%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU518^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:01:48 PM UTC 2025 % Result : Theorem 3.96s 4.16s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU518^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n003.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 05:40:38 EDT 2025 % 0.14/0.34 % CPUTime : % 3.96/4.16 SZS status Theorem for theBenchmark.p % 3.96/4.16 SZS output start Proof for theBenchmark.p % 3.96/4.16 Clause #0 (by assumption #[]): Eq (Eq powersetAx (∀ (A B : Iota), Iff (in B (powerset A)) (∀ (Xx : Iota), in Xx B → in Xx A))) True % 3.96/4.16 Clause #1 (by assumption #[]): Eq (Not (powersetAx → ∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 3.96/4.16 Clause #2 (by clausification #[1]): Eq (powersetAx → ∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) False % 3.96/4.16 Clause #3 (by clausification #[2]): Eq powersetAx True % 3.96/4.16 Clause #4 (by clausification #[2]): Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) False % 3.96/4.16 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx (skS.0 0 a)) → in B (powerset (skS.0 0 a)))) True % 3.96/4.16 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx (skS.0 0 a)) → in B (powerset (skS.0 0 a))) False % 3.96/4.16 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.96/4.16 Eq (Not ((∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) → in (skS.0 1 a a_1) (powerset (skS.0 0 a)))) True % 3.96/4.16 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 3.96/4.16 Eq ((∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) → in (skS.0 1 a a_1) (powerset (skS.0 0 a))) False % 3.96/4.16 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) True % 3.96/4.16 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) False % 3.96/4.16 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 1 a_1 a_2) → in a (skS.0 0 a_1)) True % 3.96/4.16 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Eq (in a (skS.0 0 a_1)) True) % 3.96/4.16 Clause #13 (by clausification #[0]): Eq powersetAx (∀ (A B : Iota), Iff (in B (powerset A)) (∀ (Xx : Iota), in Xx B → in Xx A)) % 3.96/4.16 Clause #14 (by forward demodulation #[13, 3]): Eq True (∀ (A B : Iota), Iff (in B (powerset A)) (∀ (Xx : Iota), in Xx B → in Xx A)) % 3.96/4.16 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (in B (powerset a)) (∀ (Xx : Iota), in Xx B → in Xx a)) True % 3.96/4.16 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (in a (powerset a_1)) (∀ (Xx : Iota), in Xx a → in Xx a_1)) True % 3.96/4.16 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) % 3.96/4.16 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.96/4.16 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) % 3.96/4.16 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.96/4.16 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) % 3.96/4.16 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) % 3.96/4.16 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) % 3.96/4.16 Clause #23 (by superposition #[21, 12]): ∀ (a a_1 a_2 a_3 : Iota), % 3.96/4.16 Or (Eq (in (skS.0 1 a a_1) (powerset a_2)) True) % 3.96/4.16 (Or (Eq True False) (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True)) % 3.96/4.16 Clause #34 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 3.96/4.16 Or (Eq (in (skS.0 1 a a_1) (powerset a_2)) True) (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True) % 3.96/4.16 Clause #35 (by superposition #[34, 22]): ∀ (a a_1 : Iota), % 3.96/4.16 Or (Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True) % 3.96/4.16 (Or (Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True) (Eq True False)) % 3.96/4.16 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.96/4.16 Or (Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True) (Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True) % 3.96/4.16 Clause #37 (by eliminate duplicate literals #[36]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True % 3.96/4.16 Clause #38 (by superposition #[37, 10]): Eq True False % 3.96/4.16 Clause #45 (by clausification #[38]): False % 3.96/4.16 SZS output end Proof for theBenchmark.p 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