%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU718^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:02:17 PM UTC 2025 % Result : Theorem 3.78s 3.94s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU718^2 : TPTP v9.2.0. Released v3.7.0. % 0.14/0.13 % Command : duper %s % 0.14/0.34 % Computer : n002.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 04:55:38 EDT 2025 % 0.14/0.34 % CPUTime : % 3.78/3.94 SZS status Theorem for theBenchmark.p % 3.78/3.94 SZS output start Proof for theBenchmark.p % 3.78/3.94 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 3.78/3.94 Clause #1 (by assumption #[]): Eq (Eq powersetE1 (∀ (A B : Iota), in B (powerset A) → subset B A)) True % 3.78/3.94 Clause #2 (by assumption #[]): Eq % 3.78/3.94 (Not % 3.78/3.94 (subsetE → % 3.78/3.94 powersetE1 → % 3.78/3.94 ∀ (A X : Iota), % 3.78/3.94 in X (powerset A) → % 3.78/3.94 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in X (powerset Y) → in Xx X → in Xx Y)) % 3.78/3.94 True % 3.78/3.94 Clause #3 (by clausification #[1]): Eq powersetE1 (∀ (A B : Iota), in B (powerset A) → subset B A) % 3.78/3.94 Clause #16 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.78/3.94 Clause #20 (by clausification #[2]): Eq % 3.78/3.94 (subsetE → % 3.78/3.94 powersetE1 → % 3.78/3.94 ∀ (A X : Iota), % 3.78/3.94 in X (powerset A) → % 3.78/3.94 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in X (powerset Y) → in Xx X → in Xx Y) % 3.78/3.94 False % 3.78/3.94 Clause #21 (by clausification #[20]): Eq subsetE True % 3.78/3.94 Clause #22 (by clausification #[20]): Eq % 3.78/3.94 (powersetE1 → % 3.78/3.94 ∀ (A X : Iota), % 3.78/3.94 in X (powerset A) → % 3.78/3.94 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in X (powerset Y) → in Xx X → in Xx Y) % 3.78/3.94 False % 3.78/3.94 Clause #23 (by backward demodulation #[21, 16]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.78/3.94 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 3.78/3.94 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 3.78/3.94 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 3.78/3.94 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.78/3.94 Clause #28 (by clausification #[27]): ∀ (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)) % 3.78/3.94 Clause #44 (by clausification #[22]): Eq powersetE1 True % 3.78/3.94 Clause #45 (by clausification #[22]): Eq % 3.78/3.94 (∀ (A X : Iota), % 3.78/3.94 in X (powerset A) → % 3.78/3.94 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in X (powerset Y) → in Xx X → in Xx Y) % 3.78/3.94 False % 3.78/3.94 Clause #46 (by backward demodulation #[44, 3]): Eq True (∀ (A B : Iota), in B (powerset A) → subset B A) % 3.78/3.94 Clause #50 (by clausification #[46]): ∀ (a : Iota), Eq (∀ (B : Iota), in B (powerset a) → subset B a) True % 3.78/3.94 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (in a (powerset a_1) → subset a a_1) True % 3.78/3.94 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (subset a a_1) True) % 3.78/3.94 Clause #53 (by clausification #[45]): ∀ (a : Iota), % 3.78/3.94 Eq % 3.78/3.94 (Not % 3.78/3.94 (∀ (X : Iota), % 3.78/3.94 in X (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Y : Iota), % 3.78/3.94 in Y (powerset (skS.0 5 a)) → ∀ (Xx : Iota), in Xx (skS.0 5 a) → in X (powerset Y) → in Xx X → in Xx Y)) % 3.78/3.94 True % 3.78/3.94 Clause #54 (by clausification #[53]): ∀ (a : Iota), % 3.78/3.94 Eq % 3.78/3.94 (∀ (X : Iota), % 3.78/3.94 in X (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Y : Iota), % 3.78/3.94 in Y (powerset (skS.0 5 a)) → ∀ (Xx : Iota), in Xx (skS.0 5 a) → in X (powerset Y) → in Xx X → in Xx Y) % 3.78/3.94 False % 3.78/3.94 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 3.78/3.94 Eq % 3.78/3.94 (Not % 3.78/3.94 (in (skS.0 6 a a_1) (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Y : Iota), % 3.78/3.94 in Y (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Xx : Iota), in Xx (skS.0 5 a) → in (skS.0 6 a a_1) (powerset Y) → in Xx (skS.0 6 a a_1) → in Xx Y)) % 3.78/3.94 True % 3.78/3.94 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 3.78/3.94 Eq % 3.78/3.94 (in (skS.0 6 a a_1) (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Y : Iota), % 3.78/3.94 in Y (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Xx : Iota), in Xx (skS.0 5 a) → in (skS.0 6 a a_1) (powerset Y) → in Xx (skS.0 6 a a_1) → in Xx Y) % 3.78/3.94 False % 3.78/3.94 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), % 3.78/3.94 Eq % 3.78/3.94 (∀ (Y : Iota), % 3.78/3.94 in Y (powerset (skS.0 5 a)) → % 3.78/3.94 ∀ (Xx : Iota), in Xx (skS.0 5 a) → in (skS.0 6 a a_1) (powerset Y) → in Xx (skS.0 6 a a_1) → in Xx Y) % 3.78/3.96 False % 3.78/3.96 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 3.78/3.96 Eq % 3.78/3.96 (Not % 3.78/3.96 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 5 a)) → % 3.78/3.96 ∀ (Xx : Iota), % 3.78/3.96 in Xx (skS.0 5 a) → % 3.78/3.96 in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2)) → in Xx (skS.0 6 a a_1) → in Xx (skS.0 7 a a_1 a_2))) % 3.78/3.96 True % 3.78/3.96 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 3.78/3.96 Eq % 3.78/3.96 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 5 a)) → % 3.78/3.96 ∀ (Xx : Iota), % 3.78/3.96 in Xx (skS.0 5 a) → % 3.78/3.96 in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2)) → in Xx (skS.0 6 a a_1) → in Xx (skS.0 7 a a_1 a_2)) % 3.78/3.96 False % 3.78/3.96 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 3.78/3.96 Eq % 3.78/3.96 (∀ (Xx : Iota), % 3.78/3.96 in Xx (skS.0 5 a) → % 3.78/3.96 in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2)) → in Xx (skS.0 6 a a_1) → in Xx (skS.0 7 a a_1 a_2)) % 3.78/3.96 False % 3.78/3.96 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 3.78/3.96 Eq % 3.78/3.96 (Not % 3.78/3.96 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 5 a) → % 3.78/3.96 in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2)) → % 3.78/3.96 in (skS.0 8 a a_1 a_2 a_3) (skS.0 6 a a_1) → in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2))) % 3.78/3.96 True % 3.78/3.96 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 3.78/3.96 Eq % 3.78/3.96 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 5 a) → % 3.78/3.96 in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2)) → % 3.78/3.96 in (skS.0 8 a a_1 a_2 a_3) (skS.0 6 a a_1) → in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2)) % 3.78/3.96 False % 3.78/3.96 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 3.78/3.96 Eq % 3.78/3.96 (in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2)) → % 3.78/3.96 in (skS.0 8 a a_1 a_2 a_3) (skS.0 6 a a_1) → in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2)) % 3.78/3.96 False % 3.78/3.96 Clause #78 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1) (powerset (skS.0 7 a a_1 a_2))) True % 3.78/3.96 Clause #79 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 3.78/3.96 Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 6 a a_1) → in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2)) False % 3.78/3.96 Clause #80 (by superposition #[78, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (subset (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)) True) % 3.78/3.96 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)) True % 3.78/3.96 Clause #82 (by superposition #[81, 28]): ∀ (a a_1 a_2 a_3 : Iota), % 3.78/3.96 Or (Eq True False) (Or (Eq (in a (skS.0 6 a_1 a_2)) False) (Eq (in a (skS.0 7 a_1 a_2 a_3)) True)) % 3.78/3.96 Clause #84 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 6 a a_1)) True % 3.78/3.96 Clause #85 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2)) False % 3.78/3.96 Clause #87 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 6 a_1 a_2)) False) (Eq (in a (skS.0 7 a_1 a_2 a_3)) True) % 3.78/3.96 Clause #88 (by superposition #[87, 84]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_4)) True) (Eq False True) % 3.78/3.96 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 7 a a_1 a_4)) True % 3.78/3.96 Clause #90 (by superposition #[89, 85]): Eq True False % 3.78/3.96 Clause #91 (by clausification #[90]): False % 3.78/3.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------