%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU719^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 3.79s 3.94s % Output : Proof 3.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU719^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 06:43:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.79/3.94 SZS status Theorem for theBenchmark.p % 3.79/3.94 SZS output start Proof for theBenchmark.p % 3.79/3.94 Clause #0 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 3.79/3.94 Clause #1 (by assumption #[]): Eq % 3.79/3.94 (Not (setminusER → ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → Not (in Xx (setminus A X)))) % 3.79/3.94 True % 3.79/3.94 Clause #2 (by clausification #[0]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.79/3.94 Clause #19 (by clausification #[1]): Eq (setminusER → ∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → Not (in Xx (setminus A X))) % 3.79/3.94 False % 3.79/3.94 Clause #20 (by clausification #[19]): Eq setminusER True % 3.79/3.94 Clause #21 (by clausification #[19]): Eq (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → Not (in Xx (setminus A X))) False % 3.79/3.94 Clause #22 (by backward demodulation #[20, 2]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.79/3.94 Clause #27 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 3.79/3.94 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 3.79/3.94 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True % 3.79/3.94 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 3.79/3.94 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 3.79/3.94 Clause #32 (by clausification #[21]): ∀ (a : Iota), % 3.79/3.94 Eq % 3.79/3.94 (Not % 3.79/3.94 (∀ (X : Iota), % 3.79/3.94 in X (powerset (skS.0 3 a)) → % 3.79/3.94 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx X → Not (in Xx (setminus (skS.0 3 a) X)))) % 3.79/3.94 True % 3.79/3.94 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 3.79/3.94 Eq % 3.79/3.94 (∀ (X : Iota), % 3.79/3.94 in X (powerset (skS.0 3 a)) → ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx X → Not (in Xx (setminus (skS.0 3 a) X))) % 3.79/3.94 False % 3.79/3.94 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 3.79/3.94 Eq % 3.79/3.94 (Not % 3.79/3.94 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.79/3.94 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (skS.0 4 a a_1) → Not (in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1))))) % 3.79/3.94 True % 3.79/3.94 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.79/3.94 Eq % 3.79/3.94 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.79/3.94 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (skS.0 4 a a_1) → Not (in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 3.79/3.94 False % 3.79/3.94 Clause #37 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.79/3.94 Eq (∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (skS.0 4 a a_1) → Not (in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 3.79/3.94 False % 3.79/3.94 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 3.79/3.94 Eq % 3.79/3.94 (Not % 3.79/3.94 (in (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 3.79/3.94 in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1) → Not (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1))))) % 3.79/3.94 True % 3.79/3.94 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.79/3.94 Eq % 3.79/3.94 (in (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 3.79/3.94 in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1) → Not (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 3.79/3.94 False % 3.79/3.94 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 3.79/3.94 Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1) → Not (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1)))) % 3.79/3.94 False % 3.79/3.94 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) True % 3.79/3.94 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1)))) False % 3.79/3.94 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1))) True % 3.79/3.94 Clause #45 (by superposition #[44, 31]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) False) % 3.79/3.94 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) False % 3.79/3.94 Clause #47 (by superposition #[46, 42]): Eq False True % 3.79/3.94 Clause #48 (by clausification #[47]): False % 3.79/3.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------