TSTP Solution File: SET628+3 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET628+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 : Thu Aug 31 14:47:09 EDT 2023
% Result : Theorem 4.79s 5.10s
% Output : Proof 4.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET628+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 15:29:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.79/5.10 SZS status Theorem for theBenchmark.p
% 4.79/5.10 SZS output start Proof for theBenchmark.p
% 4.79/5.10 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True
% 4.79/5.10 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True
% 4.79/5.10 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (∀ (D : Iota), Iff (member D B) (member D C))) True
% 4.79/5.10 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (not_equal B C) (Ne B C)) True
% 4.79/5.10 Clause #5 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True
% 4.79/5.10 Clause #6 (by assumption #[]): Eq (Not (∀ (B : Iota), Iff (intersect B B) (not_equal B empty_set))) True
% 4.79/5.10 Clause #7 (by clausification #[1]): ∀ (a : Iota), Eq (Not (member a empty_set)) True
% 4.79/5.10 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (member a empty_set) False
% 4.79/5.10 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True
% 4.79/5.10 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False)
% 4.79/5.10 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True)
% 4.79/5.10 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)
% 4.79/5.10 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)
% 4.79/5.10 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 0 a a_1) a) True)
% 4.79/5.10 Clause #18 (by superposition #[17, 8]): Or (Eq (empty empty_set) True) (Eq True False)
% 4.79/5.10 Clause #19 (by clausification #[18]): Eq (empty empty_set) True
% 4.79/5.10 Clause #20 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True)
% 4.79/5.10 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False)
% 4.79/5.10 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
% 4.79/5.10 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
% 4.79/5.10 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)
% 4.79/5.10 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)
% 4.79/5.10 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)
% 4.79/5.10 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))
% 4.79/5.10 Clause #29 (by superposition #[28, 17]): ∀ (a a_1 a_2 : Iota),
% 4.79/5.10 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)))
% 4.79/5.10 Clause #30 (by clausification #[6]): Eq (∀ (B : Iota), Iff (intersect B B) (not_equal B empty_set)) False
% 4.79/5.10 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
% 4.79/5.10 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
% 4.79/5.10 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)
% 4.79/5.10 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)
% 4.79/5.10 Clause #35 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (not_equal a C) (Ne a C)) True
% 4.79/5.10 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Iff (not_equal a a_1) (Ne a a_1)) True
% 4.79/5.10 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) True) (Eq (Ne a a_1) False)
% 4.79/5.10 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) False) (Eq (Ne a a_1) True)
% 4.79/5.12 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) True) (Eq a a_1)
% 4.79/5.12 Clause #52 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (∀ (D : Iota), Iff (member D a) (member D C))) True
% 4.79/5.12 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
% 4.79/5.12 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)
% 4.79/5.12 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)
% 4.79/5.12 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 4.79/5.12 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)
% 4.79/5.12 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)
% 4.79/5.12 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota),
% 4.79/5.12 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))
% 4.79/5.12 Clause #65 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) False) (Ne a a_1)
% 4.79/5.12 Clause #66 (by destructive equality resolution #[65]): ∀ (a : Iota), Eq (not_equal a a) False
% 4.79/5.12 Clause #68 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 4.79/5.12 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)
% 4.79/5.12 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)
% 4.79/5.12 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))
% 4.79/5.12 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)))
% 4.79/5.12 Clause #95 (by superposition #[34, 69]): ∀ (a a_1 : Iota),
% 4.79/5.12 Or (Eq (member (skS.0 3 (skS.0 1 a) (skS.0 1 a) a_1) (skS.0 1 a)) True)
% 4.79/5.12 (Or (Eq False True) (Eq (not_equal (skS.0 1 a) empty_set) True))
% 4.79/5.12 Clause #110 (by clausification #[82]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Or (Eq (empty a) True) (Eq (empty a) True))
% 4.79/5.12 Clause #111 (by eliminate duplicate literals #[110]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Eq (empty a) True)
% 4.79/5.12 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))
% 4.79/5.12 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))
% 4.79/5.12 Clause #365 (by clausification #[95]): ∀ (a a_1 : Iota),
% 4.79/5.12 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)
% 4.79/5.12 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)
% 4.79/5.12 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)
% 4.79/5.12 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))
% 4.79/5.12 Clause #515 (by superposition #[480, 39]): ∀ (a a_1 : Iota),
% 4.79/5.12 Or (Eq (not_equal a (skS.0 1 a_1)) True) (Or (Eq (empty a) True) (Or (Eq False True) (Eq a empty_set)))
% 4.79/5.12 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))
% 4.79/5.12 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))
% 4.79/5.12 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)
% 4.79/5.12 Clause #566 (by superposition #[565, 66]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq True False)
% 4.79/5.12 Clause #581 (by clausification #[566]): ∀ (a : Iota), Eq (empty (skS.0 1 a)) True
% 4.79/5.13 Clause #583 (by superposition #[581, 21]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member a (skS.0 1 a_1)) False)
% 4.79/5.13 Clause #587 (by clausification #[583]): ∀ (a a_1 : Iota), Eq (member a (skS.0 1 a_1)) False
% 4.79/5.13 Clause #588 (by superposition #[587, 365]): ∀ (a : Iota), Or (Eq False True) (Eq (not_equal (skS.0 1 a) empty_set) True)
% 4.79/5.13 Clause #594 (by superposition #[587, 411]): ∀ (a : Iota), Or (Eq empty_set (skS.0 1 a)) (Eq False True)
% 4.79/5.13 Clause #599 (by clausification #[594]): ∀ (a : Iota), Eq empty_set (skS.0 1 a)
% 4.79/5.13 Clause #610 (by clausification #[588]): ∀ (a : Iota), Eq (not_equal (skS.0 1 a) empty_set) True
% 4.79/5.13 Clause #611 (by forward demodulation #[610, 599]): Eq (not_equal empty_set empty_set) True
% 4.79/5.13 Clause #612 (by superposition #[611, 66]): Eq True False
% 4.79/5.13 Clause #619 (by clausification #[612]): False
% 4.79/5.13 SZS output end Proof for theBenchmark.p
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