%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET063+1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 3.91s 4.06s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SET063+1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.04/0.14 % Command : duper %s % 0.14/0.35 % Computer : n009.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 14:32:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.91/4.06 SZS status Theorem for theBenchmark.p % 3.91/4.06 SZS output start Proof for theBenchmark.p % 3.91/4.06 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (subclass X Y) (∀ (U : Iota), member U X → member U Y)) True % 3.91/4.06 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (Eq X Y) (And (subclass X Y) (subclass Y X))) True % 3.91/4.06 Clause #15 (by assumption #[]): Eq (∀ (X : Iota), Not (member X null_class)) True % 3.91/4.06 Clause #43 (by assumption #[]): Eq (Not (∀ (X : Iota), subclass X null_class → Eq X null_class)) True % 3.91/4.06 Clause #45 (by clausification #[15]): ∀ (a : Iota), Eq (Not (member a null_class)) True % 3.91/4.06 Clause #46 (by clausification #[45]): ∀ (a : Iota), Eq (member a null_class) False % 3.91/4.06 Clause #49 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (subclass a Y) (∀ (U : Iota), member U a → member U Y)) True % 3.91/4.06 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 % 3.91/4.06 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) % 3.91/4.06 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 3.91/4.06 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) % 3.91/4.06 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 3.91/4.06 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) % 3.91/4.06 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) % 3.91/4.06 Clause #57 (by superposition #[55, 46]): ∀ (a : Iota), Or (Eq (subclass null_class a) True) (Eq True False) % 3.91/4.06 Clause #59 (by clausification #[57]): ∀ (a : Iota), Eq (subclass null_class a) True % 3.91/4.06 Clause #67 (by clausification #[43]): Eq (∀ (X : Iota), subclass X null_class → Eq X null_class) False % 3.91/4.06 Clause #68 (by clausification #[67]): ∀ (a : Iota), Eq (Not (subclass (skS.0 1 a) null_class → Eq (skS.0 1 a) null_class)) True % 3.91/4.06 Clause #69 (by clausification #[68]): ∀ (a : Iota), Eq (subclass (skS.0 1 a) null_class → Eq (skS.0 1 a) null_class) False % 3.91/4.06 Clause #70 (by clausification #[69]): ∀ (a : Iota), Eq (subclass (skS.0 1 a) null_class) True % 3.91/4.06 Clause #71 (by clausification #[69]): ∀ (a : Iota), Eq (Eq (skS.0 1 a) null_class) False % 3.91/4.06 Clause #75 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (Eq a Y) (And (subclass a Y) (subclass Y a))) True % 3.91/4.06 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subclass a a_1) (subclass a_1 a))) True % 3.91/4.06 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subclass a a_1) (subclass a_1 a)) False) % 3.91/4.06 Clause #79 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (And (subclass a a_1) (subclass a_1 a)) False) (Eq a a_1) % 3.91/4.06 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subclass a a_1) False) (Eq (subclass a_1 a) False)) % 3.91/4.06 Clause #85 (by superposition #[80, 59]): ∀ (a : Iota), Or (Eq null_class a) (Or (Eq (subclass a null_class) False) (Eq False True)) % 3.91/4.06 Clause #86 (by clausification #[85]): ∀ (a : Iota), Or (Eq null_class a) (Eq (subclass a null_class) False) % 3.91/4.06 Clause #87 (by superposition #[86, 70]): ∀ (a : Iota), Or (Eq null_class (skS.0 1 a)) (Eq False True) % 3.91/4.06 Clause #93 (by clausification #[87]): ∀ (a : Iota), Eq null_class (skS.0 1 a) % 3.91/4.06 Clause #299 (by clausification #[71]): ∀ (a : Iota), Ne (skS.0 1 a) null_class % 3.91/4.06 Clause #300 (by forward demodulation #[299, 93]): Ne null_class null_class % 3.91/4.06 Clause #301 (by eliminate resolved literals #[300]): False % 3.91/4.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------