%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU727^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 3.81s 3.97s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU727^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n011.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 06:30:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.81/3.97 SZS status Theorem for theBenchmark.p % 3.81/3.97 SZS output start Proof for theBenchmark.p % 3.81/3.97 Clause #0 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True % 3.81/3.97 Clause #1 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 3.81/3.97 Clause #2 (by assumption #[]): Eq % 3.81/3.97 (Not % 3.81/3.97 (setminusI → % 3.81/3.97 setminusER → % 3.81/3.97 ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X)))) % 3.81/3.97 True % 3.81/3.97 Clause #3 (by clausification #[1]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.81/3.97 Clause #20 (by clausification #[0]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 3.81/3.97 Clause #24 (by clausification #[2]): Eq % 3.81/3.97 (setminusI → % 3.81/3.97 setminusER → % 3.81/3.97 ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X))) % 3.81/3.97 False % 3.81/3.97 Clause #25 (by clausification #[24]): Eq setminusI True % 3.81/3.97 Clause #26 (by clausification #[24]): Eq % 3.81/3.97 (setminusER → % 3.81/3.97 ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X))) % 3.81/3.97 False % 3.81/3.97 Clause #27 (by backward demodulation #[25, 20]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 3.81/3.97 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True % 3.81/3.97 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True % 3.81/3.97 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True % 3.81/3.97 Clause #31 (by clausification #[30]): ∀ (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) % 3.81/3.97 Clause #32 (by clausification #[31]): ∀ (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)) % 3.81/3.97 Clause #33 (by clausification #[32]): ∀ (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)) % 3.81/3.97 Clause #51 (by clausification #[26]): Eq setminusER True % 3.81/3.97 Clause #52 (by clausification #[26]): Eq (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X))) False % 3.81/3.97 Clause #53 (by backward demodulation #[51, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.81/3.97 Clause #58 (by clausification #[53]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 3.81/3.97 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 3.81/3.97 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True % 3.81/3.97 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 3.81/3.97 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 3.81/3.97 Clause #63 (by clausification #[52]): ∀ (a : Iota), % 3.81/3.97 Eq % 3.81/3.97 (Not % 3.81/3.97 (∀ (X : Iota), % 3.81/3.97 in X (powerset (skS.0 6 a)) → % 3.81/3.97 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx X → in Xx (setminus (skS.0 6 a) (setminus (skS.0 6 a) X)))) % 3.81/3.97 True % 3.81/3.97 Clause #64 (by clausification #[63]): ∀ (a : Iota), % 3.81/3.97 Eq % 3.81/3.97 (∀ (X : Iota), % 3.81/3.97 in X (powerset (skS.0 6 a)) → % 3.81/3.97 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx X → in Xx (setminus (skS.0 6 a) (setminus (skS.0 6 a) X))) % 3.81/3.97 False % 3.81/3.97 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), % 3.81/3.97 Eq % 3.81/3.97 (Not % 3.81/3.97 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 3.81/3.97 ∀ (Xx : Iota), % 3.81/3.97 in Xx (skS.0 6 a) → % 3.81/3.97 in Xx (skS.0 7 a a_1) → in Xx (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1))))) % 3.81/3.97 True % 3.81/3.97 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 3.81/3.97 Eq % 3.81/3.97 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 3.81/3.97 ∀ (Xx : Iota), % 3.81/3.97 in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 3.81/3.98 False % 3.81/3.98 Clause #68 (by clausification #[66]): ∀ (a a_1 : Iota), % 3.81/3.98 Eq % 3.81/3.98 (∀ (Xx : Iota), % 3.81/3.98 in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 3.81/3.98 False % 3.81/3.98 Clause #70 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 3.81/3.98 Eq % 3.81/3.98 (Not % 3.81/3.98 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) → % 3.81/3.98 in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → % 3.81/3.98 in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1))))) % 3.81/3.98 True % 3.81/3.98 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 3.81/3.98 Eq % 3.81/3.98 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) → % 3.81/3.98 in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → % 3.81/3.98 in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 3.81/3.98 False % 3.81/3.98 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 6 a)) True % 3.81/3.98 Clause #73 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 3.81/3.98 Eq % 3.81/3.98 (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → % 3.81/3.98 in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 3.81/3.98 False % 3.81/3.98 Clause #74 (by superposition #[72, 33]): ∀ (a a_1 a_2 a_3 : Iota), % 3.81/3.98 Or (Eq True False) % 3.81/3.98 (Or (Eq (in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) a_3)) True) (Eq (in (skS.0 8 a a_1 a_2) a_3) True)) % 3.81/3.98 Clause #86 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True % 3.81/3.98 Clause #87 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) False % 3.81/3.98 Clause #89 (by clausification #[74]): ∀ (a a_1 a_2 a_3 : Iota), % 3.81/3.98 Or (Eq (in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) a_3)) True) (Eq (in (skS.0 8 a a_1 a_2) a_3) True) % 3.81/3.98 Clause #93 (by superposition #[87, 89]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True) (Eq True False) % 3.81/3.98 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True % 3.81/3.98 Clause #95 (by superposition #[94, 62]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False) % 3.81/3.98 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False % 3.81/3.98 Clause #98 (by superposition #[97, 86]): Eq False True % 3.81/3.98 Clause #99 (by clausification #[98]): False % 3.81/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------