%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET628+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:00:18 PM UTC 2025 % Result : Theorem 6.17s 6.40s % Output : Proof 6.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET628+3 : TPTP v9.2.0. Released v2.2.0. % 0.03/0.14 % Command : duper %s % 0.14/0.34 % Computer : n028.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 : Thu Oct 2 13:50:38 EDT 2025 % 0.14/0.35 % CPUTime : % 6.17/6.40 SZS status Theorem for theBenchmark.p % 6.17/6.40 SZS output start Proof for theBenchmark.p % 6.17/6.40 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 6.17/6.40 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 6.17/6.40 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (∀ (D : Iota), Iff (member D B) (member D C))) True % 6.17/6.40 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (not_equal B C) (Ne B C)) True % 6.17/6.40 Clause #5 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True % 6.17/6.40 Clause #6 (by assumption #[]): Eq (Not (∀ (B : Iota), Iff (intersect B B) (not_equal B empty_set))) True % 6.17/6.40 Clause #7 (by clausification #[1]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 6.17/6.40 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (member a empty_set) False % 6.17/6.40 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True % 6.17/6.40 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False) % 6.17/6.40 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True) % 6.17/6.40 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (Not (member (skS.0 0 a a_1) a))) True) % 6.17/6.40 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (member (skS.0 0 a a_1) a)) False) % 6.17/6.40 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 0 a a_1) a) True) % 6.17/6.40 Clause #18 (by superposition #[17, 8]): Or (Eq (empty empty_set) True) (Eq True False) % 6.17/6.40 Clause #19 (by clausification #[18]): Eq (empty empty_set) True % 6.17/6.40 Clause #20 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True) % 6.17/6.40 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False) % 6.17/6.40 Clause #23 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 6.17/6.40 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 6.17/6.40 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) True) (Eq (Exists fun D => And (member D a) (member D a_1)) False) % 6.17/6.40 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 6.17/6.40 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Eq (And (member a_2 a) (member a_2 a_1)) False) % 6.17/6.40 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) False)) % 6.17/6.40 Clause #29 (by superposition #[28, 17]): ∀ (a a_1 a_2 : Iota), % 6.17/6.40 Or (Eq (intersect a a_1) True) (Or (Eq (member (skS.0 0 a a_2) a_1) False) (Or (Eq (empty a) True) (Eq False True))) % 6.17/6.40 Clause #30 (by clausification #[6]): Eq (∀ (B : Iota), Iff (intersect B B) (not_equal B empty_set)) False % 6.17/6.40 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (Not (Iff (intersect (skS.0 1 a) (skS.0 1 a)) (not_equal (skS.0 1 a) empty_set))) True % 6.17/6.40 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (Iff (intersect (skS.0 1 a) (skS.0 1 a)) (not_equal (skS.0 1 a) empty_set)) False % 6.17/6.40 Clause #33 (by clausification #[32]): ∀ (a : Iota), Or (Eq (intersect (skS.0 1 a) (skS.0 1 a)) False) (Eq (not_equal (skS.0 1 a) empty_set) False) % 6.17/6.40 Clause #34 (by clausification #[32]): ∀ (a : Iota), Or (Eq (intersect (skS.0 1 a) (skS.0 1 a)) True) (Eq (not_equal (skS.0 1 a) empty_set) True) % 6.17/6.40 Clause #35 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (not_equal a C) (Ne a C)) True % 6.17/6.40 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Iff (not_equal a a_1) (Ne a a_1)) True % 6.17/6.40 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) True) (Eq (Ne a a_1) False) % 6.17/6.40 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) False) (Eq (Ne a a_1) True) % 6.25/6.42 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) True) (Eq a a_1) % 6.25/6.42 Clause #52 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (∀ (D : Iota), Iff (member D a) (member D C))) True % 6.25/6.42 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (∀ (D : Iota), Iff (member D a) (member D a_1))) True % 6.25/6.42 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (∀ (D : Iota), Iff (member D a) (member D a_1)) False) % 6.25/6.42 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (∀ (D : Iota), Iff (member D a) (member D a_1)) False) (Eq a a_1) % 6.25/6.42 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 6.25/6.42 Or (Eq a a_1) (Eq (Not (Iff (member (skS.0 2 a a_1 a_2) a) (member (skS.0 2 a a_1 a_2) a_1))) True) % 6.25/6.42 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Eq a a_1) (Eq (Iff (member (skS.0 2 a a_1 a_2) a) (member (skS.0 2 a a_1 a_2) a_1)) False) % 6.25/6.42 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 6.25/6.42 Or (Eq a a_1) (Or (Eq (member (skS.0 2 a a_1 a_2) a) True) (Eq (member (skS.0 2 a a_1 a_2) a_1) True)) % 6.25/6.42 Clause #65 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) False) (Ne a a_1) % 6.25/6.42 Clause #66 (by destructive equality resolution #[65]): ∀ (a : Iota), Eq (not_equal a a) False % 6.25/6.42 Clause #68 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 6.25/6.42 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 3 a a_1 a_2) a) (member (skS.0 3 a a_1 a_2) a_1)) True) % 6.25/6.42 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 3 a a_1 a_2) a_1) True) % 6.25/6.42 Clause #81 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Or (Eq (member (skS.0 0 a a_2) a_1) False) (Eq (empty a) True)) % 6.25/6.42 Clause #82 (by superposition #[81, 17]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Or (Eq (empty a) True) (Or (Eq (empty a) True) (Eq False True))) % 6.25/6.42 Clause #95 (by superposition #[34, 69]): ∀ (a a_1 : Iota), % 6.25/6.42 Or (Eq (member (skS.0 3 (skS.0 1 a) (skS.0 1 a) a_1) (skS.0 1 a)) True) % 6.25/6.42 (Or (Eq False True) (Eq (not_equal (skS.0 1 a) empty_set) True)) % 6.25/6.42 Clause #110 (by clausification #[82]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Or (Eq (empty a) True) (Eq (empty a) True)) % 6.25/6.42 Clause #111 (by eliminate duplicate literals #[110]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Eq (empty a) True) % 6.25/6.42 Clause #112 (by superposition #[111, 33]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Or (Eq True False) (Eq (not_equal (skS.0 1 a) empty_set) False)) % 6.25/6.42 Clause #214 (by superposition #[60, 8]): ∀ (a a_1 : Iota), Or (Eq empty_set a) (Or (Eq (member (skS.0 2 empty_set a a_1) a) True) (Eq True False)) % 6.25/6.42 Clause #365 (by clausification #[95]): ∀ (a a_1 : Iota), % 6.25/6.42 Or (Eq (member (skS.0 3 (skS.0 1 a) (skS.0 1 a) a_1) (skS.0 1 a)) True) (Eq (not_equal (skS.0 1 a) empty_set) True) % 6.25/6.42 Clause #411 (by clausification #[214]): ∀ (a a_1 : Iota), Or (Eq empty_set a) (Eq (member (skS.0 2 empty_set a a_1) a) True) % 6.25/6.42 Clause #449 (by clausification #[112]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq (not_equal (skS.0 1 a) empty_set) False) % 6.25/6.42 Clause #480 (by superposition #[449, 39]): ∀ (a a_1 : Iota), Or (Eq (not_equal a (skS.0 1 a_1)) True) (Or (Eq (empty a) True) (Eq (not_equal a empty_set) False)) % 6.25/6.42 Clause #515 (by superposition #[480, 39]): ∀ (a a_1 : Iota), % 6.25/6.42 Or (Eq (not_equal a (skS.0 1 a_1)) True) (Or (Eq (empty a) True) (Or (Eq False True) (Eq a empty_set))) % 6.25/6.42 Clause #536 (by clausification #[515]): ∀ (a a_1 : Iota), Or (Eq (not_equal a (skS.0 1 a_1)) True) (Or (Eq (empty a) True) (Eq a empty_set)) % 6.25/6.42 Clause #539 (by superposition #[536, 19]): ∀ (a a_1 : Iota), Or (Eq (not_equal a (skS.0 1 a_1)) True) (Or (Eq (empty a) True) (Eq (empty a) True)) % 6.25/6.42 Clause #565 (by eliminate duplicate literals #[539]): ∀ (a a_1 : Iota), Or (Eq (not_equal a (skS.0 1 a_1)) True) (Eq (empty a) True) % 6.25/6.42 Clause #566 (by superposition #[565, 66]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq True False) % 6.25/6.42 Clause #581 (by clausification #[566]): ∀ (a : Iota), Eq (empty (skS.0 1 a)) True % 6.25/6.43 Clause #583 (by superposition #[581, 21]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member a (skS.0 1 a_1)) False) % 6.25/6.43 Clause #587 (by clausification #[583]): ∀ (a a_1 : Iota), Eq (member a (skS.0 1 a_1)) False % 6.25/6.43 Clause #588 (by superposition #[587, 365]): ∀ (a : Iota), Or (Eq False True) (Eq (not_equal (skS.0 1 a) empty_set) True) % 6.25/6.43 Clause #594 (by superposition #[587, 411]): ∀ (a : Iota), Or (Eq empty_set (skS.0 1 a)) (Eq False True) % 6.25/6.43 Clause #599 (by clausification #[594]): ∀ (a : Iota), Eq empty_set (skS.0 1 a) % 6.25/6.43 Clause #610 (by clausification #[588]): ∀ (a : Iota), Eq (not_equal (skS.0 1 a) empty_set) True % 6.25/6.43 Clause #611 (by forward demodulation #[610, 599]): Eq (not_equal empty_set empty_set) True % 6.25/6.43 Clause #612 (by superposition #[611, 66]): Eq True False % 6.25/6.43 Clause #619 (by clausification #[612]): False % 6.25/6.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------