%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU712^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:02:16 PM UTC 2025 % Result : Theorem 5.35s 5.56s % Output : Proof 5.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU712^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:46:53 EDT 2025 % 0.13/0.34 % CPUTime : % 5.35/5.56 SZS status Theorem for theBenchmark.p % 5.35/5.56 SZS output start Proof for theBenchmark.p % 5.35/5.56 Clause #0 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 5.35/5.56 Clause #1 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True % 5.35/5.56 Clause #2 (by assumption #[]): Eq (Not (powersetI → powersetE → ∀ (A X : Iota), in X (powerset A) → in (powerset X) (powerset (powerset A)))) True % 5.35/5.56 Clause #3 (by clausification #[0]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 5.35/5.56 Clause #22 (by clausification #[1]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 5.35/5.56 Clause #26 (by clausification #[2]): Eq (powersetI → powersetE → ∀ (A X : Iota), in X (powerset A) → in (powerset X) (powerset (powerset A))) False % 5.35/5.56 Clause #27 (by clausification #[26]): Eq powersetI True % 5.35/5.56 Clause #28 (by clausification #[26]): Eq (powersetE → ∀ (A X : Iota), in X (powerset A) → in (powerset X) (powerset (powerset A))) False % 5.35/5.56 Clause #29 (by backward demodulation #[27, 3]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 5.35/5.56 Clause #32 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True % 5.35/5.56 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True % 5.35/5.56 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True) % 5.35/5.56 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 5.35/5.56 Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 5.35/5.56 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 5.35/5.56 Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1) False) % 5.35/5.56 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 3 a a_1 a_2) a) True) % 5.35/5.56 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 3 a a_1 a_2) a_1) False) % 5.35/5.56 Clause #39 (by clausification #[28]): Eq powersetE True % 5.35/5.56 Clause #40 (by clausification #[28]): Eq (∀ (A X : Iota), in X (powerset A) → in (powerset X) (powerset (powerset A))) False % 5.35/5.56 Clause #41 (by backward demodulation #[39, 22]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 5.35/5.56 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True % 5.35/5.56 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True % 5.35/5.56 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True % 5.35/5.56 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True) % 5.35/5.56 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 5.35/5.56 Clause #47 (by superposition #[46, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 5.35/5.56 Or (Eq (in a (skS.0 3 (powerset a_1) a_2 a_3)) False) % 5.35/5.56 (Or (Eq (in a a_1) True) (Or (Eq (in (powerset a_1) (powerset a_2)) True) (Eq False True))) % 5.35/5.56 Clause #48 (by clausification #[40]): ∀ (a : Iota), % 5.35/5.56 Eq (Not (∀ (X : Iota), in X (powerset (skS.0 4 a)) → in (powerset X) (powerset (powerset (skS.0 4 a))))) True % 5.35/5.56 Clause #49 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (X : Iota), in X (powerset (skS.0 4 a)) → in (powerset X) (powerset (powerset (skS.0 4 a)))) False % 5.35/5.56 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 5.35/5.56 Eq (Not (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) → in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a))))) % 5.35/5.56 True % 5.35/5.56 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 5.35/5.56 Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) → in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) False % 5.35/5.59 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True % 5.35/5.59 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) False % 5.35/5.59 Clause #54 (by superposition #[52, 46]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1)) True)) % 5.35/5.59 Clause #85 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1)) True) % 5.35/5.59 Clause #88 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 5.35/5.59 Or (Eq (in a (skS.0 3 (powerset a_1) a_2 a_3)) False) % 5.35/5.59 (Or (Eq (in a a_1) True) (Eq (in (powerset a_1) (powerset a_2)) True)) % 5.35/5.59 Clause #89 (by superposition #[88, 37]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.59 Or (Eq (in (skS.0 3 (skS.0 3 (powerset a) a_1 a_2) a_3 a_4) a) True) % 5.35/5.59 (Or (Eq (in (powerset a) (powerset a_1)) True) % 5.35/5.59 (Or (Eq (in (skS.0 3 (powerset a) a_1 a_2) (powerset a_3)) True) (Eq False True))) % 5.35/5.59 Clause #106 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.59 Or (Eq (in (skS.0 3 (skS.0 3 (powerset a) a_1 a_2) a_3 a_4) a) True) % 5.35/5.59 (Or (Eq (in (powerset a) (powerset a_1)) True) (Eq (in (skS.0 3 (powerset a) a_1 a_2) (powerset a_3)) True)) % 5.35/5.59 Clause #108 (by superposition #[106, 85]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset a_2)) True) % 5.35/5.59 (Or (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset a_4)) True) % 5.35/5.59 (Or (Eq True False) (Eq (in (skS.0 3 (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) a_4 a_5) (skS.0 4 a)) True))) % 5.35/5.59 Clause #152 (by clausification #[108]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset a_2)) True) % 5.35/5.59 (Or (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset a_4)) True) % 5.35/5.59 (Eq (in (skS.0 3 (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) a_4 a_5) (skS.0 4 a)) True)) % 5.35/5.59 Clause #153 (by superposition #[152, 38]): ∀ (a a_1 a_2 a_3 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset a_2)) True) % 5.35/5.59 (Or (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset (skS.0 4 a))) True) % 5.35/5.59 (Or (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset (skS.0 4 a))) True) (Eq True False))) % 5.35/5.59 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 a_3 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset a_2)) True) % 5.35/5.59 (Or (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset (skS.0 4 a))) True) % 5.35/5.59 (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset (skS.0 4 a))) True)) % 5.35/5.59 Clause #156 (by eliminate duplicate literals #[155]): ∀ (a a_1 a_2 a_3 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset a_2)) True) % 5.35/5.59 (Eq (in (skS.0 3 (powerset (skS.0 5 a a_1)) a_2 a_3) (powerset (skS.0 4 a))) True) % 5.35/5.59 Clause #158 (by superposition #[156, 38]): ∀ (a a_1 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) True) % 5.35/5.59 (Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) True) (Eq True False)) % 5.35/5.59 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), % 5.35/5.59 Or (Eq (in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) True) % 5.35/5.59 (Eq (in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) True) % 5.35/5.59 Clause #160 (by eliminate duplicate literals #[159]): ∀ (a a_1 : Iota), Eq (in (powerset (skS.0 5 a a_1)) (powerset (powerset (skS.0 4 a)))) True % 5.35/5.59 Clause #161 (by superposition #[160, 53]): Eq True False % 5.35/5.59 Clause #163 (by clausification #[161]): False % 5.35/5.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------