%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU121+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:00:54 PM UTC 2025 % Result : Theorem 5.33s 5.48s % Output : Proof 5.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : SEU121+1 : TPTP v9.2.0. Released v3.3.0. % 0.02/0.12 % Command : duper %s % 0.10/0.31 % Computer : n015.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Fri Oct 3 06:37:53 EDT 2025 % 0.10/0.32 % CPUTime : % 5.33/5.48 SZS status Theorem for theBenchmark.p % 5.33/5.48 SZS output start Proof for theBenchmark.p % 5.33/5.48 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 5.33/5.48 Clause #7 (by assumption #[]): Eq (Not (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C)) True % 5.33/5.48 Clause #27 (by clausification #[7]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) False % 5.33/5.48 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), And (subset (skS.0 2 a) B) (subset B C) → subset (skS.0 2 a) C)) True % 5.33/5.48 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset (skS.0 2 a) B) (subset B C) → subset (skS.0 2 a) C) False % 5.33/5.48 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 5.33/5.48 Eq (Not (∀ (C : Iota), And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 3 a a_1) C) → subset (skS.0 2 a) C)) % 5.33/5.48 True % 5.33/5.48 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 5.33/5.48 Eq (∀ (C : Iota), And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 3 a a_1) C) → subset (skS.0 2 a) C) False % 5.33/5.48 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 5.33/5.48 Eq % 5.33/5.48 (Not % 5.33/5.48 (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) → % 5.33/5.48 subset (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 5.33/5.48 True % 5.33/5.48 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 5.33/5.48 Eq % 5.33/5.48 (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) → % 5.33/5.48 subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 5.33/5.48 False % 5.33/5.48 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True % 5.33/5.48 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) False % 5.33/5.48 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True % 5.33/5.48 Clause #37 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True % 5.33/5.48 Clause #43 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 5.33/5.48 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 5.33/5.48 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 5.33/5.48 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 5.33/5.48 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 5.33/5.48 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1)) True) % 5.33/5.48 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1) False) % 5.33/5.48 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a) True) % 5.33/5.48 Clause #50 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a_1) False) % 5.33/5.48 Clause #56 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 5.33/5.48 Clause #57 (by clausification #[56]): ∀ (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)) % 5.33/5.48 Clause #58 (by superposition #[57, 36]): ∀ (a a_1 a_2 a_3 : Iota), % 5.33/5.48 Or (Eq (in a (skS.0 3 a_1 a_2)) False) (Or (Eq (in a (skS.0 4 a_1 a_2 a_3)) True) (Eq False True)) % 5.33/5.48 Clause #71 (by superposition #[37, 57]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Or (Eq (in a (skS.0 3 a_1 a_2)) True) (Eq False True)) % 5.33/5.48 Clause #78 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq (in a (skS.0 3 a_1 a_2)) True) % 5.33/5.48 Clause #79 (by superposition #[78, 49]): ∀ (a a_1 a_2 a_3 : Iota), % 5.33/5.48 Or (Eq (in (skS.0 5 (skS.0 2 a) a_1 a_2) (skS.0 3 a a_3)) True) % 5.33/5.48 (Or (Eq (subset (skS.0 2 a) a_1) True) (Eq False True)) % 5.33/5.48 Clause #80 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 3 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1 a_2 a_3)) True) % 5.35/5.50 Clause #82 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 5.35/5.50 Or (Eq (in (skS.0 5 (skS.0 2 a) a_1 a_2) (skS.0 3 a a_3)) True) (Eq (subset (skS.0 2 a) a_1) True) % 5.35/5.50 Clause #83 (by superposition #[82, 80]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.50 Or (Eq (subset (skS.0 2 a) a_1) True) % 5.35/5.50 (Or (Eq True False) (Eq (in (skS.0 5 (skS.0 2 a) a_1 a_2) (skS.0 4 a a_3 a_4)) True)) % 5.35/5.50 Clause #95 (by clausification #[83]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.50 Or (Eq (subset (skS.0 2 a) a_1) True) (Eq (in (skS.0 5 (skS.0 2 a) a_1 a_2) (skS.0 4 a a_3 a_4)) True) % 5.35/5.50 Clause #96 (by superposition #[95, 50]): ∀ (a a_1 a_2 : Iota), % 5.35/5.50 Or (Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 5.35/5.50 (Or (Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq True False)) % 5.35/5.50 Clause #102 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 5.35/5.50 Or (Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 5.35/5.50 Clause #103 (by eliminate duplicate literals #[102]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 5.35/5.50 Clause #104 (by superposition #[103, 35]): Eq True False % 5.35/5.50 Clause #106 (by clausification #[104]): False % 5.35/5.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------