%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU717^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 7.12s 7.36s % Output : Proof 7.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU717^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n022.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 04:53:38 EDT 2025 % 0.13/0.35 % CPUTime : % 7.12/7.36 SZS status Theorem for theBenchmark.p % 7.12/7.36 SZS output start Proof for theBenchmark.p % 7.12/7.36 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True % 7.12/7.36 Clause #1 (by assumption #[]): Eq % 7.12/7.36 (Eq subsetTI % 7.12/7.36 (∀ (A X : Iota), % 7.12/7.36 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)) % 7.12/7.36 True % 7.12/7.36 Clause #2 (by assumption #[]): Eq % 7.12/7.36 (Not % 7.12/7.36 (powersetI1 → % 7.12/7.36 subsetTI → % 7.12/7.36 ∀ (A X : Iota), % 7.12/7.36 in X (powerset A) → % 7.12/7.36 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y))) % 7.12/7.36 True % 7.12/7.36 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A)) % 7.12/7.36 Clause #16 (by clausification #[1]): Eq subsetTI % 7.12/7.36 (∀ (A X : Iota), % 7.12/7.36 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 7.12/7.36 Clause #18 (by clausify Prop equality #[16]): Or (Eq subsetTI False) % 7.12/7.36 (Eq % 7.12/7.36 (∀ (A X : Iota), % 7.12/7.36 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y) % 7.12/7.36 True) % 7.12/7.36 Clause #20 (by clausification #[2]): Eq % 7.12/7.36 (powersetI1 → % 7.12/7.36 subsetTI → % 7.12/7.36 ∀ (A X : Iota), % 7.12/7.36 in X (powerset A) → % 7.12/7.36 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y)) % 7.12/7.36 False % 7.12/7.36 Clause #21 (by clausification #[20]): Eq powersetI1 True % 7.12/7.36 Clause #22 (by clausification #[20]): Eq % 7.12/7.36 (subsetTI → % 7.12/7.36 ∀ (A X : Iota), % 7.12/7.36 in X (powerset A) → % 7.12/7.36 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y)) % 7.12/7.36 False % 7.12/7.36 Clause #23 (by backward demodulation #[21, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A)) % 7.12/7.36 Clause #26 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True % 7.12/7.36 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True % 7.12/7.36 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True) % 7.12/7.36 Clause #35 (by clausification #[18]): ∀ (a : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Eq % 7.12/7.36 (∀ (X : Iota), % 7.12/7.36 in X (powerset a) → ∀ (Y : Iota), in Y (powerset a) → (∀ (Xx : Iota), in Xx a → in Xx X → in Xx Y) → subset X Y) % 7.12/7.36 True) % 7.12/7.36 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Eq % 7.12/7.36 (in a (powerset a_1) → % 7.12/7.36 ∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) % 7.12/7.36 True) % 7.12/7.36 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Or (Eq (in a (powerset a_1)) False) % 7.12/7.36 (Eq (∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) True)) % 7.12/7.36 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Or (Eq (in a (powerset a_1)) False) % 7.12/7.36 (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)) % 7.12/7.36 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Or (Eq (in a (powerset a_1)) False) % 7.12/7.36 (Or (Eq (in a_2 (powerset a_1)) False) % 7.12/7.36 (Eq ((∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) → subset a a_2) True))) % 7.12/7.36 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Or (Eq (in a (powerset a_1)) False) % 7.12/7.36 (Or (Eq (in a_2 (powerset a_1)) False) % 7.12/7.36 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) False) (Eq (subset a a_2) True)))) % 7.12/7.36 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 7.12/7.36 Or (Eq subsetTI False) % 7.12/7.36 (Or (Eq (in a (powerset a_1)) False) % 7.12/7.36 (Or (Eq (in a_2 (powerset a_1)) False) % 7.12/7.36 (Or (Eq (subset a a_2) True) % 7.12/7.36 (Eq (Not (in (skS.0 4 a_1 a a_2 a_3) a_1 → in (skS.0 4 a_1 a a_2 a_3) a → in (skS.0 4 a_1 a a_2 a_3) a_2)) % 7.21/7.39 True)))) % 7.21/7.39 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 7.21/7.39 Or (Eq subsetTI False) % 7.21/7.39 (Or (Eq (in a (powerset a_1)) False) % 7.21/7.39 (Or (Eq (in a_2 (powerset a_1)) False) % 7.21/7.39 (Or (Eq (subset a a_2) True) % 7.21/7.39 (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1 → in (skS.0 4 a_1 a a_2 a_3) a → in (skS.0 4 a_1 a a_2 a_3) a_2) False)))) % 7.21/7.39 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 7.21/7.39 Or (Eq subsetTI False) % 7.21/7.39 (Or (Eq (in a (powerset a_1)) False) % 7.21/7.39 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1) True)))) % 7.21/7.39 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 7.21/7.39 Or (Eq subsetTI False) % 7.21/7.39 (Or (Eq (in a (powerset a_1)) False) % 7.21/7.39 (Or (Eq (in a_2 (powerset a_1)) False) % 7.21/7.39 (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a → in (skS.0 4 a_1 a a_2 a_3) a_2) False)))) % 7.21/7.39 Clause #45 (by clausification #[22]): Eq subsetTI True % 7.21/7.39 Clause #46 (by clausification #[22]): Eq % 7.21/7.39 (∀ (A X : Iota), % 7.21/7.39 in X (powerset A) → % 7.21/7.39 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y)) % 7.21/7.39 False % 7.21/7.39 Clause #49 (by backward demodulation #[45, 43]): ∀ (a a_1 a_2 a_3 : Iota), % 7.21/7.39 Or (Eq True False) % 7.21/7.39 (Or (Eq (in a (powerset a_1)) False) % 7.21/7.39 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1) True)))) % 7.21/7.39 Clause #61 (by clausification #[46]): ∀ (a : Iota), % 7.21/7.39 Eq % 7.21/7.39 (Not % 7.21/7.39 (∀ (X : Iota), % 7.21/7.39 in X (powerset (skS.0 6 a)) → % 7.21/7.39 ∀ (Y : Iota), % 7.21/7.39 in Y (powerset (skS.0 6 a)) → (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx X → in Xx Y) → in X (powerset Y))) % 7.21/7.39 True % 7.21/7.39 Clause #62 (by clausification #[61]): ∀ (a : Iota), % 7.21/7.39 Eq % 7.21/7.39 (∀ (X : Iota), % 7.21/7.39 in X (powerset (skS.0 6 a)) → % 7.21/7.39 ∀ (Y : Iota), % 7.21/7.39 in Y (powerset (skS.0 6 a)) → (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx X → in Xx Y) → in X (powerset Y)) % 7.21/7.39 False % 7.21/7.39 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 7.21/7.39 Eq % 7.21/7.39 (Not % 7.21/7.39 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 7.21/7.39 ∀ (Y : Iota), % 7.21/7.39 in Y (powerset (skS.0 6 a)) → % 7.21/7.39 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx Y) → in (skS.0 7 a a_1) (powerset Y))) % 7.21/7.39 True % 7.21/7.39 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 7.21/7.39 Eq % 7.21/7.39 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 7.21/7.39 ∀ (Y : Iota), % 7.21/7.39 in Y (powerset (skS.0 6 a)) → % 7.21/7.39 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx Y) → in (skS.0 7 a a_1) (powerset Y)) % 7.21/7.39 False % 7.21/7.39 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 6 a))) True % 7.21/7.39 Clause #66 (by clausification #[64]): ∀ (a a_1 : Iota), % 7.21/7.39 Eq % 7.21/7.39 (∀ (Y : Iota), % 7.21/7.39 in Y (powerset (skS.0 6 a)) → % 7.21/7.39 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx Y) → in (skS.0 7 a a_1) (powerset Y)) % 7.21/7.39 False % 7.21/7.39 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 7.21/7.39 Eq % 7.21/7.39 (Not % 7.21/7.39 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 7.21/7.39 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) → % 7.21/7.39 in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2)))) % 7.21/7.39 True % 7.21/7.39 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 7.21/7.39 Eq % 7.21/7.39 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 7.21/7.39 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) → % 7.21/7.39 in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) % 7.21/7.39 False % 7.21/7.39 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a))) True % 7.21/7.39 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 7.21/7.39 Eq % 7.21/7.39 ((∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) → % 7.21/7.39 in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) % 7.21/7.39 False % 7.21/7.39 Clause #78 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) True % 7.24/7.42 Clause #79 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) False % 7.24/7.42 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in a (skS.0 6 a_1) → in a (skS.0 7 a_1 a_2) → in a (skS.0 8 a_1 a_2 a_3)) True % 7.24/7.42 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (skS.0 6 a_1)) False) (Eq (in a (skS.0 7 a_1 a_2) → in a (skS.0 8 a_1 a_2 a_3)) True) % 7.24/7.42 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (skS.0 6 a_1)) False) (Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 8 a_1 a_2 a_3)) True)) % 7.24/7.42 Clause #90 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq subsetTI False) % 7.24/7.42 (Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a) True)))) % 7.24/7.42 Clause #91 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq subsetTI False) % 7.24/7.42 (Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_2) False)))) % 7.24/7.42 Clause #92 (by forward demodulation #[90, 45]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq True False) % 7.24/7.42 (Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a) True)))) % 7.24/7.42 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a) True))) % 7.24/7.42 Clause #94 (by superposition #[93, 65]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 7.24/7.42 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 7.24/7.42 (Or (Eq (in (skS.0 4 (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))) % 7.24/7.42 Clause #102 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1) True))) % 7.24/7.42 Clause #103 (by superposition #[102, 65]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 7.24/7.42 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 7.24/7.42 (Or (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 6 a_1)) True) (Eq False True))) % 7.24/7.42 Clause #105 (by forward demodulation #[91, 45]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq True False) % 7.24/7.42 (Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_2) False)))) % 7.24/7.42 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset a_1)) False) % 7.24/7.42 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_2) False))) % 7.24/7.42 Clause #107 (by superposition #[106, 65]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 7.24/7.42 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 7.24/7.42 (Or (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) a) False) (Eq False True))) % 7.24/7.42 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 7.24/7.42 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) a) False)) % 7.24/7.42 Clause #111 (by superposition #[109, 70]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.24/7.42 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.24/7.42 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_2 a_3)) False) % 7.24/7.42 (Eq False True)) % 7.24/7.42 Clause #124 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 7.24/7.42 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 7.24/7.42 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 7.24/7.42 (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 6 a_1)) True)) % 7.24/7.42 Clause #126 (by superposition #[124, 70]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.24/7.42 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.24/7.42 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 6 a)) True) (Eq False True)) % 7.27/7.44 Clause #127 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 7.27/7.44 Or (Eq (in a (powerset (skS.0 6 a_1))) False) % 7.27/7.44 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 7 a_1 a_2)) True)) % 7.27/7.44 Clause #129 (by superposition #[127, 70]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_1)) True) (Eq False True)) % 7.27/7.44 Clause #171 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_2 a_3)) False) % 7.27/7.44 Clause #184 (by clausification #[126]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 6 a)) True) % 7.27/7.44 Clause #185 (by superposition #[184, 82]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Or (Eq True False) % 7.27/7.44 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_5)) False) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_5 a_6)) True))) % 7.27/7.44 Clause #189 (by clausification #[129]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_1)) True) % 7.27/7.44 Clause #237 (by clausification #[185]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_5)) False) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_5 a_6)) True)) % 7.27/7.44 Clause #238 (by superposition #[237, 189]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_1 a_5)) True) % 7.27/7.44 (Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) (Eq False True))) % 7.27/7.44 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_1 a_5)) True) % 7.27/7.44 (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)) % 7.27/7.44 Clause #240 (by eliminate duplicate literals #[239]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) % 7.27/7.44 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_1 a_5)) True) % 7.27/7.44 Clause #241 (by superposition #[240, 171]): ∀ (a a_1 a_2 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True) % 7.27/7.44 (Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True) (Eq True False)) % 7.27/7.44 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 : Iota), % 7.27/7.44 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True) (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True) % 7.27/7.44 Clause #243 (by eliminate duplicate literals #[242]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True % 7.27/7.44 Clause #244 (by superposition #[243, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) True) % 7.27/7.44 Clause #245 (by clausification #[244]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) True % 7.27/7.44 Clause #246 (by superposition #[245, 79]): Eq True False % 7.27/7.44 Clause #257 (by clausification #[246]): False % 7.27/7.44 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------