%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU732^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:02:19 PM UTC 2025 % Result : Theorem 4.17s 4.36s % Output : Proof 4.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU732^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 04:32:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.17/4.36 SZS status Theorem for theBenchmark.p % 4.17/4.36 SZS output start Proof for theBenchmark.p % 4.17/4.36 Clause #0 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 4.17/4.36 Clause #1 (by assumption #[]): Eq % 4.17/4.36 (Eq binintersectTELcontra % 4.17/4.36 (∀ (A X : Iota), % 4.17/4.36 in X (powerset A) → % 4.17/4.36 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y)))) % 4.17/4.36 True % 4.17/4.36 Clause #2 (by assumption #[]): Eq % 4.17/4.36 (Not % 4.17/4.36 (setminusER → % 4.17/4.36 binintersectTELcontra → % 4.17/4.36 ∀ (A X : Iota), % 4.17/4.36 in X (powerset A) → % 4.17/4.36 ∀ (Y : Iota), % 4.17/4.36 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y)))) % 4.17/4.36 True % 4.17/4.36 Clause #3 (by clausification #[0]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 4.17/4.36 Clause #20 (by clausification #[1]): Eq binintersectTELcontra % 4.17/4.36 (∀ (A X : Iota), % 4.17/4.36 in X (powerset A) → % 4.17/4.36 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y))) % 4.17/4.36 Clause #24 (by clausification #[2]): Eq % 4.17/4.36 (setminusER → % 4.17/4.36 binintersectTELcontra → % 4.17/4.36 ∀ (A X : Iota), % 4.17/4.36 in X (powerset A) → % 4.17/4.36 ∀ (Y : Iota), % 4.17/4.36 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y))) % 4.17/4.36 False % 4.17/4.36 Clause #25 (by clausification #[24]): Eq setminusER True % 4.17/4.36 Clause #26 (by clausification #[24]): Eq % 4.17/4.36 (binintersectTELcontra → % 4.17/4.36 ∀ (A X : Iota), % 4.17/4.36 in X (powerset A) → % 4.17/4.36 ∀ (Y : Iota), % 4.17/4.36 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y))) % 4.17/4.36 False % 4.17/4.36 Clause #27 (by backward demodulation #[25, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 4.17/4.36 Clause #30 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 4.17/4.36 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 4.17/4.37 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 % 4.17/4.37 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) % 4.17/4.37 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) % 4.17/4.37 Clause #35 (by clausification #[26]): Eq binintersectTELcontra True % 4.17/4.37 Clause #36 (by clausification #[26]): Eq % 4.17/4.37 (∀ (A X : Iota), % 4.17/4.37 in X (powerset A) → % 4.17/4.37 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y))) % 4.17/4.37 False % 4.17/4.37 Clause #37 (by backward demodulation #[35, 20]): Eq True % 4.17/4.37 (∀ (A X : Iota), % 4.17/4.37 in X (powerset A) → % 4.17/4.37 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y))) % 4.17/4.37 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 4.17/4.37 Eq % 4.17/4.37 (∀ (X : Iota), % 4.17/4.37 in X (powerset a) → % 4.17/4.37 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx X) → Not (in Xx (binintersect X Y))) % 4.17/4.37 True % 4.17/4.37 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.17/4.37 Eq % 4.17/4.37 (in a (powerset a_1) → % 4.17/4.37 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a Y))) % 4.17/4.37 True % 4.17/4.37 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 4.17/4.37 Or (Eq (in a (powerset a_1)) False) % 4.17/4.37 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a Y))) % 4.17/4.37 True) % 4.17/4.37 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.17/4.37 Or (Eq (in a (powerset a_1)) False) % 4.17/4.37 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a a_2))) True) % 4.17/4.37 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.17/4.37 Or (Eq (in a (powerset a_1)) False) % 4.17/4.37 (Or (Eq (in a_2 (powerset a_1)) False) % 4.17/4.37 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a a_2))) True)) % 4.24/4.39 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.39 Or (Eq (in a (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (in a_3 a_1 → Not (in a_3 a) → Not (in a_3 (binintersect a a_2))) True)) % 4.24/4.39 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.39 Or (Eq (in a (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_2 (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 a) → Not (in a_3 (binintersect a a_2))) True))) % 4.24/4.39 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.39 Or (Eq (in a (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_2 (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a)) False) (Eq (Not (in a_3 (binintersect a a_2))) True)))) % 4.24/4.39 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.39 Or (Eq (in a (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_2 (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binintersect a a_2))) True) (Eq (in a_3 a) True)))) % 4.24/4.39 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.39 Or (Eq (in a (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_2 (powerset a_1)) False) % 4.24/4.39 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 a) True) (Eq (in a_3 (binintersect a a_2)) False)))) % 4.24/4.39 Clause #48 (by clausification #[36]): ∀ (a : Iota), % 4.24/4.39 Eq % 4.24/4.39 (Not % 4.24/4.39 (∀ (X : Iota), % 4.24/4.39 in X (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Y : Iota), % 4.24/4.39 in Y (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) X) → Not (in Xx (binintersect X Y)))) % 4.24/4.39 True % 4.24/4.39 Clause #49 (by clausification #[48]): ∀ (a : Iota), % 4.24/4.39 Eq % 4.24/4.39 (∀ (X : Iota), % 4.24/4.39 in X (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Y : Iota), % 4.24/4.39 in Y (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) X) → Not (in Xx (binintersect X Y))) % 4.24/4.39 False % 4.24/4.39 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 4.24/4.39 Eq % 4.24/4.39 (Not % 4.24/4.39 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Y : Iota), % 4.24/4.39 in Y (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), % 4.24/4.39 in Xx (skS.0 3 a) → % 4.24/4.39 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y)))) % 4.24/4.39 True % 4.24/4.39 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 4.24/4.39 Eq % 4.24/4.39 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Y : Iota), % 4.24/4.39 in Y (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), % 4.24/4.39 in Xx (skS.0 3 a) → % 4.24/4.39 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))) % 4.24/4.39 False % 4.24/4.39 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (powerset (skS.0 3 a))) True % 4.24/4.39 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), % 4.24/4.39 Eq % 4.24/4.39 (∀ (Y : Iota), % 4.24/4.39 in Y (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), % 4.24/4.39 in Xx (skS.0 3 a) → % 4.24/4.39 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))) % 4.24/4.39 False % 4.24/4.39 Clause #54 (by superposition #[52, 47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.39 Or (Eq True False) % 4.24/4.39 (Or (Eq (in a (powerset (skS.0 3 a_1))) False) % 4.24/4.39 (Or (Eq (in a_2 (skS.0 3 a_1)) False) % 4.24/4.39 (Or (Eq (in a_2 (skS.0 4 a_1 a_3)) True) (Eq (in a_2 (binintersect (skS.0 4 a_1 a_3) a)) False)))) % 4.24/4.39 Clause #75 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.24/4.39 Eq % 4.24/4.39 (Not % 4.24/4.39 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), % 4.24/4.39 in Xx (skS.0 3 a) → % 4.24/4.39 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → % 4.24/4.39 Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))))) % 4.24/4.39 True % 4.24/4.39 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 4.24/4.39 Eq % 4.24/4.39 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.24/4.39 ∀ (Xx : Iota), % 4.24/4.39 in Xx (skS.0 3 a) → % 4.24/4.39 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) % 4.24/4.39 False % 4.24/4.39 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 % 4.24/4.41 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), % 4.24/4.41 Eq % 4.24/4.41 (∀ (Xx : Iota), % 4.24/4.41 in Xx (skS.0 3 a) → % 4.24/4.41 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) % 4.24/4.41 False % 4.24/4.41 Clause #85 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.41 Eq % 4.24/4.41 (Not % 4.24/4.41 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 3 a) → % 4.24/4.41 in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)) → % 4.24/4.41 Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))))) % 4.24/4.41 True % 4.24/4.41 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.41 Eq % 4.24/4.41 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 3 a) → % 4.24/4.41 in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)) → % 4.24/4.41 Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) % 4.24/4.41 False % 4.24/4.41 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 3 a)) True % 4.24/4.41 Clause #88 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.41 Eq % 4.24/4.41 (in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)) → % 4.24/4.41 Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) % 4.24/4.41 False % 4.24/4.41 Clause #94 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1))) True % 4.24/4.41 Clause #95 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) False % 4.24/4.41 Clause #96 (by superposition #[94, 34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) False) % 4.24/4.41 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) False % 4.24/4.41 Clause #98 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) True % 4.24/4.41 Clause #99 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.41 Or (Eq (in a (powerset (skS.0 3 a_1))) False) % 4.24/4.41 (Or (Eq (in a_2 (skS.0 3 a_1)) False) % 4.24/4.41 (Or (Eq (in a_2 (skS.0 4 a_1 a_3)) True) (Eq (in a_2 (binintersect (skS.0 4 a_1 a_3) a)) False))) % 4.24/4.41 Clause #101 (by superposition #[99, 77]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.41 Or (Eq (in a (skS.0 3 a_1)) False) % 4.24/4.41 (Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 4.24/4.41 (Or (Eq (in a (binintersect (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) False) (Eq False True))) % 4.24/4.41 Clause #110 (by clausification #[101]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.41 Or (Eq (in a (skS.0 3 a_1)) False) % 4.24/4.41 (Or (Eq (in a (skS.0 4 a_1 a_2)) True) (Eq (in a (binintersect (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) False)) % 4.24/4.41 Clause #111 (by superposition #[110, 87]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.24/4.41 Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_4)) True) % 4.24/4.41 (Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) False) (Eq False True)) % 4.24/4.41 Clause #120 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.24/4.41 Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_4)) True) % 4.24/4.41 (Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) False) % 4.24/4.41 Clause #121 (by superposition #[120, 98]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) (Eq False True) % 4.24/4.41 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) True % 4.24/4.41 Clause #123 (by superposition #[122, 97]): Eq True False % 4.24/4.41 Clause #124 (by clausification #[123]): False % 4.24/4.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------