%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU723^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 3.86s 4.07s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU723^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : duper %s % 0.13/0.35 % Computer : n024.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 04:58:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.86/4.07 SZS status Theorem for theBenchmark.p % 3.86/4.07 SZS output start Proof for theBenchmark.p % 3.86/4.07 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 3.86/4.07 Clause #1 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 3.86/4.07 Clause #2 (by assumption #[]): Eq % 3.86/4.07 (Not % 3.86/4.07 (subsetE → % 3.86/4.07 setminusER → % 3.86/4.07 ∀ (A X : Iota), % 3.86/4.07 in X (powerset A) → % 3.86/4.07 ∀ (Y : Iota), % 3.86/4.07 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X (setminus A Y) → in Xx Y → Not (in Xx X))) % 3.86/4.07 True % 3.86/4.07 Clause #3 (by clausification #[1]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.86/4.07 Clause #20 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.86/4.07 Clause #24 (by clausification #[2]): Eq % 3.86/4.07 (subsetE → % 3.86/4.07 setminusER → % 3.86/4.07 ∀ (A X : Iota), % 3.86/4.07 in X (powerset A) → % 3.86/4.07 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X (setminus A Y) → in Xx Y → Not (in Xx X)) % 3.86/4.07 False % 3.86/4.07 Clause #25 (by clausification #[24]): Eq subsetE True % 3.86/4.07 Clause #26 (by clausification #[24]): Eq % 3.86/4.07 (setminusER → % 3.86/4.07 ∀ (A X : Iota), % 3.86/4.07 in X (powerset A) → % 3.86/4.07 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X (setminus A Y) → in Xx Y → Not (in Xx X)) % 3.86/4.07 False % 3.86/4.07 Clause #27 (by backward demodulation #[25, 20]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.86/4.07 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 3.86/4.07 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 3.86/4.07 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 3.86/4.07 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.86/4.07 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 3.86/4.07 Clause #48 (by clausification #[26]): Eq setminusER True % 3.86/4.07 Clause #49 (by clausification #[26]): Eq % 3.86/4.07 (∀ (A X : Iota), % 3.86/4.07 in X (powerset A) → % 3.86/4.07 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X (setminus A Y) → in Xx Y → Not (in Xx X)) % 3.86/4.07 False % 3.86/4.07 Clause #50 (by backward demodulation #[48, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 3.86/4.07 Clause #55 (by clausification #[50]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 3.86/4.07 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 3.86/4.07 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True % 3.86/4.07 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 3.86/4.07 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 3.86/4.07 Clause #60 (by clausification #[49]): ∀ (a : Iota), % 3.86/4.07 Eq % 3.86/4.07 (Not % 3.86/4.07 (∀ (X : Iota), % 3.86/4.07 in X (powerset (skS.0 6 a)) → % 3.86/4.07 ∀ (Y : Iota), % 3.86/4.07 in Y (powerset (skS.0 6 a)) → % 3.86/4.07 ∀ (Xx : Iota), in Xx (skS.0 6 a) → subset X (setminus (skS.0 6 a) Y) → in Xx Y → Not (in Xx X))) % 3.86/4.07 True % 3.86/4.07 Clause #61 (by clausification #[60]): ∀ (a : Iota), % 3.86/4.07 Eq % 3.86/4.07 (∀ (X : Iota), % 3.86/4.07 in X (powerset (skS.0 6 a)) → % 3.86/4.07 ∀ (Y : Iota), % 3.86/4.07 in Y (powerset (skS.0 6 a)) → % 3.86/4.07 ∀ (Xx : Iota), in Xx (skS.0 6 a) → subset X (setminus (skS.0 6 a) Y) → in Xx Y → Not (in Xx X)) % 3.86/4.07 False % 3.86/4.07 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 3.86/4.07 Eq % 3.86/4.07 (Not % 3.86/4.07 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 3.86/4.07 ∀ (Y : Iota), % 3.86/4.07 in Y (powerset (skS.0 6 a)) → % 3.86/4.07 ∀ (Xx : Iota), % 3.86/4.07 in Xx (skS.0 6 a) → % 3.86/4.07 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) Y) → in Xx Y → Not (in Xx (skS.0 7 a a_1)))) % 3.86/4.09 True % 3.86/4.09 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 3.86/4.09 ∀ (Y : Iota), % 3.86/4.09 in Y (powerset (skS.0 6 a)) → % 3.86/4.09 ∀ (Xx : Iota), % 3.86/4.09 in Xx (skS.0 6 a) → subset (skS.0 7 a a_1) (setminus (skS.0 6 a) Y) → in Xx Y → Not (in Xx (skS.0 7 a a_1))) % 3.86/4.09 False % 3.86/4.09 Clause #65 (by clausification #[63]): ∀ (a a_1 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (∀ (Y : Iota), % 3.86/4.09 in Y (powerset (skS.0 6 a)) → % 3.86/4.09 ∀ (Xx : Iota), % 3.86/4.09 in Xx (skS.0 6 a) → subset (skS.0 7 a a_1) (setminus (skS.0 6 a) Y) → in Xx Y → Not (in Xx (skS.0 7 a a_1))) % 3.86/4.09 False % 3.86/4.09 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (Not % 3.86/4.09 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 3.86/4.09 ∀ (Xx : Iota), % 3.86/4.09 in Xx (skS.0 6 a) → % 3.86/4.09 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2)) → % 3.86/4.09 in Xx (skS.0 8 a a_1 a_2) → Not (in Xx (skS.0 7 a a_1)))) % 3.86/4.09 True % 3.86/4.09 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 3.86/4.09 ∀ (Xx : Iota), % 3.86/4.09 in Xx (skS.0 6 a) → % 3.86/4.09 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2)) → % 3.86/4.09 in Xx (skS.0 8 a a_1 a_2) → Not (in Xx (skS.0 7 a a_1))) % 3.86/4.09 False % 3.86/4.09 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (∀ (Xx : Iota), % 3.86/4.09 in Xx (skS.0 6 a) → % 3.86/4.09 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2)) → % 3.86/4.09 in Xx (skS.0 8 a a_1 a_2) → Not (in Xx (skS.0 7 a a_1))) % 3.86/4.09 False % 3.86/4.09 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (Not % 3.86/4.09 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a) → % 3.86/4.09 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2)) → % 3.86/4.09 in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_2) → Not (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1)))) % 3.86/4.09 True % 3.86/4.09 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a) → % 3.86/4.09 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2)) → % 3.86/4.09 in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_2) → Not (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1))) % 3.86/4.09 False % 3.86/4.09 Clause #73 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.09 Eq % 3.86/4.09 (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2)) → % 3.86/4.09 in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_2) → Not (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1))) % 3.86/4.09 False % 3.86/4.09 Clause #78 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_2))) True % 3.86/4.09 Clause #79 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.09 Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_2) → Not (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1))) False % 3.86/4.09 Clause #80 (by superposition #[78, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.09 Or (Eq True False) % 3.86/4.09 (Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (setminus (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3))) True)) % 3.86/4.09 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_2)) True % 3.86/4.09 Clause #82 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1))) False % 3.86/4.09 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1)) True % 3.86/4.09 Clause #84 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.09 Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (setminus (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3))) True) % 3.86/4.09 Clause #85 (by superposition #[84, 83]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.86/4.09 Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_4))) True) (Eq False True) % 3.86/4.09 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 6 a) (skS.0 8 a a_1 a_4))) True % 3.86/4.09 Clause #87 (by superposition #[86, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq True False) (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_4)) False) % 3.86/4.09 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 8 a a_1 a_4)) False % 3.86/4.10 Clause #89 (by superposition #[88, 81]): Eq False True % 3.86/4.10 Clause #90 (by clausification #[89]): False % 3.86/4.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------