5.06 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 4.89/5.06 Or (Eq (iext uri_rdf_first (skS.0 3 a a_1 a_2) a_3) False) % 4.89/5.06 (Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_4 a_5 a_6 a_7)) False) % 4.89/5.06 (Or (Eq (icext (skS.0 1 a) a_8) False) (Eq (icext (skS.0 2 a_4 a_5) a_8) True))) % 4.89/5.06 Clause #175 (by superposition #[174, 105]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.89/5.06 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False) % 4.89/5.06 (Or (Eq (icext (skS.0 1 a) a_7) False) (Or (Eq (icext (skS.0 2 a_3 a_4) a_7) True) (Eq False True))) % 4.89/5.06 Clause #176 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.89/5.06 Or (Eq (iext uri_rdf_rest (skS.0 3 a a_1 a_2) (skS.0 4 a_3 a_4 a_5 a_6)) False) % 4.89/5.06 (Or (Eq (icext (skS.0 1 a) a_7) False) (Eq (icext (skS.0 2 a_3 a_4) a_7) True)) % 4.89/5.06 Clause #177 (by superposition #[176, 103]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Or (Eq (icext (skS.0 2 a a_2) a_1) True) (Eq False True)) % 4.89/5.06 Clause #178 (by clausification #[177]): ∀ (a a_1 a_2 : Iota), Or (Eq (icext (skS.0 1 a) a_1) False) (Eq (icext (skS.0 2 a a_2) a_1) True) % 4.89/5.06 Clause #179 (by superposition #[178, 131]): ∀ (a a_1 : Iota), Or (Eq (icext (skS.0 2 a a_1) uri_ex_w) True) (Eq False True) % 4.89/5.06 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), Eq (icext (skS.0 2 a a_1) uri_ex_w) True % 4.89/5.06 Clause #181 (by superposition #[180, 66]): Or (Eq True False) (Eq (icext uri_ex_A uri_ex_w) False) % 4.89/5.06 Clause #185 (by clausification #[181]): Eq (icext uri_ex_A uri_ex_w) False % 4.89/5.06 Clause #186 (by superposition #[185, 168]): Eq False True % 4.89/5.06 Clause #187 (by clausification #[186]): False % 4.89/5.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------