TSTP Solution File: SET633+3 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 14:47:11 EDT 2023
% Result : Theorem 8.05s 8.40s
% Output : Proof 8.21s
% 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 : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n004.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 09:18:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.05/8.40 SZS status Theorem for theBenchmark.p
% 8.05/8.40 SZS output start Proof for theBenchmark.p
% 8.05/8.40 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True
% 8.05/8.40 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), And (subset B C) (subset D C) → subset (union B D) C) True
% 8.05/8.40 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (symmetric_difference C B)) True
% 8.05/8.40 Clause #8 (by assumption #[]): Eq
% 8.05/8.40 (Not
% 8.05/8.40 (∀ (B C D : Iota),
% 8.05/8.40 And (subset (difference B C) D) (subset (difference C B) D) → subset (symmetric_difference B C) D))
% 8.05/8.40 True
% 8.05/8.40 Clause #10 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (subset a C) (subset D C) → subset (union a D) C) True
% 8.05/8.40 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), And (subset a a_1) (subset D a_1) → subset (union a D) a_1) True
% 8.05/8.40 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_2 a_1) → subset (union a a_2) a_1) True
% 8.05/8.40 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_2 a_1)) False) (Eq (subset (union a a_2) a_1) True)
% 8.05/8.40 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (union a a_1) a_2) True) (Or (Eq (subset a a_2) False) (Eq (subset a_1 a_2) False))
% 8.05/8.40 Clause #16 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (symmetric_difference C a)) True
% 8.05/8.40 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (symmetric_difference a_1 a)) True
% 8.05/8.40 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (symmetric_difference a_1 a)
% 8.05/8.40 Clause #22 (by clausification #[8]): Eq (∀ (B C D : Iota), And (subset (difference B C) D) (subset (difference C B) D) → subset (symmetric_difference B C) D)
% 8.05/8.40 False
% 8.05/8.40 Clause #23 (by clausification #[22]): ∀ (a : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (Not
% 8.05/8.40 (∀ (C D : Iota),
% 8.05/8.40 And (subset (difference (skS.0 0 a) C) D) (subset (difference C (skS.0 0 a)) D) →
% 8.05/8.40 subset (symmetric_difference (skS.0 0 a) C) D))
% 8.05/8.40 True
% 8.05/8.40 Clause #24 (by clausification #[23]): ∀ (a : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (∀ (C D : Iota),
% 8.05/8.40 And (subset (difference (skS.0 0 a) C) D) (subset (difference C (skS.0 0 a)) D) →
% 8.05/8.40 subset (symmetric_difference (skS.0 0 a) C) D)
% 8.05/8.40 False
% 8.05/8.40 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (Not
% 8.05/8.40 (∀ (D : Iota),
% 8.05/8.40 And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) D) (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) D) →
% 8.05/8.40 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) D))
% 8.05/8.40 True
% 8.05/8.40 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (∀ (D : Iota),
% 8.05/8.40 And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) D) (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) D) →
% 8.05/8.40 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) D)
% 8.05/8.40 False
% 8.05/8.40 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (Not
% 8.05/8.40 (And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))
% 8.05/8.40 (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) →
% 8.05/8.40 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)))
% 8.05/8.40 True
% 8.05/8.40 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))
% 8.05/8.40 (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) →
% 8.05/8.40 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))
% 8.05/8.40 False
% 8.05/8.40 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.40 Eq
% 8.05/8.40 (And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))
% 8.05/8.40 (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)))
% 8.05/8.40 True
% 8.05/8.40 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) False
% 8.05/8.40 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) True
% 8.21/8.42 Clause #32 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) True
% 8.21/8.42 Clause #33 (by superposition #[31, 14]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.21/8.42 Or (Eq (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) a_2) (skS.0 2 a a_1 a_3)) True)
% 8.21/8.42 (Or (Eq True False) (Eq (subset a_2 (skS.0 2 a a_1 a_3)) False))
% 8.21/8.42 Clause #34 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True
% 8.21/8.42 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True
% 8.21/8.42 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))
% 8.21/8.42 Clause #141 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.21/8.42 Or (Eq (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) a_2) (skS.0 2 a a_1 a_3)) True)
% 8.21/8.42 (Eq (subset a_2 (skS.0 2 a a_1 a_3)) False)
% 8.21/8.42 Clause #143 (by superposition #[141, 32]): ∀ (a a_1 a_2 : Iota),
% 8.21/8.42 Or
% 8.21/8.42 (Eq
% 8.21/8.42 (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) (difference (skS.0 0 a) (skS.0 1 a a_1)))
% 8.21/8.42 (skS.0 2 a a_1 a_2))
% 8.21/8.42 True)
% 8.21/8.42 (Eq False True)
% 8.21/8.42 Clause #2269 (by clausification #[143]): ∀ (a a_1 a_2 : Iota),
% 8.21/8.42 Eq
% 8.21/8.42 (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) (difference (skS.0 0 a) (skS.0 1 a a_1)))
% 8.21/8.42 (skS.0 2 a a_1 a_2))
% 8.21/8.42 True
% 8.21/8.42 Clause #2270 (by forward demodulation #[2269, 36]): ∀ (a a_1 a_2 : Iota), Eq (subset (symmetric_difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) True
% 8.21/8.42 Clause #2271 (by forward demodulation #[2270, 18]): ∀ (a a_1 a_2 : Iota), Eq (subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) True
% 8.21/8.42 Clause #2272 (by superposition #[2271, 30]): Eq True False
% 8.21/8.42 Clause #2293 (by clausification #[2272]): False
% 8.21/8.42 SZS output end Proof for theBenchmark.p
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