%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU737^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:02:20 PM UTC 2025 % Result : Theorem 175.25s 175.49s % Output : Proof 175.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU737^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.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 06:08:53 EDT 2025 % 0.13/0.34 % CPUTime : % 175.25/175.49 SZS status Theorem for theBenchmark.p % 175.25/175.49 SZS output start Proof for theBenchmark.p % 175.25/175.49 Clause #0 (by assumption #[]): Eq (Eq complementT_lem (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A))) True % 175.25/175.49 Clause #1 (by assumption #[]): Eq % 175.25/175.49 (Eq subsetTI % 175.25/175.49 (∀ (A X : Iota), % 175.25/175.49 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)) % 175.25/175.49 True % 175.25/175.49 Clause #2 (by assumption #[]): Eq % 175.25/175.49 (Eq contraSubsetComplement % 175.25/175.49 (∀ (A X : Iota), % 175.25/175.49 in X (powerset A) → % 175.25/175.49 ∀ (Y : Iota), % 175.25/175.49 in Y (powerset A) → subset X (setminus A Y) → ∀ (Xx : Iota), in Xx A → in Xx Y → in Xx (setminus A X))) % 175.25/175.49 True % 175.25/175.49 Clause #3 (by assumption #[]): Eq % 175.25/175.49 (Not % 175.25/175.49 (complementT_lem → % 175.25/175.49 subsetTI → % 175.25/175.49 contraSubsetComplement → % 175.25/175.49 ∀ (A X : Iota), % 175.25/175.49 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset X (setminus A Y) → subset Y (setminus A X))) % 175.25/175.49 True % 175.25/175.49 Clause #4 (by clausification #[1]): Eq subsetTI % 175.25/175.49 (∀ (A X : Iota), % 175.25/175.49 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 175.25/175.49 Clause #6 (by clausify Prop equality #[4]): Or (Eq subsetTI False) % 175.25/175.49 (Eq % 175.25/175.49 (∀ (A X : Iota), % 175.25/175.49 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 175.25/175.49 True) % 175.25/175.49 Clause #8 (by clausification #[6]): ∀ (a : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Eq % 175.25/175.49 (∀ (X : Iota), % 175.25/175.49 in X (powerset a) → ∀ (Y : Iota), in Y (powerset a) → (∀ (Xx : Iota), in Xx a → in Xx X → in Xx Y) → subset X Y) % 175.25/175.49 True) % 175.25/175.49 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Eq % 175.25/175.49 (in a (powerset a_1) → % 175.25/175.49 ∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) % 175.25/175.49 True) % 175.25/175.49 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (Eq (∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) True)) % 175.25/175.49 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (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)) % 175.25/175.49 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (Or (Eq (in a_2 (powerset a_1)) False) % 175.25/175.49 (Eq ((∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) → subset a a_2) True))) % 175.25/175.49 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (Or (Eq (in a_2 (powerset a_1)) False) % 175.25/175.49 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) False) (Eq (subset a a_2) True)))) % 175.25/175.49 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (Or (Eq (in a_2 (powerset a_1)) False) % 175.25/175.49 (Or (Eq (subset a a_2) True) % 175.25/175.49 (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)) % 175.25/175.49 True)))) % 175.25/175.49 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (Or (Eq (in a_2 (powerset a_1)) False) % 175.25/175.49 (Or (Eq (subset a a_2) True) % 175.25/175.49 (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)))) % 175.25/175.49 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (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)))) % 175.25/175.49 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.49 Or (Eq subsetTI False) % 175.25/175.49 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.49 (Or (Eq (in a_2 (powerset a_1)) False) % 175.25/175.49 (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)))) % 175.25/175.51 Clause #24 (by clausification #[0]): Eq complementT_lem (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) % 175.25/175.51 Clause #28 (by clausification #[2]): Eq contraSubsetComplement % 175.25/175.51 (∀ (A X : Iota), % 175.25/175.51 in X (powerset A) → % 175.25/175.51 ∀ (Y : Iota), % 175.25/175.51 in Y (powerset A) → subset X (setminus A Y) → ∀ (Xx : Iota), in Xx A → in Xx Y → in Xx (setminus A X)) % 175.25/175.51 Clause #41 (by clausification #[3]): Eq % 175.25/175.51 (complementT_lem → % 175.25/175.51 subsetTI → % 175.25/175.51 contraSubsetComplement → % 175.25/175.51 ∀ (A X : Iota), % 175.25/175.51 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset X (setminus A Y) → subset Y (setminus A X)) % 175.25/175.51 False % 175.25/175.51 Clause #42 (by clausification #[41]): Eq complementT_lem True % 175.25/175.51 Clause #43 (by clausification #[41]): Eq % 175.25/175.51 (subsetTI → % 175.25/175.51 contraSubsetComplement → % 175.25/175.51 ∀ (A X : Iota), % 175.25/175.51 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset X (setminus A Y) → subset Y (setminus A X)) % 175.25/175.51 False % 175.25/175.51 Clause #44 (by backward demodulation #[42, 24]): Eq True (∀ (A X : Iota), in X (powerset A) → in (setminus A X) (powerset A)) % 175.25/175.51 Clause #47 (by clausification #[44]): ∀ (a : Iota), Eq (∀ (X : Iota), in X (powerset a) → in (setminus a X) (powerset a)) True % 175.25/175.51 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (in a (powerset a_1) → in (setminus a_1 a) (powerset a_1)) True % 175.25/175.51 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) % 175.25/175.51 Clause #51 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.51 Or (Eq subsetTI False) % 175.25/175.51 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.51 (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)))) % 175.25/175.51 Clause #52 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.51 Or (Eq subsetTI False) % 175.25/175.51 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.51 (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)))) % 175.25/175.51 Clause #53 (by clausification #[43]): Eq subsetTI True % 175.25/175.51 Clause #54 (by clausification #[43]): Eq % 175.25/175.51 (contraSubsetComplement → % 175.25/175.51 ∀ (A X : Iota), % 175.25/175.51 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset X (setminus A Y) → subset Y (setminus A X)) % 175.25/175.51 False % 175.25/175.51 Clause #56 (by backward demodulation #[53, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.51 Or (Eq True False) % 175.25/175.51 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.51 (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)))) % 175.25/175.51 Clause #58 (by backward demodulation #[53, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 175.25/175.51 Or (Eq True False) % 175.25/175.51 (Or (Eq (in a (powerset a_1)) False) % 175.25/175.51 (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)))) % 175.25/175.51 Clause #69 (by clausification #[54]): Eq contraSubsetComplement True % 175.25/175.51 Clause #70 (by clausification #[54]): Eq % 175.25/175.51 (∀ (A X : Iota), % 175.25/175.51 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset X (setminus A Y) → subset Y (setminus A X)) % 175.25/175.51 False % 175.25/175.51 Clause #71 (by backward demodulation #[69, 28]): Eq True % 175.25/175.51 (∀ (A X : Iota), % 175.25/175.51 in X (powerset A) → % 175.25/175.51 ∀ (Y : Iota), % 175.25/175.51 in Y (powerset A) → subset X (setminus A Y) → ∀ (Xx : Iota), in Xx A → in Xx Y → in Xx (setminus A X)) % 175.25/175.51 Clause #72 (by clausification #[70]): ∀ (a : Iota), % 175.25/175.51 Eq % 175.25/175.51 (Not % 175.25/175.51 (∀ (X : Iota), % 175.25/175.51 in X (powerset (skS.0 6 a)) → % 175.25/175.51 ∀ (Y : Iota), % 175.25/175.51 in Y (powerset (skS.0 6 a)) → subset X (setminus (skS.0 6 a) Y) → subset Y (setminus (skS.0 6 a) X))) % 175.25/175.51 True % 175.25/175.51 Clause #73 (by clausification #[72]): ∀ (a : Iota), % 175.25/175.51 Eq % 175.25/175.51 (∀ (X : Iota), % 175.25/175.51 in X (powerset (skS.0 6 a)) → % 175.25/175.51 ∀ (Y : Iota), % 175.25/175.51 in Y (powerset (skS.0 6 a)) → subset X (setminus (skS.0 6 a) Y) → subset Y (setminus (skS.0 6 a) X)) % 175.25/175.51 False % 175.25/175.51 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 175.25/175.51 Eq % 175.25/175.51 (Not % 175.25/175.51 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 175.25/175.51 ∀ (Y : Iota), % 175.25/175.51 in Y (powerset (skS.0 6 a)) → % 175.35/175.54 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) Y) → subset Y (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 175.35/175.54 True % 175.35/175.54 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 175.35/175.54 Eq % 175.35/175.54 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 175.35/175.54 ∀ (Y : Iota), % 175.35/175.54 in Y (powerset (skS.0 6 a)) → % 175.35/175.54 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) Y) → subset Y (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.35/175.54 False % 175.35/175.54 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 6 a))) True % 175.35/175.54 Clause #77 (by clausification #[75]): ∀ (a a_1 : Iota), % 175.35/175.54 Eq % 175.35/175.54 (∀ (Y : Iota), % 175.35/175.54 in Y (powerset (skS.0 6 a)) → % 175.35/175.54 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) Y) → subset Y (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.35/175.54 False % 175.35/175.54 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) % 175.35/175.54 Clause #85 (by clausification #[71]): ∀ (a : Iota), % 175.35/175.54 Eq % 175.35/175.54 (∀ (X : Iota), % 175.35/175.54 in X (powerset a) → % 175.35/175.54 ∀ (Y : Iota), % 175.35/175.54 in Y (powerset a) → subset X (setminus a Y) → ∀ (Xx : Iota), in Xx a → in Xx Y → in Xx (setminus a X)) % 175.35/175.54 True % 175.35/175.54 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), % 175.35/175.54 Eq % 175.35/175.54 (in a (powerset a_1) → % 175.35/175.54 ∀ (Y : Iota), % 175.35/175.54 in Y (powerset a_1) → subset a (setminus a_1 Y) → ∀ (Xx : Iota), in Xx a_1 → in Xx Y → in Xx (setminus a_1 a)) % 175.35/175.54 True % 175.35/175.54 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Eq % 175.35/175.54 (∀ (Y : Iota), % 175.35/175.54 in Y (powerset a_1) → subset a (setminus a_1 Y) → ∀ (Xx : Iota), in Xx a_1 → in Xx Y → in Xx (setminus a_1 a)) % 175.35/175.54 True) % 175.35/175.54 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Eq % 175.35/175.54 (in a_2 (powerset a_1) → % 175.35/175.54 subset a (setminus a_1 a_2) → ∀ (Xx : Iota), in Xx a_1 → in Xx a_2 → in Xx (setminus a_1 a)) % 175.35/175.54 True) % 175.35/175.54 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Or (Eq (in a_2 (powerset a_1)) False) % 175.35/175.54 (Eq (subset a (setminus a_1 a_2) → ∀ (Xx : Iota), in Xx a_1 → in Xx a_2 → in Xx (setminus a_1 a)) True)) % 175.35/175.54 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Or (Eq (in a_2 (powerset a_1)) False) % 175.35/175.54 (Or (Eq (subset a (setminus a_1 a_2)) False) % 175.35/175.54 (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a_2 → in Xx (setminus a_1 a)) True))) % 175.35/175.54 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Or (Eq (in a_2 (powerset a_1)) False) % 175.35/175.54 (Or (Eq (subset a (setminus a_1 a_2)) False) (Eq (in a_3 a_1 → in a_3 a_2 → in a_3 (setminus a_1 a)) True))) % 175.35/175.54 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Or (Eq (in a_2 (powerset a_1)) False) % 175.35/175.54 (Or (Eq (subset a (setminus a_1 a_2)) False) % 175.35/175.54 (Or (Eq (in a_3 a_1) False) (Eq (in a_3 a_2 → in a_3 (setminus a_1 a)) True)))) % 175.35/175.54 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.54 Or (Eq (in a (powerset a_1)) False) % 175.35/175.54 (Or (Eq (in a_2 (powerset a_1)) False) % 175.35/175.54 (Or (Eq (subset a (setminus a_1 a_2)) False) % 175.35/175.54 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 a_2) False) (Eq (in a_3 (setminus a_1 a)) True))))) % 175.35/175.54 Clause #94 (by superposition #[93, 76]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.54 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.54 (Or (Eq (subset (skS.0 7 a_1 a_2) (setminus (skS.0 6 a_1) a)) False) % 175.35/175.54 (Or (Eq (in a_3 (skS.0 6 a_1)) False) % 175.35/175.54 (Or (Eq (in a_3 a) False) (Or (Eq (in a_3 (setminus (skS.0 6 a_1) (skS.0 7 a_1 a_2))) True) (Eq False True))))) % 175.35/175.54 Clause #113 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 175.35/175.54 Eq % 175.35/175.54 (Not % 175.35/175.54 (in (skS.0 11 a a_1 a_2) (powerset (skS.0 6 a)) → % 175.35/175.54 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 11 a a_1 a_2)) → % 175.35/175.54 subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1)))) % 175.35/175.54 True % 175.35/175.54 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), % 175.35/175.56 Eq % 175.35/175.56 (in (skS.0 11 a a_1 a_2) (powerset (skS.0 6 a)) → % 175.35/175.56 subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 11 a a_1 a_2)) → % 175.35/175.56 subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.35/175.56 False % 175.35/175.56 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 11 a a_1 a_2) (powerset (skS.0 6 a))) True % 175.35/175.56 Clause #116 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), % 175.35/175.56 Eq % 175.35/175.56 (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 11 a a_1 a_2)) → % 175.35/175.56 subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.35/175.56 False % 175.35/175.56 Clause #142 (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 % 175.35/175.56 Clause #146 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 11 a a_1 a_2))) True % 175.35/175.56 Clause #147 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) False % 175.35/175.56 Clause #148 (by forward demodulation #[52, 53]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.56 Or (Eq True False) % 175.35/175.56 (Or (Eq (in a (powerset a_1)) False) % 175.35/175.56 (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)))) % 175.35/175.56 Clause #149 (by clausification #[148]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.56 Or (Eq (in a (powerset a_1)) False) % 175.35/175.56 (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))) % 175.35/175.56 Clause #151 (by superposition #[149, 115]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.56 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.56 (Or (Eq (subset (skS.0 11 a_1 a_2 a_3) a) True) % 175.35/175.56 (Or (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 11 a_1 a_2 a_3) a a_4) a) False) (Eq False True))) % 175.35/175.56 Clause #168 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.56 Or (Eq (in a (powerset a_1)) False) % 175.35/175.56 (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))) % 175.35/175.56 Clause #170 (by superposition #[168, 115]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.56 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.56 (Or (Eq (subset (skS.0 11 a_1 a_2 a_3) a) True) % 175.35/175.56 (Or (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 11 a_1 a_2 a_3) a a_4) (skS.0 6 a_1)) True) (Eq False True))) % 175.35/175.56 Clause #173 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.56 Or (Eq (in a (powerset a_1)) False) % 175.35/175.56 (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))) % 175.35/175.56 Clause #175 (by superposition #[173, 115]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.56 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.56 (Or (Eq (subset (skS.0 11 a_1 a_2 a_3) a) True) % 175.35/175.56 (Or (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 11 a_1 a_2 a_3) a a_4) (skS.0 11 a_1 a_2 a_3)) True) (Eq False True))) % 175.35/175.56 Clause #217 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.56 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.56 (Or (Eq (subset (skS.0 7 a_1 a_2) (setminus (skS.0 6 a_1) a)) False) % 175.35/175.56 (Or (Eq (in a_3 (skS.0 6 a_1)) False) % 175.35/175.56 (Or (Eq (in a_3 a) False) (Eq (in a_3 (setminus (skS.0 6 a_1) (skS.0 7 a_1 a_2))) True)))) % 175.35/175.56 Clause #219 (by superposition #[217, 115]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.56 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 11 a a_2 a_3))) False) % 175.35/175.56 (Or (Eq (in a_4 (skS.0 6 a)) False) % 175.35/175.56 (Or (Eq (in a_4 (skS.0 11 a a_2 a_3)) False) % 175.35/175.56 (Or (Eq (in a_4 (setminus (skS.0 6 a) (skS.0 7 a a_1))) True) (Eq False True)))) % 175.35/175.56 Clause #302 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.56 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.56 (Or (Eq (subset (skS.0 11 a_1 a_2 a_3) a) True) % 175.35/175.56 (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 11 a_1 a_2 a_3) a a_4) a) False)) % 175.35/175.56 Clause #305 (by superposition #[302, 142]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.56 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.56 (Or % 175.35/175.56 (Eq % 175.35/175.56 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.35/175.56 (setminus (skS.0 6 a) (skS.0 7 a a_3))) % 175.35/175.56 False) % 175.35/175.56 (Eq False True)) % 175.35/175.56 Clause #397 (by clausification #[170]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.59 (Or (Eq (subset (skS.0 11 a_1 a_2 a_3) a) True) % 175.35/175.59 (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 11 a_1 a_2 a_3) a a_4) (skS.0 6 a_1)) True)) % 175.35/175.59 Clause #400 (by superposition #[397, 142]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Or (Eq (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) (skS.0 6 a)) True) % 175.35/175.59 (Eq False True)) % 175.35/175.59 Clause #493 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 175.35/175.59 (Or (Eq (subset (skS.0 11 a_1 a_2 a_3) a) True) % 175.35/175.59 (Eq (in (skS.0 0 (skS.0 6 a_1) (skS.0 11 a_1 a_2 a_3) a a_4) (skS.0 11 a_1 a_2 a_3)) True)) % 175.35/175.59 Clause #496 (by superposition #[493, 142]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Or % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) (skS.0 11 a a_1 a_2)) % 175.35/175.59 True) % 175.35/175.59 (Eq False True)) % 175.35/175.59 Clause #658 (by clausification #[219]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 7 a a_1) (setminus (skS.0 6 a) (skS.0 11 a a_2 a_3))) False) % 175.35/175.59 (Or (Eq (in a_4 (skS.0 6 a)) False) % 175.35/175.59 (Or (Eq (in a_4 (skS.0 11 a a_2 a_3)) False) (Eq (in a_4 (setminus (skS.0 6 a) (skS.0 7 a a_1))) True))) % 175.35/175.59 Clause #659 (by superposition #[658, 146]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.59 Or (Eq (in a (skS.0 6 a_1)) False) % 175.35/175.59 (Or (Eq (in a (skS.0 11 a_1 a_2 a_3)) False) % 175.35/175.59 (Or (Eq (in a (setminus (skS.0 6 a_1) (skS.0 7 a_1 a_2))) True) (Eq False True))) % 175.35/175.59 Clause #660 (by clausification #[659]): ∀ (a a_1 a_2 a_3 : Iota), % 175.35/175.59 Or (Eq (in a (skS.0 6 a_1)) False) % 175.35/175.59 (Or (Eq (in a (skS.0 11 a_1 a_2 a_3)) False) (Eq (in a (setminus (skS.0 6 a_1) (skS.0 7 a_1 a_2))) True)) % 175.35/175.59 Clause #844 (by clausification #[400]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Eq (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) (skS.0 6 a)) True) % 175.35/175.59 Clause #845 (by superposition #[844, 660]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Or (Eq True False) % 175.35/175.59 (Or % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.35/175.59 (skS.0 11 a a_5 a_6)) % 175.35/175.59 False) % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.35/175.59 (setminus (skS.0 6 a) (skS.0 7 a a_5))) % 175.35/175.59 True))) % 175.35/175.59 Clause #1019 (by clausification #[496]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Eq (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) (skS.0 11 a a_1 a_2)) % 175.35/175.59 True) % 175.35/175.59 Clause #1251 (by clausification #[305]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.35/175.59 (setminus (skS.0 6 a) (skS.0 7 a a_3))) % 175.35/175.59 False) % 175.35/175.59 Clause #4598 (by clausification #[845]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Or % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) (skS.0 11 a a_5 a_6)) % 175.35/175.59 False) % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.35/175.59 (setminus (skS.0 6 a) (skS.0 7 a a_5))) % 175.35/175.59 True)) % 175.35/175.59 Clause #4599 (by superposition #[4598, 1019]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.35/175.59 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.35/175.59 (Or % 175.35/175.59 (Eq % 175.35/175.59 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.42/175.65 (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.42/175.65 True) % 175.42/175.65 (Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) (Eq False True))) % 175.42/175.65 Clause #4600 (by clausification #[4599]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.42/175.65 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.42/175.65 (Or % 175.42/175.65 (Eq % 175.42/175.65 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.42/175.65 (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.42/175.65 True) % 175.42/175.65 (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True)) % 175.42/175.65 Clause #4601 (by eliminate duplicate literals #[4600]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 175.42/175.65 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3))) True) % 175.42/175.65 (Eq % 175.42/175.65 (in (skS.0 0 (skS.0 6 a) (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_3)) a_4) % 175.42/175.65 (setminus (skS.0 6 a) (skS.0 7 a a_1))) % 175.42/175.65 True) % 175.42/175.65 Clause #4602 (by superposition #[4601, 1251]): ∀ (a a_1 a_2 : Iota), % 175.42/175.65 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True) % 175.42/175.65 (Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True) (Eq True False)) % 175.42/175.65 Clause #4603 (by clausification #[4602]): ∀ (a a_1 a_2 : Iota), % 175.42/175.65 Or (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True) % 175.42/175.65 (Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True) % 175.42/175.65 Clause #4604 (by eliminate duplicate literals #[4603]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 11 a a_1 a_2) (setminus (skS.0 6 a) (skS.0 7 a a_1))) True % 175.42/175.65 Clause #4605 (by superposition #[4604, 147]): Eq True False % 175.42/175.65 Clause #4642 (by clausification #[4605]): False % 175.42/175.65 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------