%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET603+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:00:14 PM UTC 2025 % Result : Theorem 32.73s 32.98s % Output : Proof 32.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : SET603+3 : TPTP v9.2.0. Released v2.2.0. % 0.06/0.11 % Command : duper %s % 0.10/0.32 % Computer : n020.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % 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 : Thu Oct 2 13:31:23 EDT 2025 % 0.10/0.32 % CPUTime : % 32.73/32.98 SZS status Theorem for theBenchmark.p % 32.73/32.98 SZS output start Proof for theBenchmark.p % 32.73/32.98 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True % 32.73/32.98 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 32.73/32.98 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True % 32.73/32.98 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 32.73/32.98 Clause #8 (by assumption #[]): Eq (Not (∀ (B : Iota), Eq (difference B empty_set) B)) True % 32.73/32.98 Clause #10 (by clausification #[2]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 32.73/32.98 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (member a empty_set) False % 32.73/32.98 Clause #20 (by clausification #[8]): Eq (∀ (B : Iota), Eq (difference B empty_set) B) False % 32.73/32.98 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (Not (Eq (difference (skS.0 1 a) empty_set) (skS.0 1 a))) True % 32.73/32.98 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq (Eq (difference (skS.0 1 a) empty_set) (skS.0 1 a)) False % 32.73/32.98 Clause #23 (by clausification #[22]): ∀ (a : Iota), Ne (difference (skS.0 1 a) empty_set) (skS.0 1 a) % 32.73/32.98 Clause #31 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True % 32.73/32.98 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True % 32.73/32.98 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (difference a_1 a_2)) (And (member a a_1) (Not (member a a_2)))) True % 32.73/32.98 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) True) (Eq (And (member a a_1) (Not (member a a_2))) False) % 32.73/32.98 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (And (member a a_1) (Not (member a a_2))) True) % 32.73/32.98 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 32.73/32.98 Or (Eq (member a (difference a_1 a_2)) True) (Or (Eq (member a a_1) False) (Eq (Not (member a a_2)) False)) % 32.73/32.98 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 32.73/32.98 Or (Eq (member a (difference a_1 a_2)) True) (Or (Eq (member a a_1) False) (Eq (member a a_2) True)) % 32.73/32.98 Clause #43 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 32.73/32.98 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 32.73/32.98 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 32.73/32.98 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 32.73/32.98 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) % 32.73/32.98 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 32.73/32.98 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) % 32.73/32.98 Clause #49 (by clausification #[48]): ∀ (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) % 32.73/32.98 Clause #50 (by clausification #[48]): ∀ (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) % 32.73/32.98 Clause #52 (by superposition #[49, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 32.73/32.98 Or (Eq (subset a a_1) True) % 32.73/32.98 (Or (Eq (member (skS.0 3 a a_1 a_2) (difference a a_3)) True) % 32.73/32.98 (Or (Eq True False) (Eq (member (skS.0 3 a a_1 a_2) a_3) True))) % 32.73/32.98 Clause #54 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True % 32.73/32.98 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 32.73/32.98 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 32.73/32.98 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 32.73/32.98 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 32.84/33.09 Clause #120 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_1) True) % 32.84/33.09 Clause #129 (by superposition #[120, 49]): ∀ (a a_1 a_2 a_3 : Iota), % 32.84/33.09 Or (Eq (member (skS.0 3 (difference a a_1) a_2 a_3) a) True) % 32.84/33.09 (Or (Eq (subset (difference a a_1) a_2) True) (Eq False True)) % 32.84/33.09 Clause #191 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), % 32.84/33.09 Or (Eq (subset a a_1) True) % 32.84/33.09 (Or (Eq (member (skS.0 3 a a_1 a_2) (difference a a_3)) True) (Eq (member (skS.0 3 a a_1 a_2) a_3) True)) % 32.84/33.09 Clause #194 (by superposition #[191, 50]): ∀ (a a_1 a_2 : Iota), % 32.84/33.09 Or (Eq (subset a (difference a a_1)) True) % 32.84/33.09 (Or (Eq (member (skS.0 3 a (difference a a_1) a_2) a_1) True) % 32.84/33.09 (Or (Eq (subset a (difference a a_1)) True) (Eq True False))) % 32.84/33.09 Clause #3315 (by clausification #[129]): ∀ (a a_1 a_2 a_3 : Iota), % 32.84/33.09 Or (Eq (member (skS.0 3 (difference a a_1) a_2 a_3) a) True) (Eq (subset (difference a a_1) a_2) True) % 32.84/33.09 Clause #3318 (by superposition #[3315, 50]): ∀ (a a_1 : Iota), % 32.84/33.09 Or (Eq (subset (difference a a_1) a) True) (Or (Eq (subset (difference a a_1) a) True) (Eq True False)) % 32.84/33.09 Clause #3364 (by clausification #[3318]): ∀ (a a_1 : Iota), Or (Eq (subset (difference a a_1) a) True) (Eq (subset (difference a a_1) a) True) % 32.84/33.09 Clause #3365 (by eliminate duplicate literals #[3364]): ∀ (a a_1 : Iota), Eq (subset (difference a a_1) a) True % 32.84/33.09 Clause #3366 (by superposition #[3365, 59]): ∀ (a a_1 : Iota), Or (Eq (difference a a_1) a) (Or (Eq True False) (Eq (subset a (difference a a_1)) False)) % 32.84/33.09 Clause #3395 (by clausification #[3366]): ∀ (a a_1 : Iota), Or (Eq (difference a a_1) a) (Eq (subset a (difference a a_1)) False) % 32.84/33.09 Clause #11625 (by clausification #[194]): ∀ (a a_1 a_2 : Iota), % 32.84/33.09 Or (Eq (subset a (difference a a_1)) True) % 32.84/33.09 (Or (Eq (member (skS.0 3 a (difference a a_1) a_2) a_1) True) (Eq (subset a (difference a a_1)) True)) % 32.84/33.09 Clause #11626 (by eliminate duplicate literals #[11625]): ∀ (a a_1 a_2 : Iota), % 32.84/33.09 Or (Eq (subset a (difference a a_1)) True) (Eq (member (skS.0 3 a (difference a a_1) a_2) a_1) True) % 32.84/33.09 Clause #11627 (by superposition #[11626, 11]): ∀ (a : Iota), Or (Eq (subset a (difference a empty_set)) True) (Eq True False) % 32.84/33.09 Clause #11708 (by clausification #[11627]): ∀ (a : Iota), Eq (subset a (difference a empty_set)) True % 32.84/33.09 Clause #11709 (by superposition #[11708, 3395]): ∀ (a : Iota), Or (Eq (difference a empty_set) a) (Eq True False) % 32.84/33.09 Clause #11768 (by clausification #[11709]): ∀ (a : Iota), Eq (difference a empty_set) a % 32.84/33.09 Clause #11774 (by backward contextual literal cutting #[11768, 23]): False % 32.84/33.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------