%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET366+4 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:59:58 PM UTC 2025 % Result : Theorem 4.00s 4.20s % Output : Proof 4.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET366+4 : TPTP v9.2.0. Released v2.2.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 13:28:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.00/4.20 SZS status Theorem for theBenchmark.p % 4.00/4.20 SZS output start Proof for theBenchmark.p % 4.00/4.20 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (X : Iota), member X A → member X B)) True % 4.00/4.20 Clause #2 (by assumption #[]): Eq (∀ (X A : Iota), Iff (member X (power_set A)) (subset X A)) True % 4.00/4.20 Clause #5 (by assumption #[]): Eq (∀ (X : Iota), Not (member X empty_set)) True % 4.00/4.20 Clause #11 (by assumption #[]): Eq (Not (∀ (A : Iota), member empty_set (power_set A))) True % 4.00/4.20 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 4.00/4.20 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (member a empty_set) False % 4.00/4.20 Clause #14 (by clausification #[11]): Eq (∀ (A : Iota), member empty_set (power_set A)) False % 4.00/4.20 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (Not (member empty_set (power_set (skS.0 0 a)))) True % 4.00/4.20 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (member empty_set (power_set (skS.0 0 a))) False % 4.00/4.20 Clause #17 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (A : Iota), Iff (member a (power_set A)) (subset a A)) True % 4.00/4.20 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Iff (member a (power_set a_1)) (subset a a_1)) True % 4.00/4.20 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (member a (power_set a_1)) True) (Eq (subset a a_1) False) % 4.00/4.20 Clause #27 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (X : Iota), member X a → member X B)) True % 4.00/4.20 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (X : Iota), member X a → member X a_1)) True % 4.00/4.20 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (X : Iota), member X a → member X a_1) False) % 4.00/4.20 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 4.00/4.20 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 1 a a_1 a_2) a → member (skS.0 1 a a_1 a_2) a_1)) True) % 4.00/4.20 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 4.00/4.20 Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a → member (skS.0 1 a a_1 a_2) a_1) False) % 4.00/4.20 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a) True) % 4.00/4.20 Clause #35 (by superposition #[33, 13]): ∀ (a : Iota), Or (Eq (subset empty_set a) True) (Eq True False) % 4.00/4.20 Clause #37 (by clausification #[35]): ∀ (a : Iota), Eq (subset empty_set a) True % 4.00/4.20 Clause #38 (by superposition #[37, 19]): ∀ (a : Iota), Or (Eq (member empty_set (power_set a)) True) (Eq True False) % 4.00/4.20 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (member empty_set (power_set a)) True % 4.00/4.20 Clause #40 (by superposition #[39, 16]): Eq True False % 4.00/4.20 Clause #42 (by clausification #[40]): False % 4.00/4.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------