%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU716^2 : 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 08:02:16 PM UTC 2025 % Result : Theorem 4.68s 4.83s % Output : Proof 4.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU716^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 05:20:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.68/4.83 SZS status Theorem for theBenchmark.p % 4.68/4.83 SZS output start Proof for theBenchmark.p % 4.68/4.83 Clause #0 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True % 4.68/4.83 Clause #1 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 4.68/4.83 Clause #2 (by assumption #[]): Eq % 4.68/4.83 (Not % 4.68/4.83 (powersetE → % 4.68/4.83 subsetI2 → % 4.68/4.83 ∀ (A X : Iota), % 4.68/4.83 in X (powerset A) → % 4.68/4.83 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)) % 4.68/4.83 True % 4.68/4.83 Clause #3 (by clausification #[1]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.68/4.83 Clause #5 (by clausify Prop equality #[3]): Or (Eq subsetI2 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True) % 4.68/4.83 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq subsetI2 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True) % 4.68/4.83 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True) % 4.68/4.83 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True)) % 4.68/4.83 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.68/4.83 Or (Eq subsetI2 False) % 4.68/4.83 (Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True)) % 4.68/4.83 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.68/4.83 Or (Eq subsetI2 False) % 4.68/4.83 (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False)) % 4.68/4.83 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.68/4.83 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.68/4.83 Clause #22 (by clausification #[0]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 4.68/4.83 Clause #26 (by clausification #[2]): Eq % 4.68/4.83 (powersetE → % 4.68/4.83 subsetI2 → % 4.68/4.83 ∀ (A X : Iota), % 4.68/4.83 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 4.68/4.83 False % 4.68/4.83 Clause #27 (by clausification #[26]): Eq powersetE True % 4.68/4.83 Clause #28 (by clausification #[26]): Eq % 4.68/4.83 (subsetI2 → % 4.68/4.83 ∀ (A X : Iota), % 4.68/4.83 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 4.68/4.83 False % 4.68/4.83 Clause #29 (by backward demodulation #[27, 22]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 4.68/4.83 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True % 4.68/4.83 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True % 4.68/4.83 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True % 4.68/4.83 Clause #33 (by clausification #[32]): ∀ (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) % 4.68/4.83 Clause #34 (by clausification #[33]): ∀ (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)) % 4.68/4.83 Clause #35 (by clausification #[28]): Eq subsetI2 True % 4.68/4.83 Clause #36 (by clausification #[28]): Eq % 4.68/4.83 (∀ (A X : Iota), % 4.68/4.83 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 4.68/4.83 False % 4.68/4.83 Clause #38 (by backward demodulation #[35, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.68/4.83 Clause #48 (by clausification #[36]): ∀ (a : Iota), % 4.68/4.83 Eq % 4.68/4.83 (Not % 4.68/4.83 (∀ (X : Iota), % 4.68/4.83 in X (powerset (skS.0 4 a)) → % 4.68/4.83 ∀ (Y : Iota), % 4.68/4.83 in Y (powerset (skS.0 4 a)) → (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx X → in Xx Y) → subset X Y)) % 4.68/4.86 True % 4.68/4.86 Clause #49 (by clausification #[48]): ∀ (a : Iota), % 4.68/4.86 Eq % 4.68/4.86 (∀ (X : Iota), % 4.68/4.86 in X (powerset (skS.0 4 a)) → % 4.68/4.86 ∀ (Y : Iota), in Y (powerset (skS.0 4 a)) → (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx X → in Xx Y) → subset X Y) % 4.68/4.86 False % 4.68/4.86 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 4.68/4.86 Eq % 4.68/4.86 (Not % 4.68/4.86 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) → % 4.68/4.86 ∀ (Y : Iota), % 4.68/4.86 in Y (powerset (skS.0 4 a)) → % 4.68/4.86 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx Y) → subset (skS.0 5 a a_1) Y)) % 4.68/4.86 True % 4.68/4.86 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 4.68/4.86 Eq % 4.68/4.86 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) → % 4.68/4.86 ∀ (Y : Iota), % 4.68/4.86 in Y (powerset (skS.0 4 a)) → % 4.68/4.86 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx Y) → subset (skS.0 5 a a_1) Y) % 4.68/4.86 False % 4.68/4.86 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True % 4.68/4.86 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), % 4.68/4.86 Eq % 4.68/4.86 (∀ (Y : Iota), % 4.68/4.86 in Y (powerset (skS.0 4 a)) → % 4.68/4.86 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx Y) → subset (skS.0 5 a a_1) Y) % 4.68/4.86 False % 4.68/4.86 Clause #54 (by superposition #[52, 34]): ∀ (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)) % 4.68/4.86 Clause #61 (by forward demodulation #[13, 35]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.68/4.86 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False) % 4.68/4.86 Clause #72 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.68/4.86 Eq % 4.68/4.86 (Not % 4.68/4.86 (in (skS.0 9 a a_1 a_2) (powerset (skS.0 4 a)) → % 4.68/4.86 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) → % 4.68/4.86 subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2))) % 4.68/4.86 True % 4.68/4.86 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 4.68/4.86 Eq % 4.68/4.86 (in (skS.0 9 a a_1 a_2) (powerset (skS.0 4 a)) → % 4.68/4.86 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) → % 4.68/4.86 subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) % 4.68/4.86 False % 4.68/4.86 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 4.68/4.86 Eq % 4.68/4.86 ((∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) → % 4.68/4.86 subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) % 4.68/4.86 False % 4.68/4.86 Clause #81 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True) % 4.68/4.86 Clause #88 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) True % 4.68/4.86 Clause #89 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) False % 4.68/4.86 Clause #90 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in a (skS.0 4 a_1) → in a (skS.0 5 a_1 a_2) → in a (skS.0 9 a_1 a_2 a_3)) True % 4.68/4.86 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.86 Or (Eq (in a (skS.0 4 a_1)) False) (Eq (in a (skS.0 5 a_1 a_2) → in a (skS.0 9 a_1 a_2 a_3)) True) % 4.68/4.86 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.86 Or (Eq (in a (skS.0 4 a_1)) False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 9 a_1 a_2 a_3)) True)) % 4.68/4.86 Clause #95 (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) % 4.68/4.86 Clause #97 (by superposition #[95, 81]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.86 Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 4 a)) True) % 4.68/4.86 (Or (Eq (subset (skS.0 5 a a_1) a_2) True) (Eq False True)) % 4.68/4.86 Clause #108 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.86 Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 4 a)) True) (Eq (subset (skS.0 5 a a_1) a_2) True) % 4.68/4.86 Clause #109 (by superposition #[108, 92]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.68/4.86 Or (Eq (subset (skS.0 5 a a_1) a_2) True) % 4.68/4.86 (Or (Eq True False) % 4.71/4.87 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 5 a a_4)) False) % 4.71/4.87 (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_4 a_5)) True))) % 4.71/4.87 Clause #185 (by clausification #[109]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.71/4.87 Or (Eq (subset (skS.0 5 a a_1) a_2) True) % 4.71/4.87 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 5 a a_4)) False) % 4.71/4.87 (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_4 a_5)) True)) % 4.71/4.87 Clause #186 (by superposition #[185, 81]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.71/4.87 Or (Eq (subset (skS.0 5 a a_1) a_2) True) % 4.71/4.87 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_1 a_4)) True) % 4.71/4.87 (Or (Eq (subset (skS.0 5 a a_1) a_2) True) (Eq False True))) % 4.71/4.87 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.71/4.87 Or (Eq (subset (skS.0 5 a a_1) a_2) True) % 4.71/4.87 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_1 a_4)) True) (Eq (subset (skS.0 5 a a_1) a_2) True)) % 4.71/4.87 Clause #188 (by eliminate duplicate literals #[187]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.71/4.87 Or (Eq (subset (skS.0 5 a a_1) a_2) True) (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_1 a_4)) True) % 4.71/4.87 Clause #190 (by superposition #[188, 62]): ∀ (a a_1 a_2 : Iota), % 4.71/4.87 Or (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True) % 4.71/4.87 (Or (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True) (Eq True False)) % 4.71/4.87 Clause #192 (by clausification #[190]): ∀ (a a_1 a_2 : Iota), % 4.71/4.87 Or (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True) (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True) % 4.71/4.87 Clause #193 (by eliminate duplicate literals #[192]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True % 4.71/4.87 Clause #194 (by superposition #[193, 89]): Eq True False % 4.71/4.87 Clause #195 (by clausification #[194]): False % 4.71/4.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------