%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU729^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 75.15s 75.34s % Output : Proof 75.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU729^2 : TPTP v9.2.0. Released v3.7.0. % 0.14/0.14 % Command : duper %s % 0.14/0.35 % Computer : n001.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 05:46:53 EDT 2025 % 0.14/0.36 % CPUTime : % 75.15/75.34 SZS status Theorem for theBenchmark.p % 75.15/75.34 SZS output start Proof for theBenchmark.p % 75.15/75.34 Clause #0 (by assumption #[]): Eq (Eq complementT_lem (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A))) True % 75.15/75.34 Clause #1 (by assumption #[]): Eq % 75.15/75.34 (Eq subsetTI % 75.15/75.34 (∀ (A X : Iota), % 75.15/75.34 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)) % 75.15/75.34 True % 75.15/75.34 Clause #2 (by assumption #[]): Eq % 75.15/75.34 (Eq doubleComplementI1 % 75.15/75.34 (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X)))) % 75.15/75.34 True % 75.15/75.34 Clause #3 (by assumption #[]): Eq % 75.15/75.34 (Not % 75.15/75.34 (complementT_lem → % 75.15/75.34 subsetTI → doubleComplementI1 → ∀ (A X : Iota), in X (powerset A) → subset X (setminus A (setminus A X)))) % 75.15/75.34 True % 75.15/75.34 Clause #4 (by clausification #[1]): Eq subsetTI % 75.15/75.34 (∀ (A X : Iota), % 75.15/75.34 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 75.15/75.34 Clause #6 (by clausify Prop equality #[4]): Or (Eq subsetTI False) % 75.15/75.34 (Eq % 75.15/75.34 (∀ (A X : Iota), % 75.15/75.34 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 75.15/75.34 True) % 75.15/75.34 Clause #8 (by clausification #[6]): ∀ (a : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Eq % 75.15/75.34 (∀ (X : Iota), % 75.15/75.34 in X (powerset a) → ∀ (Y : Iota), in Y (powerset a) → (∀ (Xx : Iota), in Xx a → in Xx X → in Xx Y) → subset X Y) % 75.15/75.34 True) % 75.15/75.34 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Eq % 75.15/75.34 (in a (powerset a_1) → % 75.15/75.34 ∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) % 75.15/75.34 True) % 75.15/75.34 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Eq (∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) True)) % 75.15/75.34 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Eq (in a_2 (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) → subset a a_2) True)) % 75.15/75.34 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Or (Eq (in a_2 (powerset a_1)) False) % 75.15/75.34 (Eq ((∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) → subset a a_2) True))) % 75.15/75.34 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Or (Eq (in a_2 (powerset a_1)) False) % 75.15/75.34 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) False) (Eq (subset a a_2) True)))) % 75.15/75.34 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Or (Eq (in a_2 (powerset a_1)) False) % 75.15/75.34 (Or (Eq (subset a a_2) True) % 75.15/75.34 (Eq (Not (in (skS.0 0 a_1 a a_2 a_3) a_1 → in (skS.0 0 a_1 a a_2 a_3) a → in (skS.0 0 a_1 a a_2 a_3) a_2)) % 75.15/75.34 True)))) % 75.15/75.34 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Or (Eq (in a_2 (powerset a_1)) False) % 75.15/75.34 (Or (Eq (subset a a_2) True) % 75.15/75.34 (Eq (in (skS.0 0 a_1 a a_2 a_3) a_1 → in (skS.0 0 a_1 a a_2 a_3) a → in (skS.0 0 a_1 a a_2 a_3) a_2) False)))) % 75.15/75.34 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a_1) True)))) % 75.15/75.34 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.34 Or (Eq subsetTI False) % 75.15/75.34 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.34 (Or (Eq (in a_2 (powerset a_1)) False) % 75.15/75.34 (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a → in (skS.0 0 a_1 a a_2 a_3) a_2) False)))) % 75.15/75.34 Clause #24 (by clausification #[0]): Eq complementT_lem (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) % 75.15/75.37 Clause #28 (by clausification #[2]): Eq doubleComplementI1 % 75.15/75.37 (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X))) % 75.15/75.37 Clause #41 (by clausification #[3]): Eq % 75.15/75.37 (complementT_lem → % 75.15/75.37 subsetTI → doubleComplementI1 → ∀ (A X : Iota), in X (powerset A) → subset X (setminus A (setminus A X))) % 75.15/75.37 False % 75.15/75.37 Clause #42 (by clausification #[41]): Eq complementT_lem True % 75.15/75.37 Clause #43 (by clausification #[41]): Eq (subsetTI → doubleComplementI1 → ∀ (A X : Iota), in X (powerset A) → subset X (setminus A (setminus A X))) False % 75.15/75.37 Clause #44 (by backward demodulation #[42, 24]): Eq True (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) % 75.15/75.37 Clause #47 (by clausification #[44]): ∀ (a : Iota), Eq (∀ (X : Iota), in X (powerset a) → in (setminus a X) (powerset a)) True % 75.15/75.37 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (in a (powerset a_1) → in (setminus a_1 a) (powerset a_1)) True % 75.15/75.37 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in (setminus a_1 a) (powerset a_1)) True) % 75.15/75.37 Clause #51 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.37 Or (Eq subsetTI False) % 75.15/75.37 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.37 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a) True)))) % 75.15/75.37 Clause #52 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.37 Or (Eq subsetTI False) % 75.15/75.37 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.37 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a_2) False)))) % 75.15/75.37 Clause #53 (by clausification #[43]): Eq subsetTI True % 75.15/75.37 Clause #54 (by clausification #[43]): Eq (doubleComplementI1 → ∀ (A X : Iota), in X (powerset A) → subset X (setminus A (setminus A X))) False % 75.15/75.37 Clause #56 (by backward demodulation #[53, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.37 Or (Eq True False) % 75.15/75.37 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.37 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a_1) True)))) % 75.15/75.37 Clause #58 (by backward demodulation #[53, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 75.15/75.37 Or (Eq True False) % 75.15/75.37 (Or (Eq (in a (powerset a_1)) False) % 75.15/75.37 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a) True)))) % 75.15/75.37 Clause #69 (by clausification #[54]): Eq doubleComplementI1 True % 75.15/75.37 Clause #70 (by clausification #[54]): Eq (∀ (A X : Iota), in X (powerset A) → subset X (setminus A (setminus A X))) False % 75.15/75.37 Clause #71 (by backward demodulation #[69, 28]): Eq True (∀ (A X : Iota), in X (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx X → in Xx (setminus A (setminus A X))) % 75.15/75.37 Clause #72 (by clausification #[70]): ∀ (a : Iota), % 75.15/75.37 Eq (Not (∀ (X : Iota), in X (powerset (skS.0 6 a)) → subset X (setminus (skS.0 6 a) (setminus (skS.0 6 a) X)))) True % 75.15/75.37 Clause #73 (by clausification #[72]): ∀ (a : Iota), % 75.15/75.37 Eq (∀ (X : Iota), in X (powerset (skS.0 6 a)) → subset X (setminus (skS.0 6 a) (setminus (skS.0 6 a) X))) False % 75.15/75.37 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 75.15/75.37 Eq % 75.15/75.37 (Not % 75.15/75.37 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 75.15/75.37 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1))))) % 75.15/75.37 True % 75.15/75.37 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 75.15/75.37 Eq % 75.15/75.37 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 75.15/75.37 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 75.15/75.37 False % 75.15/75.37 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 6 a))) True % 75.15/75.37 Clause #77 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) False % 75.15/75.37 Clause #78 (by superposition #[76, 49]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (setminus (skS.0 6 a) (skS.0 7 a a_1)) (powerset (skS.0 6 a))) True) % 75.15/75.37 Clause #80 (by clausification #[71]): ∀ (a : Iota), % 75.15/75.37 Eq (∀ (X : Iota), in X (powerset a) → ∀ (Xx : Iota), in Xx a → in Xx X → in Xx (setminus a (setminus a X))) True % 75.22/75.40 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), % 75.22/75.40 Eq (in a (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx (setminus a_1 (setminus a_1 a))) True % 75.22/75.40 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx (setminus a_1 (setminus a_1 a))) True) % 75.22/75.40 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a_1 → in a_2 a → in a_2 (setminus a_1 (setminus a_1 a))) True) % 75.22/75.40 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Or (Eq (in a_2 a_1) False) (Eq (in a_2 a → in a_2 (setminus a_1 (setminus a_1 a))) True)) % 75.22/75.40 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Or (Eq (in a_2 a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 (setminus a_1 (setminus a_1 a))) True))) % 75.22/75.40 Clause #86 (by superposition #[85, 76]): ∀ (a a_1 a_2 : Iota), % 75.22/75.40 Or (Eq (in a (skS.0 6 a_1)) False) % 75.22/75.40 (Or (Eq (in a (skS.0 7 a_1 a_2)) False) % 75.22/75.40 (Or (Eq (in a (setminus (skS.0 6 a_1) (setminus (skS.0 6 a_1) (skS.0 7 a_1 a_2)))) True) (Eq False True))) % 75.22/75.40 Clause #114 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (in (setminus (skS.0 6 a) (skS.0 7 a a_1)) (powerset (skS.0 6 a))) True % 75.22/75.40 Clause #115 (by superposition #[114, 49]): ∀ (a a_1 : Iota), % 75.22/75.40 Or (Eq True False) (Eq (in (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1))) (powerset (skS.0 6 a))) True) % 75.22/75.40 Clause #120 (by forward demodulation #[52, 53]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq True False) % 75.22/75.40 (Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a_2) False)))) % 75.22/75.40 Clause #121 (by clausification #[120]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a_2) False))) % 75.22/75.40 Clause #122 (by superposition #[121, 76]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 75.22/75.40 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 75.22/75.40 (Or (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) a) False) (Eq False True))) % 75.22/75.40 Clause #135 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a_1) True))) % 75.22/75.40 Clause #136 (by superposition #[135, 76]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 75.22/75.40 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 75.22/75.40 (Or (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 6 a_1)) True) (Eq False True))) % 75.22/75.40 Clause #138 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset a_1)) False) % 75.22/75.40 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 0 a_1 a a_2 a_3) a) True))) % 75.22/75.40 Clause #139 (by superposition #[138, 76]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 75.22/75.40 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 75.22/75.40 (Or (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 7 a_1 a_2)) True) (Eq False True))) % 75.22/75.40 Clause #141 (by clausification #[115]): ∀ (a a_1 : Iota), Eq (in (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1))) (powerset (skS.0 6 a))) True % 75.22/75.40 Clause #163 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 75.22/75.40 Or (Eq (in a (skS.0 6 a_1)) False) % 75.22/75.40 (Or (Eq (in a (skS.0 7 a_1 a_2)) False) % 75.22/75.40 (Eq (in a (setminus (skS.0 6 a_1) (setminus (skS.0 6 a_1) (skS.0 7 a_1 a_2)))) True)) % 75.22/75.40 Clause #185 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 75.22/75.40 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) a) False)) % 75.22/75.40 Clause #188 (by superposition #[185, 141]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.40 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Or % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) % 75.22/75.43 False) % 75.22/75.43 (Eq False True)) % 75.22/75.43 Clause #203 (by clausification #[136]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 75.22/75.43 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 75.22/75.43 (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 6 a_1)) True)) % 75.22/75.43 Clause #206 (by superposition #[203, 141]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Or % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (skS.0 6 a)) % 75.22/75.43 True) % 75.22/75.43 (Eq False True)) % 75.22/75.43 Clause #224 (by clausification #[139]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 75.22/75.43 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 75.22/75.43 (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 7 a_1 a_2)) True)) % 75.22/75.43 Clause #227 (by superposition #[224, 141]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Or % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (skS.0 7 a a_1)) % 75.22/75.43 True) % 75.22/75.43 (Eq False True)) % 75.22/75.43 Clause #446 (by clausification #[206]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (skS.0 6 a)) % 75.22/75.43 True) % 75.22/75.43 Clause #447 (by superposition #[446, 163]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Or (Eq True False) % 75.22/75.43 (Or % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (skS.0 7 a a_4)) % 75.22/75.43 False) % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_4)))) % 75.22/75.43 True))) % 75.22/75.43 Clause #536 (by clausification #[227]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (skS.0 7 a a_1)) % 75.22/75.43 True) % 75.22/75.43 Clause #714 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) % 75.22/75.43 False) % 75.22/75.43 Clause #2114 (by clausification #[447]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Or % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (skS.0 7 a a_4)) % 75.22/75.43 False) % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_4)))) % 75.22/75.43 True)) % 75.22/75.43 Clause #2115 (by superposition #[2114, 536]): ∀ (a a_1 a_2 a_3 : Iota), % 75.22/75.43 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.22/75.43 (Or % 75.22/75.43 (Eq % 75.22/75.43 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.22/75.43 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 75.31/75.47 True) % 75.31/75.47 (Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.31/75.47 (Eq False True))) % 75.31/75.47 Clause #2116 (by clausification #[2115]): ∀ (a a_1 a_2 a_3 : Iota), % 75.31/75.47 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.31/75.47 (Or % 75.31/75.47 (Eq % 75.31/75.47 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.31/75.47 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 75.31/75.47 True) % 75.31/75.47 (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True)) % 75.31/75.47 Clause #2117 (by eliminate duplicate literals #[2116]): ∀ (a a_1 a_2 a_3 : Iota), % 75.31/75.47 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2)))) True) % 75.31/75.47 (Eq % 75.31/75.47 (in (skS.0 0 (skS.0 6 a) (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_2))) a_3) % 75.31/75.47 (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 75.31/75.47 True) % 75.31/75.47 Clause #2118 (by superposition #[2117, 714]): ∀ (a a_1 : Iota), % 75.31/75.47 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) True) % 75.31/75.47 (Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) True) % 75.31/75.47 (Eq True False)) % 75.31/75.47 Clause #2119 (by clausification #[2118]): ∀ (a a_1 : Iota), % 75.31/75.47 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) True) % 75.31/75.47 (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) True) % 75.31/75.47 Clause #2120 (by eliminate duplicate literals #[2119]): ∀ (a a_1 : Iota), Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) True % 75.31/75.47 Clause #2121 (by superposition #[2120, 77]): Eq True False % 75.31/75.47 Clause #2122 (by clausification #[2121]): False % 75.31/75.47 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------