%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU573^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:01:56 PM UTC 2025 % Result : Theorem 4.84s 5.06s % Output : Proof 4.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : SEU573^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.10 % Command : duper %s % 0.10/0.30 % Computer : n020.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Fri Oct 3 04:12:38 EDT 2025 % 0.10/0.30 % CPUTime : % 4.84/5.06 SZS status Theorem for theBenchmark.p % 4.84/5.06 SZS output start Proof for theBenchmark.p % 4.84/5.06 Clause #0 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 4.84/5.06 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 4.84/5.06 Clause #2 (by assumption #[]): Eq (Not (powersetI → subsetE → ∀ (A B : Iota), subset A B → in A (powerset B))) True % 4.84/5.06 Clause #3 (by clausification #[2]): Eq (powersetI → subsetE → ∀ (A B : Iota), subset A B → in A (powerset B)) False % 4.84/5.06 Clause #4 (by clausification #[3]): Eq powersetI True % 4.84/5.06 Clause #5 (by clausification #[3]): Eq (subsetE → ∀ (A B : Iota), subset A B → in A (powerset B)) False % 4.84/5.06 Clause #6 (by clausification #[5]): Eq subsetE True % 4.84/5.06 Clause #7 (by clausification #[5]): Eq (∀ (A B : Iota), subset A B → in A (powerset B)) False % 4.84/5.06 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (skS.0 0 a) B → in (skS.0 0 a) (powerset B))) True % 4.84/5.06 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (skS.0 0 a) B → in (skS.0 0 a) (powerset B)) False % 4.84/5.06 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (skS.0 1 a a_1) → in (skS.0 0 a) (powerset (skS.0 1 a a_1)))) True % 4.84/5.06 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1) → in (skS.0 0 a) (powerset (skS.0 1 a a_1))) False % 4.84/5.06 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 4.84/5.06 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (powerset (skS.0 1 a a_1))) False % 4.84/5.06 Clause #14 (by clausification #[0]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 4.84/5.06 Clause #15 (by forward demodulation #[14, 4]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 4.84/5.06 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True % 4.84/5.06 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True % 4.84/5.06 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True) % 4.84/5.06 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 4.84/5.06 Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 4.84/5.06 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 4.84/5.06 Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 4.84/5.06 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 2 a a_1 a_2) a) True) % 4.84/5.06 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False) % 4.84/5.06 Clause #23 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 4.84/5.06 Clause #24 (by forward demodulation #[23, 6]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 4.84/5.06 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 4.84/5.06 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 4.84/5.06 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 4.84/5.06 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 4.84/5.06 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 4.84/5.06 Clause #30 (by superposition #[29, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (in a (skS.0 1 a_1 a_2)) True) (Eq False True)) % 4.84/5.06 Clause #34 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a (skS.0 1 a_1 a_2)) True) % 4.84/5.07 Clause #35 (by superposition #[34, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.84/5.07 Or (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) % 4.84/5.07 (Or (Eq (in (skS.0 0 a) (powerset a_1)) True) (Eq False True)) % 4.84/5.07 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 4.84/5.07 Or (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) (Eq (in (skS.0 0 a) (powerset a_1)) True) % 4.84/5.07 Clause #37 (by superposition #[36, 22]): ∀ (a a_1 : Iota), % 4.84/5.07 Or (Eq (in (skS.0 0 a) (powerset (skS.0 1 a a_1))) True) % 4.84/5.07 (Or (Eq (in (skS.0 0 a) (powerset (skS.0 1 a a_1))) True) (Eq True False)) % 4.84/5.07 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 4.84/5.07 Or (Eq (in (skS.0 0 a) (powerset (skS.0 1 a a_1))) True) (Eq (in (skS.0 0 a) (powerset (skS.0 1 a a_1))) True) % 4.84/5.07 Clause #39 (by eliminate duplicate literals #[38]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (powerset (skS.0 1 a a_1))) True % 4.84/5.07 Clause #40 (by superposition #[39, 13]): Eq True False % 4.84/5.07 Clause #41 (by clausification #[40]): False % 4.84/5.07 SZS output end Proof for theBenchmark.p 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