%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET064+1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 07:59:32 PM UTC 2025 % Result : Theorem 10.00s 10.20s % Output : Proof 10.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET064+1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n023.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 14:32:23 EDT 2025 % 0.12/0.34 % CPUTime : % 10.00/10.20 SZS status Theorem for theBenchmark.p % 10.00/10.20 SZS output start Proof for theBenchmark.p % 10.00/10.20 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (subclass X Y) (∀ (U : Iota), member U X → member U Y)) True % 10.00/10.20 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (Eq X Y) (And (subclass X Y) (subclass Y X))) True % 10.00/10.20 Clause #15 (by assumption #[]): Eq (∀ (X : Iota), Not (member X null_class)) True % 10.00/10.20 Clause #43 (by assumption #[]): Eq (Not (∀ (Z : Iota), Or (Eq Z null_class) (Exists fun Y => member Y Z))) True % 10.00/10.20 Clause #45 (by clausification #[15]): ∀ (a : Iota), Eq (Not (member a null_class)) True % 10.00/10.20 Clause #46 (by clausification #[45]): ∀ (a : Iota), Eq (member a null_class) False % 10.00/10.20 Clause #49 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (subclass a Y) (∀ (U : Iota), member U a → member U Y)) True % 10.00/10.20 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (Iff (subclass a a_1) (∀ (U : Iota), member U a → member U a_1)) True % 10.00/10.20 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (subclass a a_1) True) (Eq (∀ (U : Iota), member U a → member U a_1) False) % 10.00/10.20 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 10.00/10.20 Or (Eq (subclass a a_1) True) (Eq (Not (member (skS.0 0 a a_1 a_2) a → member (skS.0 0 a a_1 a_2) a_1)) True) % 10.00/10.20 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 10.00/10.20 Or (Eq (subclass a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a → member (skS.0 0 a a_1 a_2) a_1) False) % 10.00/10.20 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (subclass a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a) True) % 10.00/10.20 Clause #57 (by superposition #[55, 46]): ∀ (a : Iota), Or (Eq (subclass null_class a) True) (Eq True False) % 10.00/10.20 Clause #59 (by clausification #[57]): ∀ (a : Iota), Eq (subclass null_class a) True % 10.00/10.20 Clause #72 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (Eq a Y) (And (subclass a Y) (subclass Y a))) True % 10.00/10.20 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subclass a a_1) (subclass a_1 a))) True % 10.00/10.20 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subclass a a_1) (subclass a_1 a)) False) % 10.00/10.20 Clause #76 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (And (subclass a a_1) (subclass a_1 a)) False) (Eq a a_1) % 10.00/10.20 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subclass a a_1) False) (Eq (subclass a_1 a) False)) % 10.00/10.20 Clause #81 (by superposition #[77, 59]): ∀ (a : Iota), Or (Eq null_class a) (Or (Eq (subclass a null_class) False) (Eq False True)) % 10.00/10.20 Clause #82 (by clausification #[81]): ∀ (a : Iota), Or (Eq null_class a) (Eq (subclass a null_class) False) % 10.00/10.20 Clause #1374 (by clausification #[43]): Eq (∀ (Z : Iota), Or (Eq Z null_class) (Exists fun Y => member Y Z)) False % 10.00/10.20 Clause #1375 (by clausification #[1374]): ∀ (a : Iota), Eq (Not (Or (Eq (skS.0 5 a) null_class) (Exists fun Y => member Y (skS.0 5 a)))) True % 10.00/10.20 Clause #1376 (by clausification #[1375]): ∀ (a : Iota), Eq (Or (Eq (skS.0 5 a) null_class) (Exists fun Y => member Y (skS.0 5 a))) False % 10.00/10.20 Clause #1377 (by clausification #[1376]): ∀ (a : Iota), Eq (Exists fun Y => member Y (skS.0 5 a)) False % 10.00/10.20 Clause #1378 (by clausification #[1376]): ∀ (a : Iota), Eq (Eq (skS.0 5 a) null_class) False % 10.00/10.20 Clause #1379 (by clausification #[1377]): ∀ (a a_1 : Iota), Eq (member a (skS.0 5 a_1)) False % 10.00/10.20 Clause #1380 (by superposition #[1379, 55]): ∀ (a a_1 : Iota), Or (Eq (subclass (skS.0 5 a) a_1) True) (Eq False True) % 10.00/10.20 Clause #1382 (by clausification #[1378]): ∀ (a : Iota), Ne (skS.0 5 a) null_class % 10.00/10.20 Clause #1383 (by clausification #[1380]): ∀ (a a_1 : Iota), Eq (subclass (skS.0 5 a) a_1) True % 10.00/10.20 Clause #1384 (by superposition #[1383, 82]): ∀ (a : Iota), Or (Eq null_class (skS.0 5 a)) (Eq True False) % 10.00/10.20 Clause #1388 (by clausification #[1384]): ∀ (a : Iota), Eq null_class (skS.0 5 a) % 10.00/10.20 Clause #1389 (by forward contextual literal cutting #[1388, 1382]): False % 10.00/10.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------