%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU720^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:02:17 PM UTC 2025 % Result : Theorem 5.31s 5.48s % Output : Proof 5.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SEU720^2 : TPTP v9.2.0. Released v3.7.0. % 0.00/0.10 % Command : duper %s % 0.09/0.29 % Computer : n010.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 300 % 0.09/0.29 % DateTime : Fri Oct 3 06:16:53 EDT 2025 % 0.09/0.30 % CPUTime : % 5.31/5.48 SZS status Theorem for theBenchmark.p % 5.31/5.48 SZS output start Proof for theBenchmark.p % 5.31/5.48 Clause #0 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True % 5.31/5.48 Clause #1 (by assumption #[]): Eq (Not (setminusI → ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (setminus A X)) → in Xx X)) % 5.31/5.48 True % 5.31/5.48 Clause #2 (by clausification #[1]): Eq (setminusI → ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (setminus A X)) → in Xx X) False % 5.31/5.48 Clause #3 (by clausification #[2]): Eq setminusI True % 5.31/5.48 Clause #4 (by clausification #[2]): Eq (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (setminus A X)) → in Xx X) False % 5.31/5.48 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 5.31/5.48 Eq % 5.31/5.48 (Not % 5.31/5.48 (∀ (X : Iota), % 5.31/5.48 in X (powerset (skS.0 0 a)) → % 5.31/5.48 ∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (setminus (skS.0 0 a) X)) → in Xx X)) % 5.31/5.48 True % 5.31/5.48 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 5.31/5.48 Eq % 5.31/5.48 (∀ (X : Iota), % 5.31/5.48 in X (powerset (skS.0 0 a)) → ∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (setminus (skS.0 0 a) X)) → in Xx X) % 5.31/5.48 False % 5.31/5.48 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 5.31/5.48 Eq % 5.31/5.48 (Not % 5.31/5.48 (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → % 5.31/5.48 ∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (setminus (skS.0 0 a) (skS.0 1 a a_1))) → in Xx (skS.0 1 a a_1))) % 5.31/5.48 True % 5.31/5.48 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 5.31/5.48 Eq % 5.31/5.48 (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → % 5.31/5.48 ∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (setminus (skS.0 0 a) (skS.0 1 a a_1))) → in Xx (skS.0 1 a a_1)) % 5.31/5.48 False % 5.31/5.48 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), % 5.31/5.48 Eq (∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (setminus (skS.0 0 a) (skS.0 1 a a_1))) → in Xx (skS.0 1 a a_1)) % 5.31/5.48 False % 5.31/5.48 Clause #11 (by clausification #[0]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 5.31/5.48 Clause #12 (by forward demodulation #[11, 3]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 5.31/5.48 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True % 5.31/5.48 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True % 5.31/5.48 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True % 5.31/5.48 Clause #16 (by clausification #[15]): ∀ (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) % 5.31/5.48 Clause #17 (by clausification #[16]): ∀ (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)) % 5.31/5.48 Clause #18 (by clausification #[17]): ∀ (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)) % 5.31/5.48 Clause #20 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 5.31/5.48 Eq % 5.31/5.48 (Not % 5.31/5.48 (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → % 5.31/5.48 Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 5.31/5.48 True % 5.31/5.48 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 5.31/5.48 Eq % 5.31/5.48 (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → % 5.31/5.48 Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 5.31/5.48 False % 5.31/5.48 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 5.31/5.48 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 5.31/5.48 Eq (Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 5.31/5.48 False % 5.31/5.48 Clause #24 (by superposition #[22, 18]): ∀ (a a_1 a_2 a_3 : Iota), % 5.31/5.48 Or (Eq True False) % 5.31/5.48 (Or (Eq (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) a_3)) True) (Eq (in (skS.0 2 a a_1 a_2) a_3) True)) % 5.31/5.48 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1)))) True % 5.31/5.49 Clause #26 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 5.31/5.49 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) False % 5.31/5.49 Clause #30 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), % 5.31/5.49 Or (Eq (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) a_3)) True) (Eq (in (skS.0 2 a a_1 a_2) a_3) True) % 5.31/5.49 Clause #31 (by superposition #[30, 27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq True False) % 5.31/5.49 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 5.31/5.49 Clause #34 (by superposition #[33, 26]): Eq True False % 5.31/5.49 Clause #36 (by clausification #[34]): False % 5.31/5.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------