%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU728^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:02:18 PM UTC 2025 % Result : Theorem 3.67s 3.88s % Output : Proof 3.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU728^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 05:31:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.67/3.88 SZS status Theorem for theBenchmark.p % 3.67/3.88 SZS output start Proof for theBenchmark.p % 3.67/3.88 Clause #0 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True % 3.67/3.88 Clause #1 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 3.67/3.88 Clause #2 (by assumption #[]): Eq % 3.67/3.88 (Not % 3.67/3.88 (setminusI → % 3.67/3.88 setminusER → % 3.67/3.88 ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (setminus A X)) → in Xx X)) % 3.67/3.88 True % 3.67/3.88 Clause #3 (by clausification #[1]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.67/3.88 Clause #20 (by clausification #[2]): Eq % 3.67/3.88 (setminusI → % 3.67/3.88 setminusER → % 3.67/3.88 ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (setminus A X)) → in Xx X) % 3.67/3.88 False % 3.67/3.88 Clause #21 (by clausification #[20]): Eq setminusI True % 3.67/3.88 Clause #22 (by clausification #[20]): Eq % 3.67/3.88 (setminusER → % 3.67/3.88 ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (setminus A X)) → in Xx X) % 3.67/3.88 False % 3.67/3.88 Clause #23 (by clausification #[0]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 3.67/3.88 Clause #24 (by forward demodulation #[23, 21]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 3.67/3.88 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True % 3.67/3.88 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True % 3.67/3.88 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True % 3.67/3.88 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a a_2) → in a (setminus a_1 a_2)) True) % 3.67/3.88 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (Not (in a a_2)) False) (Eq (in a (setminus a_1 a_2)) True)) % 3.67/3.88 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a (setminus a_1 a_2)) True) (Eq (in a a_2) True)) % 3.67/3.88 Clause #32 (by clausification #[22]): Eq setminusER True % 3.67/3.88 Clause #33 (by clausification #[22]): Eq (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (setminus A X)) → in Xx X) False % 3.67/3.88 Clause #34 (by backward demodulation #[32, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.67/3.88 Clause #37 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 3.67/3.88 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 3.67/3.88 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True % 3.67/3.88 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 3.67/3.88 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 3.67/3.88 Clause #42 (by clausification #[33]): ∀ (a : Iota), % 3.67/3.88 Eq % 3.67/3.88 (Not % 3.67/3.88 (∀ (X : Iota), % 3.67/3.88 in X (powerset (skS.0 3 a)) → % 3.67/3.88 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (setminus (skS.0 3 a) X)) → in Xx X)) % 3.67/3.88 True % 3.67/3.88 Clause #43 (by clausification #[42]): ∀ (a : Iota), % 3.67/3.88 Eq % 3.67/3.88 (∀ (X : Iota), % 3.67/3.88 in X (powerset (skS.0 3 a)) → % 3.67/3.88 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (setminus (skS.0 3 a) X)) → in Xx X) % 3.67/3.88 False % 3.67/3.88 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), % 3.67/3.88 Eq % 3.67/3.88 (Not % 3.67/3.88 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.67/3.88 ∀ (Xx : Iota), % 3.67/3.88 in Xx (skS.0 3 a) → % 3.67/3.88 in Xx (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1))) → in Xx (skS.0 4 a a_1))) % 3.67/3.88 True % 3.67/3.88 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), % 3.67/3.88 Eq % 3.67/3.88 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.67/3.88 ∀ (Xx : Iota), % 3.67/3.88 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1))) → in Xx (skS.0 4 a a_1)) % 3.67/3.90 False % 3.67/3.90 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota), % 3.67/3.90 Eq % 3.67/3.90 (∀ (Xx : Iota), % 3.67/3.90 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1))) → in Xx (skS.0 4 a a_1)) % 3.67/3.90 False % 3.67/3.90 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 3.67/3.90 Eq % 3.67/3.90 (Not % 3.67/3.90 (in (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 3.67/3.90 in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1))) → % 3.67/3.90 in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1))) % 3.67/3.90 True % 3.67/3.90 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 3.67/3.90 Eq % 3.67/3.90 (in (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 3.67/3.90 in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1))) → % 3.67/3.90 in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) % 3.67/3.90 False % 3.67/3.90 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 3 a)) True % 3.67/3.90 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 3.67/3.90 Eq % 3.67/3.90 (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1))) → % 3.67/3.90 in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) % 3.67/3.90 False % 3.67/3.90 Clause #53 (by superposition #[51, 30]): ∀ (a a_1 a_2 a_3 : Iota), % 3.67/3.90 Or (Eq True False) % 3.67/3.90 (Or (Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) a_3)) True) (Eq (in (skS.0 5 a a_1 a_2) a_3) True)) % 3.67/3.90 Clause #56 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (setminus (skS.0 3 a) (skS.0 4 a a_1)))) True % 3.67/3.90 Clause #57 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) False % 3.67/3.90 Clause #58 (by superposition #[56, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1))) False) % 3.67/3.90 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1))) False % 3.67/3.90 Clause #67 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 3.67/3.90 Or (Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) a_3)) True) (Eq (in (skS.0 5 a a_1 a_2) a_3) True) % 3.67/3.90 Clause #68 (by superposition #[67, 60]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) True) (Eq True False) % 3.67/3.90 Clause #71 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) True % 3.67/3.90 Clause #72 (by superposition #[71, 57]): Eq True False % 3.67/3.90 Clause #74 (by clausification #[72]): False % 3.67/3.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------