TSTP Solution File: SET991+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET991+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 14:48:14 EDT 2023
% Result : Theorem 6.23s 6.47s
% Output : Proof 6.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET991+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:46:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.23/6.47 SZS status Theorem for theBenchmark.p
% 6.23/6.47 SZS output start Proof for theBenchmark.p
% 6.23/6.47 Clause #29 (by assumption #[]): Eq (Not (∀ (A B : Iota), And (relation B) (function B) → in A (relation_dom B) → in (apply B A) (relation_rng B))) True
% 6.23/6.47 Clause #30 (by assumption #[]): Eq
% 6.23/6.47 (∀ (A : Iota),
% 6.23/6.47 And (relation A) (function A) →
% 6.23/6.47 ∀ (B : Iota),
% 6.23/6.47 Iff (Eq B (relation_rng A))
% 6.23/6.47 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom A)) (Eq C (apply A D)))))
% 6.23/6.47 True
% 6.23/6.47 Clause #225 (by clausification #[29]): Eq (∀ (A B : Iota), And (relation B) (function B) → in A (relation_dom B) → in (apply B A) (relation_rng B)) False
% 6.23/6.47 Clause #226 (by clausification #[225]): ∀ (a : Iota),
% 6.23/6.47 Eq
% 6.23/6.47 (Not
% 6.23/6.47 (∀ (B : Iota),
% 6.23/6.47 And (relation B) (function B) → in (skS.0 9 a) (relation_dom B) → in (apply B (skS.0 9 a)) (relation_rng B)))
% 6.23/6.47 True
% 6.23/6.47 Clause #227 (by clausification #[226]): ∀ (a : Iota),
% 6.23/6.47 Eq
% 6.23/6.47 (∀ (B : Iota),
% 6.23/6.47 And (relation B) (function B) → in (skS.0 9 a) (relation_dom B) → in (apply B (skS.0 9 a)) (relation_rng B))
% 6.23/6.47 False
% 6.23/6.47 Clause #228 (by clausification #[227]): ∀ (a a_1 : Iota),
% 6.23/6.47 Eq
% 6.23/6.47 (Not
% 6.23/6.47 (And (relation (skS.0 10 a a_1)) (function (skS.0 10 a a_1)) →
% 6.23/6.47 in (skS.0 9 a) (relation_dom (skS.0 10 a a_1)) →
% 6.23/6.47 in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))))
% 6.23/6.47 True
% 6.23/6.47 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota),
% 6.23/6.47 Eq
% 6.23/6.47 (And (relation (skS.0 10 a a_1)) (function (skS.0 10 a a_1)) →
% 6.23/6.47 in (skS.0 9 a) (relation_dom (skS.0 10 a a_1)) →
% 6.23/6.47 in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1)))
% 6.23/6.47 False
% 6.23/6.47 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), Eq (And (relation (skS.0 10 a a_1)) (function (skS.0 10 a a_1))) True
% 6.23/6.47 Clause #231 (by clausification #[229]): ∀ (a a_1 : Iota),
% 6.23/6.47 Eq
% 6.23/6.47 (in (skS.0 9 a) (relation_dom (skS.0 10 a a_1)) →
% 6.23/6.47 in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1)))
% 6.23/6.47 False
% 6.23/6.47 Clause #232 (by clausification #[230]): ∀ (a a_1 : Iota), Eq (function (skS.0 10 a a_1)) True
% 6.23/6.47 Clause #233 (by clausification #[230]): ∀ (a a_1 : Iota), Eq (relation (skS.0 10 a a_1)) True
% 6.23/6.47 Clause #243 (by clausification #[30]): ∀ (a : Iota),
% 6.23/6.47 Eq
% 6.23/6.47 (And (relation a) (function a) →
% 6.23/6.47 ∀ (B : Iota),
% 6.23/6.47 Iff (Eq B (relation_rng a))
% 6.23/6.47 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))))
% 6.23/6.47 True
% 6.23/6.47 Clause #244 (by clausification #[243]): ∀ (a : Iota),
% 6.23/6.47 Or (Eq (And (relation a) (function a)) False)
% 6.23/6.47 (Eq
% 6.23/6.47 (∀ (B : Iota),
% 6.23/6.47 Iff (Eq B (relation_rng a))
% 6.23/6.47 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))))
% 6.23/6.47 True)
% 6.23/6.47 Clause #245 (by clausification #[244]): ∀ (a : Iota),
% 6.23/6.47 Or
% 6.23/6.47 (Eq
% 6.23/6.47 (∀ (B : Iota),
% 6.23/6.47 Iff (Eq B (relation_rng a))
% 6.23/6.47 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))))
% 6.23/6.47 True)
% 6.23/6.47 (Or (Eq (relation a) False) (Eq (function a) False))
% 6.23/6.47 Clause #246 (by clausification #[245]): ∀ (a a_1 : Iota),
% 6.23/6.47 Or (Eq (relation a) False)
% 6.23/6.47 (Or (Eq (function a) False)
% 6.23/6.47 (Eq
% 6.23/6.47 (Iff (Eq a_1 (relation_rng a))
% 6.23/6.47 (∀ (C : Iota), Iff (in C a_1) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))))
% 6.23/6.47 True))
% 6.23/6.47 Clause #248 (by clausification #[246]): ∀ (a a_1 : Iota),
% 6.23/6.47 Or (Eq (relation a) False)
% 6.23/6.47 (Or (Eq (function a) False)
% 6.23/6.47 (Or (Eq (Eq a_1 (relation_rng a)) False)
% 6.23/6.47 (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))) True)))
% 6.23/6.47 Clause #363 (by clausification #[231]): ∀ (a a_1 : Iota), Eq (in (skS.0 9 a) (relation_dom (skS.0 10 a a_1))) True
% 6.23/6.47 Clause #364 (by clausification #[231]): ∀ (a a_1 : Iota), Eq (in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) False
% 6.23/6.47 Clause #399 (by clausification #[248]): ∀ (a a_1 : Iota),
% 6.23/6.47 Or (Eq (relation a) False)
% 6.23/6.47 (Or (Eq (function a) False)
% 6.23/6.47 (Or (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))) True)
% 6.32/6.49 (Ne a_1 (relation_rng a))))
% 6.32/6.49 Clause #400 (by clausification #[399]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False)
% 6.32/6.49 (Or (Ne a_1 (relation_rng a))
% 6.32/6.49 (Eq (Iff (in a_2 a_1) (Exists fun D => And (in D (relation_dom a)) (Eq a_2 (apply a D)))) True)))
% 6.32/6.49 Clause #401 (by clausification #[400]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False)
% 6.32/6.49 (Or (Ne a_1 (relation_rng a))
% 6.32/6.49 (Or (Eq (in a_2 a_1) True) (Eq (Exists fun D => And (in D (relation_dom a)) (Eq a_2 (apply a D))) False))))
% 6.32/6.49 Clause #403 (by clausification #[401]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False)
% 6.32/6.49 (Or (Ne a_1 (relation_rng a))
% 6.32/6.49 (Or (Eq (in a_2 a_1) True) (Eq (And (in a_3 (relation_dom a)) (Eq a_2 (apply a a_3))) False))))
% 6.32/6.49 Clause #404 (by clausification #[403]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False)
% 6.32/6.49 (Or (Ne a_1 (relation_rng a))
% 6.32/6.49 (Or (Eq (in a_2 a_1) True) (Or (Eq (in a_3 (relation_dom a)) False) (Eq (Eq a_2 (apply a a_3)) False)))))
% 6.32/6.49 Clause #405 (by clausification #[404]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False)
% 6.32/6.49 (Or (Ne a_1 (relation_rng a))
% 6.32/6.49 (Or (Eq (in a_2 a_1) True) (Or (Eq (in a_3 (relation_dom a)) False) (Ne a_2 (apply a a_3))))))
% 6.32/6.49 Clause #406 (by destructive equality resolution #[405]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False)
% 6.32/6.49 (Or (Eq (in a_1 (relation_rng a)) True) (Or (Eq (in a_2 (relation_dom a)) False) (Ne a_1 (apply a a_2)))))
% 6.32/6.49 Clause #407 (by destructive equality resolution #[406]): ∀ (a a_1 : Iota),
% 6.32/6.49 Or (Eq (relation a) False)
% 6.32/6.49 (Or (Eq (function a) False) (Or (Eq (in (apply a a_1) (relation_rng a)) True) (Eq (in a_1 (relation_dom a)) False)))
% 6.32/6.49 Clause #412 (by superposition #[407, 233]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq (function (skS.0 10 a a_1)) False)
% 6.32/6.49 (Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True)
% 6.32/6.49 (Or (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False) (Eq False True)))
% 6.32/6.49 Clause #615 (by clausification #[412]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq (function (skS.0 10 a a_1)) False)
% 6.32/6.49 (Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True)
% 6.32/6.49 (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False))
% 6.32/6.49 Clause #616 (by forward demodulation #[615, 232]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq True False)
% 6.32/6.49 (Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True)
% 6.32/6.49 (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False))
% 6.32/6.49 Clause #617 (by clausification #[616]): ∀ (a a_1 a_2 : Iota),
% 6.32/6.49 Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True)
% 6.32/6.49 (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False)
% 6.32/6.49 Clause #618 (by superposition #[617, 363]): ∀ (a a_1 : Iota), Or (Eq (in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) True) (Eq False True)
% 6.32/6.49 Clause #621 (by clausification #[618]): ∀ (a a_1 : Iota), Eq (in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) True
% 6.32/6.49 Clause #622 (by superposition #[621, 364]): Eq True False
% 6.32/6.49 Clause #628 (by clausification #[622]): False
% 6.32/6.49 SZS output end Proof for theBenchmark.p
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