%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU570^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:01:56 PM UTC 2025 % Result : Theorem 3.93s 4.14s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU570^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 04:48:38 EDT 2025 % 0.14/0.34 % CPUTime : % 3.93/4.14 SZS status Theorem for theBenchmark.p % 3.93/4.14 SZS output start Proof for theBenchmark.p % 3.93/4.14 Clause #0 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 3.93/4.14 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 3.93/4.14 Clause #2 (by assumption #[]): Eq (Not (subsetI2 → subsetE → ∀ (A B C : Iota), subset A B → subset B C → subset A C)) True % 3.93/4.14 Clause #3 (by clausification #[0]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.93/4.14 Clause #5 (by clausify Prop equality #[3]): Or (Eq subsetI2 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True) % 3.93/4.14 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq subsetI2 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True) % 3.93/4.14 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True) % 3.93/4.14 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True)) % 3.93/4.14 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.93/4.14 Or (Eq subsetI2 False) % 3.93/4.14 (Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True)) % 3.93/4.14 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 3.93/4.14 Or (Eq subsetI2 False) % 3.93/4.14 (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False)) % 3.93/4.14 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 3.93/4.14 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 3.93/4.14 Clause #22 (by clausification #[2]): Eq (subsetI2 → subsetE → ∀ (A B C : Iota), subset A B → subset B C → subset A C) False % 3.93/4.14 Clause #23 (by clausification #[22]): Eq subsetI2 True % 3.93/4.14 Clause #24 (by clausification #[22]): Eq (subsetE → ∀ (A B C : Iota), subset A B → subset B C → subset A C) False % 3.93/4.14 Clause #26 (by backward demodulation #[23, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 3.93/4.14 Clause #28 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.93/4.14 Clause #39 (by clausification #[24]): Eq subsetE True % 3.93/4.14 Clause #40 (by clausification #[24]): Eq (∀ (A B C : Iota), subset A B → subset B C → subset A C) False % 3.93/4.14 Clause #41 (by backward demodulation #[39, 28]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.93/4.14 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 3.93/4.14 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 3.93/4.14 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 3.93/4.14 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.93/4.14 Clause #46 (by clausification #[45]): ∀ (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)) % 3.93/4.14 Clause #47 (by clausification #[40]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), subset (skS.0 4 a) B → subset B C → subset (skS.0 4 a) C)) True % 3.93/4.14 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset (skS.0 4 a) B → subset B C → subset (skS.0 4 a) C) False % 3.93/4.14 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 3.93/4.14 Eq (Not (∀ (C : Iota), subset (skS.0 4 a) (skS.0 5 a a_1) → subset (skS.0 5 a a_1) C → subset (skS.0 4 a) C)) True % 3.93/4.14 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.93/4.14 Eq (∀ (C : Iota), subset (skS.0 4 a) (skS.0 5 a a_1) → subset (skS.0 5 a a_1) C → subset (skS.0 4 a) C) False % 3.93/4.14 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 3.93/4.14 Eq % 3.93/4.14 (Not % 3.93/4.14 (subset (skS.0 4 a) (skS.0 5 a a_1) → % 3.93/4.16 subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → subset (skS.0 4 a) (skS.0 6 a a_1 a_2))) % 3.93/4.16 True % 3.93/4.16 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 3.93/4.16 Eq % 3.93/4.16 (subset (skS.0 4 a) (skS.0 5 a a_1) → % 3.93/4.16 subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 3.93/4.16 False % 3.93/4.16 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (subset (skS.0 4 a) (skS.0 5 a a_1)) True % 3.93/4.16 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) False % 3.93/4.16 Clause #55 (by superposition #[53, 46]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 4 a_1)) False) (Eq (in a (skS.0 5 a_1 a_2)) True)) % 3.93/4.16 Clause #62 (by forward demodulation #[13, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 3.93/4.16 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False) % 3.93/4.16 Clause #79 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True) % 3.93/4.16 Clause #81 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True % 3.93/4.16 Clause #82 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) False % 3.93/4.16 Clause #83 (by superposition #[81, 46]): ∀ (a a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq True False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 6 a_1 a_2 a_3)) True)) % 3.93/4.16 Clause #84 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 4 a_1)) False) (Eq (in a (skS.0 5 a_1 a_2)) True) % 3.93/4.16 Clause #86 (by superposition #[84, 79]): ∀ (a a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 5 a a_3)) True) % 3.93/4.16 (Or (Eq (subset (skS.0 4 a) a_1) True) (Eq False True)) % 3.93/4.16 Clause #91 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 6 a_1 a_2 a_3)) True) % 3.93/4.16 Clause #94 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 5 a a_3)) True) (Eq (subset (skS.0 4 a) a_1) True) % 3.93/4.16 Clause #95 (by superposition #[94, 91]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.93/4.16 Or (Eq (subset (skS.0 4 a) a_1) True) % 3.93/4.16 (Or (Eq True False) (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 6 a a_3 a_4)) True)) % 3.93/4.16 Clause #100 (by clausification #[95]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.93/4.16 Or (Eq (subset (skS.0 4 a) a_1) True) (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 6 a a_3 a_4)) True) % 3.93/4.16 Clause #101 (by superposition #[100, 63]): ∀ (a a_1 a_2 : Iota), % 3.93/4.16 Or (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True) % 3.93/4.16 (Or (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True) (Eq True False)) % 3.93/4.16 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 3.93/4.16 Or (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True) (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True) % 3.93/4.16 Clause #103 (by eliminate duplicate literals #[102]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True % 3.93/4.16 Clause #104 (by superposition #[103, 82]): Eq True False % 3.93/4.16 Clause #106 (by clausification #[104]): False % 3.93/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------