TSTP Solution File: SEU096+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n032.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 16:40:12 EDT 2023
% Result : Theorem 117.68s 118.00s
% Output : Proof 117.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : duper %s
% 0.12/0.30 % Computer : n032.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Wed Aug 23 18:07:26 EDT 2023
% 0.12/0.30 % CPUTime :
% 117.68/118.00 SZS status Theorem for theBenchmark.p
% 117.68/118.00 SZS output start Proof for theBenchmark.p
% 117.68/118.00 Clause #14 (by assumption #[]): Eq (∀ (A B : Iota), And (And (relation A) (function A)) (finite B) → finite (relation_image A B)) True
% 117.68/118.00 Clause #49 (by assumption #[]): Eq
% 117.68/118.00 (∀ (A B : Iota),
% 117.68/118.00 And (relation B) (function B) → subset A (relation_rng B) → Eq (relation_image B (relation_inverse_image B A)) A)
% 117.68/118.00 True
% 117.68/118.00 Clause #52 (by assumption #[]): Eq
% 117.68/118.00 (Not
% 117.68/118.00 (∀ (A B : Iota),
% 117.68/118.00 And (relation B) (function B) → And (subset A (relation_rng B)) (finite (relation_inverse_image B A)) → finite A))
% 117.68/118.00 True
% 117.68/118.00 Clause #134 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B : Iota), And (And (relation a) (function a)) (finite B) → finite (relation_image a B)) True
% 117.68/118.00 Clause #135 (by clausification #[134]): ∀ (a a_1 : Iota), Eq (And (And (relation a) (function a)) (finite a_1) → finite (relation_image a a_1)) True
% 117.68/118.00 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota),
% 117.68/118.00 Or (Eq (And (And (relation a) (function a)) (finite a_1)) False) (Eq (finite (relation_image a a_1)) True)
% 117.68/118.00 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota),
% 117.68/118.00 Or (Eq (finite (relation_image a a_1)) True) (Or (Eq (And (relation a) (function a)) False) (Eq (finite a_1) False))
% 117.68/118.00 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota),
% 117.68/118.00 Or (Eq (finite (relation_image a a_1)) True)
% 117.68/118.00 (Or (Eq (finite a_1) False) (Or (Eq (relation a) False) (Eq (function a) False)))
% 117.68/118.00 Clause #145 (by clausification #[52]): Eq
% 117.68/118.00 (∀ (A B : Iota),
% 117.68/118.00 And (relation B) (function B) → And (subset A (relation_rng B)) (finite (relation_inverse_image B A)) → finite A)
% 117.68/118.00 False
% 117.68/118.00 Clause #146 (by clausification #[145]): ∀ (a : Iota),
% 117.68/118.00 Eq
% 117.68/118.00 (Not
% 117.68/118.00 (∀ (B : Iota),
% 117.68/118.00 And (relation B) (function B) →
% 117.68/118.00 And (subset (skS.0 2 a) (relation_rng B)) (finite (relation_inverse_image B (skS.0 2 a))) →
% 117.68/118.00 finite (skS.0 2 a)))
% 117.68/118.00 True
% 117.68/118.00 Clause #147 (by clausification #[146]): ∀ (a : Iota),
% 117.68/118.00 Eq
% 117.68/118.00 (∀ (B : Iota),
% 117.68/118.00 And (relation B) (function B) →
% 117.68/118.00 And (subset (skS.0 2 a) (relation_rng B)) (finite (relation_inverse_image B (skS.0 2 a))) → finite (skS.0 2 a))
% 117.68/118.00 False
% 117.68/118.00 Clause #148 (by clausification #[147]): ∀ (a a_1 : Iota),
% 117.68/118.00 Eq
% 117.68/118.00 (Not
% 117.68/118.00 (And (relation (skS.0 3 a a_1)) (function (skS.0 3 a a_1)) →
% 117.68/118.00 And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1)))
% 117.68/118.00 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) →
% 117.68/118.00 finite (skS.0 2 a)))
% 117.68/118.00 True
% 117.68/118.00 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota),
% 117.68/118.00 Eq
% 117.68/118.00 (And (relation (skS.0 3 a a_1)) (function (skS.0 3 a a_1)) →
% 117.68/118.00 And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1)))
% 117.68/118.00 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) →
% 117.68/118.00 finite (skS.0 2 a))
% 117.68/118.00 False
% 117.68/118.00 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (And (relation (skS.0 3 a a_1)) (function (skS.0 3 a a_1))) True
% 117.68/118.00 Clause #151 (by clausification #[149]): ∀ (a a_1 : Iota),
% 117.68/118.00 Eq
% 117.68/118.00 (And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1)))
% 117.68/118.00 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) →
% 117.68/118.00 finite (skS.0 2 a))
% 117.68/118.00 False
% 117.68/118.00 Clause #152 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (function (skS.0 3 a a_1)) True
% 117.68/118.00 Clause #153 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (relation (skS.0 3 a a_1)) True
% 117.68/118.00 Clause #202 (by clausification #[151]): ∀ (a a_1 : Iota),
% 117.68/118.00 Eq
% 117.68/118.00 (And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1)))
% 117.68/118.00 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))))
% 117.68/118.00 True
% 117.68/118.00 Clause #203 (by clausification #[151]): ∀ (a : Iota), Eq (finite (skS.0 2 a)) False
% 117.68/118.00 Clause #204 (by clausification #[202]): ∀ (a a_1 : Iota), Eq (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) True
% 117.68/118.00 Clause #205 (by clausification #[202]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1))) True
% 117.68/118.00 Clause #207 (by superposition #[204, 138]): ∀ (a a_1 a_2 : Iota),
% 117.68/118.00 Or (Eq (finite (relation_image a (relation_inverse_image (skS.0 3 a_1 a_2) (skS.0 2 a_1)))) True)
% 117.68/118.00 (Or (Eq True False) (Or (Eq (relation a) False) (Eq (function a) False)))
% 117.68/118.05 Clause #475 (by clausification #[49]): ∀ (a : Iota),
% 117.68/118.05 Eq
% 117.68/118.05 (∀ (B : Iota),
% 117.68/118.05 And (relation B) (function B) → subset a (relation_rng B) → Eq (relation_image B (relation_inverse_image B a)) a)
% 117.68/118.05 True
% 117.68/118.05 Clause #476 (by clausification #[475]): ∀ (a a_1 : Iota),
% 117.68/118.05 Eq
% 117.68/118.05 (And (relation a) (function a) →
% 117.68/118.05 subset a_1 (relation_rng a) → Eq (relation_image a (relation_inverse_image a a_1)) a_1)
% 117.68/118.05 True
% 117.68/118.05 Clause #477 (by clausification #[476]): ∀ (a a_1 : Iota),
% 117.68/118.05 Or (Eq (And (relation a) (function a)) False)
% 117.68/118.05 (Eq (subset a_1 (relation_rng a) → Eq (relation_image a (relation_inverse_image a a_1)) a_1) True)
% 117.68/118.05 Clause #478 (by clausification #[477]): ∀ (a a_1 : Iota),
% 117.68/118.05 Or (Eq (subset a (relation_rng a_1) → Eq (relation_image a_1 (relation_inverse_image a_1 a)) a) True)
% 117.68/118.05 (Or (Eq (relation a_1) False) (Eq (function a_1) False))
% 117.68/118.05 Clause #479 (by clausification #[478]): ∀ (a a_1 : Iota),
% 117.68/118.05 Or (Eq (relation a) False)
% 117.68/118.05 (Or (Eq (function a) False)
% 117.68/118.05 (Or (Eq (subset a_1 (relation_rng a)) False)
% 117.68/118.05 (Eq (Eq (relation_image a (relation_inverse_image a a_1)) a_1) True)))
% 117.68/118.05 Clause #480 (by clausification #[479]): ∀ (a a_1 : Iota),
% 117.68/118.05 Or (Eq (relation a) False)
% 117.68/118.05 (Or (Eq (function a) False)
% 117.68/118.05 (Or (Eq (subset a_1 (relation_rng a)) False) (Eq (relation_image a (relation_inverse_image a a_1)) a_1)))
% 117.68/118.05 Clause #484 (by superposition #[480, 153]): ∀ (a a_1 a_2 : Iota),
% 117.68/118.05 Or (Eq (function (skS.0 3 a a_1)) False)
% 117.68/118.05 (Or (Eq (subset a_2 (relation_rng (skS.0 3 a a_1))) False)
% 117.68/118.05 (Or (Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) a_2)) a_2) (Eq False True)))
% 117.68/118.05 Clause #682 (by clausification #[207]): ∀ (a a_1 a_2 : Iota),
% 117.68/118.05 Or (Eq (finite (relation_image a (relation_inverse_image (skS.0 3 a_1 a_2) (skS.0 2 a_1)))) True)
% 117.68/118.05 (Or (Eq (relation a) False) (Eq (function a) False))
% 117.68/118.05 Clause #686 (by superposition #[682, 153]): ∀ (a a_1 a_2 a_3 : Iota),
% 117.68/118.05 Or (Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True)
% 117.68/118.05 (Or (Eq (function (skS.0 3 a a_1)) False) (Eq False True))
% 117.68/118.05 Clause #1247 (by clausification #[484]): ∀ (a a_1 a_2 : Iota),
% 117.68/118.05 Or (Eq (function (skS.0 3 a a_1)) False)
% 117.68/118.05 (Or (Eq (subset a_2 (relation_rng (skS.0 3 a a_1))) False)
% 117.68/118.05 (Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) a_2)) a_2))
% 117.68/118.05 Clause #1248 (by forward demodulation #[1247, 152]): ∀ (a a_1 a_2 : Iota),
% 117.68/118.05 Or (Eq True False)
% 117.68/118.05 (Or (Eq (subset a (relation_rng (skS.0 3 a_1 a_2))) False)
% 117.68/118.05 (Eq (relation_image (skS.0 3 a_1 a_2) (relation_inverse_image (skS.0 3 a_1 a_2) a)) a))
% 117.68/118.05 Clause #1249 (by clausification #[1248]): ∀ (a a_1 a_2 : Iota),
% 117.68/118.05 Or (Eq (subset a (relation_rng (skS.0 3 a_1 a_2))) False)
% 117.68/118.05 (Eq (relation_image (skS.0 3 a_1 a_2) (relation_inverse_image (skS.0 3 a_1 a_2) a)) a)
% 117.68/118.05 Clause #1250 (by superposition #[1249, 205]): ∀ (a a_1 : Iota),
% 117.68/118.05 Or (Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) (skS.0 2 a))
% 117.68/118.05 (Eq False True)
% 117.68/118.05 Clause #1873 (by clausification #[686]): ∀ (a a_1 a_2 a_3 : Iota),
% 117.68/118.05 Or (Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True)
% 117.68/118.05 (Eq (function (skS.0 3 a a_1)) False)
% 117.68/118.05 Clause #1874 (by forward demodulation #[1873, 152]): ∀ (a a_1 a_2 a_3 : Iota),
% 117.68/118.05 Or (Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True)
% 117.68/118.05 (Eq True False)
% 117.68/118.05 Clause #1875 (by clausification #[1874]): ∀ (a a_1 a_2 a_3 : Iota),
% 117.68/118.05 Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True
% 117.68/118.05 Clause #5579 (by clausification #[1250]): ∀ (a a_1 : Iota), Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) (skS.0 2 a)
% 117.68/118.05 Clause #5580 (by superposition #[5579, 1875]): ∀ (a : Iota), Eq (finite (skS.0 2 a)) True
% 117.68/118.05 Clause #5581 (by superposition #[5580, 203]): Eq True False
% 117.68/118.05 Clause #5584 (by clausification #[5581]): False
% 117.68/118.05 SZS output end Proof for theBenchmark.p
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