%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU744^2 : 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 3.95s 4.17s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.14 % Problem : SEU744^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.15 % 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 06:31:38 EDT 2025 % 0.15/0.37 % CPUTime : % 3.95/4.17 SZS status Theorem for theBenchmark.p % 3.95/4.17 SZS output start Proof for theBenchmark.p % 3.95/4.17 Clause #0 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 3.95/4.17 Clause #1 (by assumption #[]): Eq % 3.95/4.17 (Eq binunionTILcontra % 3.95/4.17 (∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X))) % 3.95/4.17 True % 3.95/4.17 Clause #2 (by assumption #[]): Eq % 3.95/4.17 (Not % 3.95/4.17 (setminusER → % 3.95/4.17 binunionTILcontra → % 3.95/4.17 ∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), % 3.95/4.17 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X))) % 3.95/4.17 True % 3.95/4.17 Clause #3 (by clausification #[0]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.95/4.17 Clause #20 (by clausification #[1]): Eq binunionTILcontra % 3.95/4.17 (∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 3.95/4.17 Clause #24 (by clausification #[2]): Eq % 3.95/4.17 (setminusER → % 3.95/4.17 binunionTILcontra → % 3.95/4.17 ∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X)) % 3.95/4.17 False % 3.95/4.17 Clause #25 (by clausification #[24]): Eq setminusER True % 3.95/4.17 Clause #26 (by clausification #[24]): Eq % 3.95/4.17 (binunionTILcontra → % 3.95/4.17 ∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X)) % 3.95/4.17 False % 3.95/4.17 Clause #27 (by backward demodulation #[25, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.95/4.17 Clause #30 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 3.95/4.17 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 3.95/4.17 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True % 3.95/4.17 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 3.95/4.17 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 3.95/4.17 Clause #35 (by clausification #[26]): Eq binunionTILcontra True % 3.95/4.17 Clause #36 (by clausification #[26]): Eq % 3.95/4.17 (∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X)) % 3.95/4.17 False % 3.95/4.17 Clause #37 (by backward demodulation #[35, 20]): Eq True % 3.95/4.17 (∀ (A X : Iota), % 3.95/4.17 in X (powerset A) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 3.95/4.17 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 3.95/4.17 Eq % 3.95/4.17 (∀ (X : Iota), % 3.95/4.17 in X (powerset a) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 3.95/4.17 True % 3.95/4.17 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 3.95/4.17 Eq % 3.95/4.17 (in a (powerset a_1) → % 3.95/4.17 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx a)) % 3.95/4.17 True % 3.95/4.17 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 3.95/4.17 Or (Eq (in a (powerset a_1)) False) % 3.95/4.17 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx a)) % 3.95/4.17 True) % 3.95/4.17 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.95/4.17 Or (Eq (in a (powerset a_1)) False) % 3.95/4.17 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a)) True) % 3.95/4.17 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.95/4.17 Or (Eq (in a (powerset a_1)) False) % 3.95/4.17 (Or (Eq (in a_2 (powerset a_1)) False) % 3.95/4.17 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a)) True)) % 3.95/4.17 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (in a (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (in a_3 a_1 → Not (in a_3 (binunion a a_2)) → Not (in a_3 a)) True)) % 4.01/4.19 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (in a (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_2 (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 (binunion a a_2)) → Not (in a_3 a)) True))) % 4.01/4.19 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (in a (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_2 (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binunion a a_2))) False) (Eq (Not (in a_3 a)) True)))) % 4.01/4.19 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (in a (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_2 (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a)) True) (Eq (in a_3 (binunion a a_2)) True)))) % 4.01/4.19 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (in a (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_2 (powerset a_1)) False) % 4.01/4.19 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 (binunion a a_2)) True) (Eq (in a_3 a) False)))) % 4.01/4.19 Clause #48 (by clausification #[36]): ∀ (a : Iota), % 4.01/4.19 Eq % 4.01/4.19 (Not % 4.01/4.19 (∀ (X : Iota), % 4.01/4.19 in X (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Y : Iota), % 4.01/4.19 in Y (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion X Y)) → Not (in Xx X))) % 4.01/4.19 True % 4.01/4.19 Clause #49 (by clausification #[48]): ∀ (a : Iota), % 4.01/4.19 Eq % 4.01/4.19 (∀ (X : Iota), % 4.01/4.19 in X (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Y : Iota), % 4.01/4.19 in Y (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion X Y)) → Not (in Xx X)) % 4.01/4.19 False % 4.01/4.19 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (Not % 4.01/4.19 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Y : Iota), % 4.01/4.19 in Y (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), % 4.01/4.19 in Xx (skS.0 3 a) → % 4.01/4.19 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1)))) % 4.01/4.19 True % 4.01/4.19 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Y : Iota), % 4.01/4.19 in Y (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), % 4.01/4.19 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1))) % 4.01/4.19 False % 4.01/4.19 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (powerset (skS.0 3 a))) True % 4.01/4.19 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (∀ (Y : Iota), % 4.01/4.19 in Y (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), % 4.01/4.19 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1))) % 4.01/4.19 False % 4.01/4.19 Clause #54 (by superposition #[52, 47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq True False) % 4.01/4.19 (Or (Eq (in a (powerset (skS.0 3 a_1))) False) % 4.01/4.19 (Or (Eq (in a_2 (skS.0 3 a_1)) False) % 4.01/4.19 (Or (Eq (in a_2 (binunion (skS.0 4 a_1 a_3) a)) True) (Eq (in a_2 (skS.0 4 a_1 a_3)) False)))) % 4.01/4.19 Clause #75 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (Not % 4.01/4.19 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), % 4.01/4.19 in Xx (skS.0 3 a) → % 4.01/4.19 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1)))) % 4.01/4.19 True % 4.01/4.19 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.01/4.19 ∀ (Xx : Iota), % 4.01/4.19 in Xx (skS.0 3 a) → % 4.01/4.19 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1))) % 4.01/4.19 False % 4.01/4.19 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a))) True % 4.01/4.19 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (∀ (Xx : Iota), % 4.01/4.19 in Xx (skS.0 3 a) → % 4.01/4.19 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1))) % 4.01/4.21 False % 4.01/4.21 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Eq % 4.01/4.21 (Not % 4.01/4.21 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a) → % 4.01/4.21 in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → % 4.01/4.21 Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1)))) % 4.01/4.21 True % 4.01/4.21 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Eq % 4.01/4.21 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a) → % 4.01/4.21 in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → % 4.01/4.21 Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1))) % 4.01/4.21 False % 4.01/4.21 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a)) True % 4.01/4.21 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Eq % 4.01/4.21 (in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → % 4.01/4.21 Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1))) % 4.01/4.21 False % 4.01/4.21 Clause #94 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Eq (in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) True % 4.01/4.21 Clause #95 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1))) False % 4.01/4.21 Clause #96 (by superposition #[94, 34]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Or (Eq True False) (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) False) % 4.01/4.21 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1)) True % 4.01/4.21 Clause #102 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Or (Eq (in a (powerset (skS.0 3 a_1))) False) % 4.01/4.21 (Or (Eq (in a_2 (skS.0 3 a_1)) False) % 4.01/4.21 (Or (Eq (in a_2 (binunion (skS.0 4 a_1 a_3) a)) True) (Eq (in a_2 (skS.0 4 a_1 a_3)) False))) % 4.01/4.21 Clause #104 (by superposition #[102, 77]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.01/4.21 Or (Eq (in a (skS.0 3 a_1)) False) % 4.01/4.21 (Or (Eq (in a (binunion (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) True) % 4.01/4.21 (Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq False True))) % 4.01/4.21 Clause #107 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) False % 4.01/4.21 Clause #110 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.01/4.21 Or (Eq (in a (skS.0 3 a_1)) False) % 4.01/4.21 (Or (Eq (in a (binunion (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) True) (Eq (in a (skS.0 4 a_1 a_2)) False)) % 4.01/4.21 Clause #111 (by superposition #[110, 82]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.01/4.21 Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) True) % 4.01/4.21 (Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_4)) False) (Eq False True)) % 4.01/4.21 Clause #122 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.01/4.21 Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) True) % 4.01/4.21 (Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_4)) False) % 4.01/4.21 Clause #123 (by superposition #[122, 97]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.01/4.21 Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_4 a_5))) True) (Eq False True) % 4.01/4.21 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_4 a_5))) True % 4.01/4.21 Clause #125 (by superposition #[124, 107]): Eq True False % 4.01/4.21 Clause #127 (by clausification #[125]): False % 4.01/4.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------