%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM533+2 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:56:40 PM UTC 2025 % Result : Theorem 3.99s 4.21s % Output : Proof 3.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM533+2 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n019.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 : Fri Oct 3 07:14:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.99/4.21 SZS status Theorem for theBenchmark.p % 3.99/4.21 SZS output start Proof for theBenchmark.p % 3.99/4.21 Clause #9 (by assumption #[]): Eq % 3.99/4.21 (∀ (W0 : Iota), % 3.99/4.21 aSet0 W0 → % 3.99/4.21 ∀ (W1 : Iota), Iff (aSubsetOf0 W1 W0) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 W0))) % 3.99/4.21 True % 3.99/4.21 Clause #13 (by assumption #[]): Eq (And (And (aSet0 xA) (aSet0 xB)) (aSet0 xC)) True % 3.99/4.21 Clause #14 (by assumption #[]): Eq % 3.99/4.21 (Not % 3.99/4.21 (And % 3.99/4.21 (And (And (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xB) (aSubsetOf0 xA xB)) % 3.99/4.21 (∀ (W0 : Iota), aElementOf0 W0 xB → aElementOf0 W0 xC)) % 3.99/4.21 (aSubsetOf0 xB xC) → % 3.99/4.21 Or (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xC) (aSubsetOf0 xA xC))) % 3.99/4.21 True % 3.99/4.21 Clause #45 (by clausification #[13]): Eq (aSet0 xC) True % 3.99/4.21 Clause #74 (by clausification #[9]): ∀ (a : Iota), % 3.99/4.21 Eq % 3.99/4.21 (aSet0 a → % 3.99/4.21 ∀ (W1 : Iota), Iff (aSubsetOf0 W1 a) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 a))) % 3.99/4.21 True % 3.99/4.21 Clause #75 (by clausification #[74]): ∀ (a : Iota), % 3.99/4.21 Or (Eq (aSet0 a) False) % 3.99/4.21 (Eq (∀ (W1 : Iota), Iff (aSubsetOf0 W1 a) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 a))) % 3.99/4.21 True) % 3.99/4.21 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), % 3.99/4.21 Or (Eq (aSet0 a) False) % 3.99/4.21 (Eq (Iff (aSubsetOf0 a_1 a) (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a))) True) % 3.99/4.21 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), % 3.99/4.21 Or (Eq (aSet0 a) False) % 3.99/4.21 (Or (Eq (aSubsetOf0 a_1 a) False) % 3.99/4.21 (Eq (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a)) True)) % 3.99/4.21 Clause #106 (by clausification #[14]): Eq % 3.99/4.21 (And % 3.99/4.21 (And (And (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xB) (aSubsetOf0 xA xB)) % 3.99/4.21 (∀ (W0 : Iota), aElementOf0 W0 xB → aElementOf0 W0 xC)) % 3.99/4.21 (aSubsetOf0 xB xC) → % 3.99/4.21 Or (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xC) (aSubsetOf0 xA xC)) % 3.99/4.21 False % 3.99/4.21 Clause #107 (by clausification #[106]): Eq % 3.99/4.21 (And % 3.99/4.21 (And (And (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xB) (aSubsetOf0 xA xB)) % 3.99/4.21 (∀ (W0 : Iota), aElementOf0 W0 xB → aElementOf0 W0 xC)) % 3.99/4.21 (aSubsetOf0 xB xC)) % 3.99/4.21 True % 3.99/4.21 Clause #108 (by clausification #[106]): Eq (Or (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xC) (aSubsetOf0 xA xC)) False % 3.99/4.21 Clause #109 (by clausification #[107]): Eq (aSubsetOf0 xB xC) True % 3.99/4.21 Clause #110 (by clausification #[107]): Eq % 3.99/4.21 (And (And (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xB) (aSubsetOf0 xA xB)) % 3.99/4.21 (∀ (W0 : Iota), aElementOf0 W0 xB → aElementOf0 W0 xC)) % 3.99/4.21 True % 3.99/4.21 Clause #133 (by clausification #[108]): Eq (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xC) False % 3.99/4.21 Clause #134 (by clausification #[133]): ∀ (a : Iota), Eq (Not (aElementOf0 (skS.0 2 a) xA → aElementOf0 (skS.0 2 a) xC)) True % 3.99/4.21 Clause #135 (by clausification #[134]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 2 a) xA → aElementOf0 (skS.0 2 a) xC) False % 3.99/4.21 Clause #136 (by clausification #[135]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 2 a) xA) True % 3.99/4.21 Clause #137 (by clausification #[135]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 2 a) xC) False % 3.99/4.21 Clause #166 (by clausification #[78]): ∀ (a a_1 : Iota), % 3.99/4.21 Or (Eq (aSet0 a) False) % 3.99/4.21 (Or (Eq (aSubsetOf0 a_1 a) False) (Eq (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a) True)) % 3.99/4.21 Clause #168 (by clausification #[166]): ∀ (a a_1 a_2 : Iota), % 3.99/4.21 Or (Eq (aSet0 a) False) (Or (Eq (aSubsetOf0 a_1 a) False) (Eq (aElementOf0 a_2 a_1 → aElementOf0 a_2 a) True)) % 3.99/4.21 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 : Iota), % 3.99/4.21 Or (Eq (aSet0 a) False) % 3.99/4.21 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aElementOf0 a_2 a_1) False) (Eq (aElementOf0 a_2 a) True))) % 3.99/4.21 Clause #170 (by superposition #[169, 45]): ∀ (a a_1 : Iota), % 3.99/4.21 Or (Eq (aSubsetOf0 a xC) False) % 3.99/4.21 (Or (Eq (aElementOf0 a_1 a) False) (Or (Eq (aElementOf0 a_1 xC) True) (Eq False True))) % 3.99/4.21 Clause #211 (by clausification #[170]): ∀ (a a_1 : Iota), Or (Eq (aSubsetOf0 a xC) False) (Or (Eq (aElementOf0 a_1 a) False) (Eq (aElementOf0 a_1 xC) True)) % 3.99/4.21 Clause #213 (by superposition #[211, 109]): ∀ (a : Iota), Or (Eq (aElementOf0 a xB) False) (Or (Eq (aElementOf0 a xC) True) (Eq False True)) % 3.99/4.21 Clause #214 (by clausification #[213]): ∀ (a : Iota), Or (Eq (aElementOf0 a xB) False) (Eq (aElementOf0 a xC) True) % 3.99/4.21 Clause #243 (by clausification #[110]): Eq (And (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xB) (aSubsetOf0 xA xB)) True % 3.99/4.21 Clause #246 (by clausification #[243]): Eq (∀ (W0 : Iota), aElementOf0 W0 xA → aElementOf0 W0 xB) True % 3.99/4.21 Clause #250 (by clausification #[246]): ∀ (a : Iota), Eq (aElementOf0 a xA → aElementOf0 a xB) True % 3.99/4.21 Clause #251 (by clausification #[250]): ∀ (a : Iota), Or (Eq (aElementOf0 a xA) False) (Eq (aElementOf0 a xB) True) % 3.99/4.21 Clause #252 (by superposition #[251, 136]): ∀ (a : Iota), Or (Eq (aElementOf0 (skS.0 2 a) xB) True) (Eq False True) % 3.99/4.21 Clause #260 (by clausification #[252]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 2 a) xB) True % 3.99/4.21 Clause #261 (by superposition #[260, 214]): ∀ (a : Iota), Or (Eq True False) (Eq (aElementOf0 (skS.0 2 a) xC) True) % 3.99/4.21 Clause #262 (by clausification #[261]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 2 a) xC) True % 3.99/4.21 Clause #263 (by superposition #[262, 137]): Eq True False % 3.99/4.21 Clause #264 (by clausification #[263]): False % 3.99/4.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------