%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET027+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 07:59:25 PM UTC 2025 % Result : Theorem 3.58s 3.77s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET027+3 : TPTP v9.2.0. Released v2.2.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n011.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 : Thu Oct 2 14:48:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.58/3.77 SZS status Theorem for theBenchmark.p % 3.58/3.77 SZS output start Proof for theBenchmark.p % 3.58/3.77 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 3.58/3.77 Clause #2 (by assumption #[]): Eq (Not (∀ (B C D : Iota), And (subset B C) (subset C D) → subset B D)) True % 3.58/3.77 Clause #4 (by clausification #[2]): Eq (∀ (B C D : Iota), And (subset B C) (subset C D) → subset B D) False % 3.58/3.77 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (C D : Iota), And (subset (skS.0 0 a) C) (subset C D) → subset (skS.0 0 a) D)) True % 3.58/3.77 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (subset (skS.0 0 a) C) (subset C D) → subset (skS.0 0 a) D) False % 3.58/3.77 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.58/3.77 Eq (Not (∀ (D : Iota), And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) D) → subset (skS.0 0 a) D)) % 3.58/3.77 True % 3.58/3.77 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 3.58/3.77 Eq (∀ (D : Iota), And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) D) → subset (skS.0 0 a) D) False % 3.58/3.77 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (Not % 3.58/3.77 (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.58/3.77 subset (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 3.58/3.77 True % 3.58/3.77 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.58/3.77 subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 3.58/3.77 False % 3.58/3.77 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 3.58/3.77 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 3.58/3.77 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 3.58/3.77 Clause #14 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 3.58/3.77 Clause #15 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 3.58/3.77 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 3.58/3.77 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 3.58/3.77 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (D : Iota), member D a → member D a_1) True) % 3.58/3.77 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 3 a a_1 a_2) a → member (skS.0 3 a a_1 a_2) a_1)) True) % 3.58/3.77 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a → member (skS.0 3 a a_1 a_2) a_1) False) % 3.58/3.77 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a) True) % 3.58/3.77 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a_1) False) % 3.58/3.77 Clause #23 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (member a_2 a → member a_2 a_1) True) % 3.58/3.77 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) True)) % 3.58/3.77 Clause #25 (by superposition #[24, 13]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.77 Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Or (Eq (member a (skS.0 2 a_1 a_2 a_3)) True) (Eq False True)) % 3.58/3.77 Clause #28 (by superposition #[14, 24]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (skS.0 0 a_1)) False) (Or (Eq (member a (skS.0 1 a_1 a_2)) True) (Eq False True)) % 3.58/3.77 Clause #31 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (skS.0 0 a_1)) False) (Eq (member a (skS.0 1 a_1 a_2)) True) % 3.58/3.77 Clause #32 (by superposition #[31, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.77 Or (Eq (member (skS.0 3 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) % 3.58/3.77 (Or (Eq (subset (skS.0 0 a) a_1) True) (Eq False True)) % 3.58/3.77 Clause #33 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Eq (member a (skS.0 2 a_1 a_2 a_3)) True) % 3.58/3.77 Clause #35 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.77 Or (Eq (member (skS.0 3 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) (Eq (subset (skS.0 0 a) a_1) True) % 3.58/3.77 Clause #36 (by superposition #[35, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.58/3.77 Or (Eq (subset (skS.0 0 a) a_1) True) % 3.58/3.77 (Or (Eq True False) (Eq (member (skS.0 3 (skS.0 0 a) a_1 a_2) (skS.0 2 a a_3 a_4)) True)) % 3.58/3.77 Clause #39 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.58/3.77 Or (Eq (subset (skS.0 0 a) a_1) True) (Eq (member (skS.0 3 (skS.0 0 a) a_1 a_2) (skS.0 2 a a_3 a_4)) True) % 3.58/3.77 Clause #40 (by superposition #[39, 22]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Or (Eq (subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 3.58/3.77 (Or (Eq (subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False)) % 3.58/3.77 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Or (Eq (subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq (subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 3.58/3.77 Clause #42 (by eliminate duplicate literals #[41]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 3.58/3.77 Clause #43 (by superposition #[42, 12]): Eq True False % 3.58/3.77 Clause #45 (by clausification #[43]): False % 3.58/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------