%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU745^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:02:21 PM UTC 2025 % Result : Theorem 5.32s 5.50s % Output : Proof 5.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU745^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.15 % Command : duper %s % 0.15/0.36 % Computer : n016.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 05:46:53 EDT 2025 % 0.15/0.36 % CPUTime : % 5.32/5.50 SZS status Theorem for theBenchmark.p % 5.32/5.50 SZS output start Proof for theBenchmark.p % 5.32/5.50 Clause #0 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True % 5.32/5.50 Clause #1 (by assumption #[]): Eq % 5.32/5.50 (Eq inComplementUnionImpNotIn1 % 5.32/5.50 (∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X))) % 5.32/5.50 True % 5.32/5.50 Clause #2 (by assumption #[]): Eq % 5.32/5.50 (Not % 5.32/5.50 (setminusI → % 5.32/5.50 inComplementUnionImpNotIn1 → % 5.32/5.50 ∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), % 5.32/5.50 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (setminus A X))) % 5.32/5.50 True % 5.32/5.50 Clause #3 (by clausification #[0]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 5.32/5.50 Clause #21 (by clausification #[1]): Eq inComplementUnionImpNotIn1 % 5.32/5.50 (∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X)) % 5.32/5.50 Clause #25 (by clausification #[2]): Eq % 5.32/5.50 (setminusI → % 5.32/5.50 inComplementUnionImpNotIn1 → % 5.32/5.50 ∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), % 5.32/5.50 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (setminus A X)) % 5.32/5.50 False % 5.32/5.50 Clause #26 (by clausification #[25]): Eq setminusI True % 5.32/5.50 Clause #27 (by clausification #[25]): Eq % 5.32/5.50 (inComplementUnionImpNotIn1 → % 5.32/5.50 ∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), % 5.32/5.50 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (setminus A X)) % 5.32/5.50 False % 5.32/5.50 Clause #28 (by backward demodulation #[26, 3]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 5.32/5.50 Clause #31 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True % 5.32/5.50 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True % 5.32/5.50 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True % 5.32/5.50 Clause #34 (by clausification #[33]): ∀ (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) % 5.32/5.50 Clause #35 (by clausification #[34]): ∀ (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)) % 5.32/5.50 Clause #36 (by clausification #[35]): ∀ (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)) % 5.32/5.50 Clause #37 (by clausification #[27]): Eq inComplementUnionImpNotIn1 True % 5.32/5.50 Clause #38 (by clausification #[27]): Eq % 5.32/5.50 (∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), % 5.32/5.50 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (setminus A X)) % 5.32/5.50 False % 5.32/5.50 Clause #39 (by backward demodulation #[37, 21]): Eq True % 5.32/5.50 (∀ (A X : Iota), % 5.32/5.50 in X (powerset A) → % 5.32/5.50 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X)) % 5.32/5.50 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 5.32/5.50 Eq % 5.32/5.50 (∀ (X : Iota), % 5.32/5.50 in X (powerset a) → % 5.32/5.50 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → in Xx (setminus a (binunion X Y)) → Not (in Xx X)) % 5.32/5.50 True % 5.32/5.50 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 5.32/5.50 Eq % 5.32/5.50 (in a (powerset a_1) → % 5.32/5.50 ∀ (Y : Iota), % 5.32/5.50 in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → in Xx (setminus a_1 (binunion a Y)) → Not (in Xx a)) % 5.32/5.50 True % 5.32/5.50 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 5.32/5.50 Or (Eq (in a (powerset a_1)) False) % 5.32/5.50 (Eq % 5.32/5.50 (∀ (Y : Iota), % 5.32/5.50 in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → in Xx (setminus a_1 (binunion a Y)) → Not (in Xx a)) % 5.32/5.50 True) % 5.32/5.50 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Or (Eq (in a (powerset a_1)) False) % 5.36/5.53 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → in Xx (setminus a_1 (binunion a a_2)) → Not (in Xx a)) True) % 5.36/5.53 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Or (Eq (in a (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_2 (powerset a_1)) False) % 5.36/5.53 (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx (setminus a_1 (binunion a a_2)) → Not (in Xx a)) True)) % 5.36/5.53 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (in a (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_2 (powerset a_1)) False) % 5.36/5.53 (Eq (in a_3 a_1 → in a_3 (setminus a_1 (binunion a a_2)) → Not (in a_3 a)) True)) % 5.36/5.53 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (in a (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_2 (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_3 a_1) False) (Eq (in a_3 (setminus a_1 (binunion a a_2)) → Not (in a_3 a)) True))) % 5.36/5.53 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (in a (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_2 (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 (setminus a_1 (binunion a a_2))) False) (Eq (Not (in a_3 a)) True)))) % 5.36/5.53 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq (in a (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_2 (powerset a_1)) False) % 5.36/5.53 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 (setminus a_1 (binunion a a_2))) False) (Eq (in a_3 a) False)))) % 5.36/5.53 Clause #49 (by clausification #[38]): ∀ (a : Iota), % 5.36/5.53 Eq % 5.36/5.53 (Not % 5.36/5.53 (∀ (X : Iota), % 5.36/5.53 in X (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Y : Iota), % 5.36/5.53 in Y (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Xx : Iota), % 5.36/5.53 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion X Y)) → in Xx (setminus (skS.0 3 a) X))) % 5.36/5.53 True % 5.36/5.53 Clause #50 (by clausification #[49]): ∀ (a : Iota), % 5.36/5.53 Eq % 5.36/5.53 (∀ (X : Iota), % 5.36/5.53 in X (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Y : Iota), % 5.36/5.53 in Y (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Xx : Iota), % 5.36/5.53 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion X Y)) → in Xx (setminus (skS.0 3 a) X)) % 5.36/5.53 False % 5.36/5.53 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 5.36/5.53 Eq % 5.36/5.53 (Not % 5.36/5.53 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Y : Iota), % 5.36/5.53 in Y (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Xx : Iota), % 5.36/5.53 in Xx (skS.0 3 a) → % 5.36/5.53 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → % 5.36/5.53 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 5.36/5.53 True % 5.36/5.53 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), % 5.36/5.53 Eq % 5.36/5.53 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Y : Iota), % 5.36/5.53 in Y (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Xx : Iota), % 5.36/5.53 in Xx (skS.0 3 a) → % 5.36/5.53 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1))) % 5.36/5.53 False % 5.36/5.53 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (powerset (skS.0 3 a))) True % 5.36/5.53 Clause #54 (by clausification #[52]): ∀ (a a_1 : Iota), % 5.36/5.53 Eq % 5.36/5.53 (∀ (Y : Iota), % 5.36/5.53 in Y (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Xx : Iota), % 5.36/5.53 in Xx (skS.0 3 a) → % 5.36/5.53 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1))) % 5.36/5.53 False % 5.36/5.53 Clause #55 (by superposition #[53, 48]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.53 Or (Eq True False) % 5.36/5.53 (Or (Eq (in a (powerset (skS.0 3 a_1))) False) % 5.36/5.53 (Or (Eq (in a_2 (skS.0 3 a_1)) False) % 5.36/5.53 (Or (Eq (in a_2 (setminus (skS.0 3 a_1) (binunion (skS.0 4 a_1 a_3) a))) False) % 5.36/5.53 (Eq (in a_2 (skS.0 4 a_1 a_3)) False)))) % 5.36/5.53 Clause #88 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Eq % 5.36/5.53 (Not % 5.36/5.53 (in (skS.0 9 a a_1 a_2) (powerset (skS.0 3 a)) → % 5.36/5.53 ∀ (Xx : Iota), % 5.36/5.53 in Xx (skS.0 3 a) → % 5.36/5.53 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2))) → % 5.36/5.53 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 5.36/5.53 True % 5.36/5.53 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 5.36/5.53 Eq % 5.36/5.53 (in (skS.0 9 a a_1 a_2) (powerset (skS.0 3 a)) → % 5.36/5.55 ∀ (Xx : Iota), % 5.36/5.55 in Xx (skS.0 3 a) → % 5.36/5.55 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2))) → % 5.36/5.55 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1))) % 5.36/5.55 False % 5.36/5.55 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 9 a a_1 a_2) (powerset (skS.0 3 a))) True % 5.36/5.55 Clause #91 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 5.36/5.55 Eq % 5.36/5.55 (∀ (Xx : Iota), % 5.36/5.55 in Xx (skS.0 3 a) → % 5.36/5.55 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2))) → % 5.36/5.55 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1))) % 5.36/5.55 False % 5.36/5.55 Clause #94 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.55 Eq % 5.36/5.55 (Not % 5.36/5.55 (in (skS.0 10 a a_1 a_2 a_3) (skS.0 3 a) → % 5.36/5.55 in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2))) → % 5.36/5.55 in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 5.36/5.55 True % 5.36/5.55 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.55 Eq % 5.36/5.55 (in (skS.0 10 a a_1 a_2 a_3) (skS.0 3 a) → % 5.36/5.55 in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2))) → % 5.36/5.55 in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1))) % 5.36/5.55 False % 5.36/5.55 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 3 a)) True % 5.36/5.55 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.55 Eq % 5.36/5.55 (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2))) → % 5.36/5.55 in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1))) % 5.36/5.55 False % 5.36/5.55 Clause #98 (by superposition #[96, 36]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.36/5.55 Or (Eq True False) % 5.36/5.55 (Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) a_4)) True) (Eq (in (skS.0 10 a a_1 a_2 a_3) a_4) True)) % 5.36/5.55 Clause #105 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.55 Or (Eq (in a (powerset (skS.0 3 a_1))) False) % 5.36/5.55 (Or (Eq (in a_2 (skS.0 3 a_1)) False) % 5.36/5.55 (Or (Eq (in a_2 (setminus (skS.0 3 a_1) (binunion (skS.0 4 a_1 a_3) a))) False) % 5.36/5.55 (Eq (in a_2 (skS.0 4 a_1 a_3)) False))) % 5.36/5.55 Clause #107 (by superposition #[105, 90]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.36/5.55 Or (Eq (in a (skS.0 3 a_1)) False) % 5.36/5.55 (Or (Eq (in a (setminus (skS.0 3 a_1) (binunion (skS.0 4 a_1 a_2) (skS.0 9 a_1 a_3 a_4)))) False) % 5.36/5.55 (Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq False True))) % 5.36/5.55 Clause #108 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), % 5.36/5.55 Eq (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 9 a a_1 a_2)))) True % 5.36/5.55 Clause #109 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1))) False % 5.36/5.55 Clause #115 (by clausification #[98]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.36/5.55 Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) a_4)) True) (Eq (in (skS.0 10 a a_1 a_2 a_3) a_4) True) % 5.36/5.55 Clause #116 (by superposition #[115, 109]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) (Eq True False) % 5.36/5.55 Clause #121 (by clausification #[116]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 4 a a_1)) True % 5.36/5.55 Clause #129 (by clausification #[107]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.36/5.55 Or (Eq (in a (skS.0 3 a_1)) False) % 5.36/5.55 (Or (Eq (in a (setminus (skS.0 3 a_1) (binunion (skS.0 4 a_1 a_2) (skS.0 9 a_1 a_3 a_4)))) False) % 5.36/5.55 (Eq (in a (skS.0 4 a_1 a_2)) False)) % 5.36/5.55 Clause #130 (by superposition #[129, 96]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.36/5.55 Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_4) (skS.0 9 a a_5 a_6)))) False) % 5.36/5.55 (Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 4 a a_4)) False) (Eq False True)) % 5.36/5.55 Clause #153 (by clausification #[130]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 5.36/5.55 Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_4) (skS.0 9 a a_5 a_6)))) False) % 5.36/5.55 (Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 4 a a_4)) False) % 5.36/5.55 Clause #154 (by superposition #[153, 108]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 4 a a_1)) False) (Eq False True) % 5.36/5.56 Clause #158 (by clausification #[154]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3) (skS.0 4 a a_1)) False % 5.36/5.56 Clause #159 (by superposition #[158, 121]): Eq False True % 5.36/5.56 Clause #160 (by clausification #[159]): False % 5.36/5.56 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------