TSTP Solution File: NUM410+1 by Duper---1.0
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% File : Duper---1.0
% Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 10:55:29 EDT 2023
% Result : Theorem 7.04s 7.27s
% Output : Proof 7.04s
% 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 : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n005.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 : Fri Aug 25 09:29:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.04/7.27 SZS status Theorem for theBenchmark.p
% 7.04/7.27 SZS output start Proof for theBenchmark.p
% 7.04/7.27 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), And (relation A) (function A) → Iff (transfinite_sequence A) (ordinal (relation_dom A))) True
% 7.04/7.27 Clause #8 (by assumption #[]): Eq
% 7.04/7.27 (∀ (A B : Iota),
% 7.04/7.27 And (And (relation B) (function B)) (transfinite_sequence B) →
% 7.04/7.27 Iff (transfinite_sequence_of B A) (subset (relation_rng B) A))
% 7.04/7.27 True
% 7.04/7.27 Clause #35 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True
% 7.04/7.27 Clause #39 (by assumption #[]): Eq
% 7.04/7.27 (Not
% 7.04/7.27 (∀ (A : Iota),
% 7.04/7.27 And (relation A) (function A) → ordinal (relation_dom A) → transfinite_sequence_of A (relation_rng A)))
% 7.04/7.27 True
% 7.04/7.27 Clause #64 (by clausification #[35]): ∀ (a : Iota), Eq (Iota → subset a a) True
% 7.04/7.27 Clause #65 (by clausification #[64]): ∀ (a : Iota), Iota → Eq (subset a a) True
% 7.04/7.27 Clause #132 (by clausification #[7]): ∀ (a : Iota), Eq (And (relation a) (function a) → Iff (transfinite_sequence a) (ordinal (relation_dom a))) True
% 7.04/7.27 Clause #133 (by clausification #[132]): ∀ (a : Iota),
% 7.04/7.27 Or (Eq (And (relation a) (function a)) False) (Eq (Iff (transfinite_sequence a) (ordinal (relation_dom a))) True)
% 7.04/7.27 Clause #134 (by clausification #[133]): ∀ (a : Iota),
% 7.04/7.27 Or (Eq (Iff (transfinite_sequence a) (ordinal (relation_dom a))) True)
% 7.04/7.27 (Or (Eq (relation a) False) (Eq (function a) False))
% 7.04/7.27 Clause #135 (by clausification #[134]): ∀ (a : Iota),
% 7.04/7.27 Or (Eq (relation a) False)
% 7.04/7.27 (Or (Eq (function a) False) (Or (Eq (transfinite_sequence a) True) (Eq (ordinal (relation_dom a)) False)))
% 7.04/7.27 Clause #152 (by clausification #[8]): ∀ (a : Iota),
% 7.04/7.27 Eq
% 7.04/7.27 (∀ (B : Iota),
% 7.04/7.27 And (And (relation B) (function B)) (transfinite_sequence B) →
% 7.04/7.27 Iff (transfinite_sequence_of B a) (subset (relation_rng B) a))
% 7.04/7.27 True
% 7.04/7.27 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota),
% 7.04/7.27 Eq
% 7.04/7.27 (And (And (relation a) (function a)) (transfinite_sequence a) →
% 7.04/7.27 Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1))
% 7.04/7.27 True
% 7.04/7.27 Clause #154 (by clausification #[153]): ∀ (a a_1 : Iota),
% 7.04/7.27 Or (Eq (And (And (relation a) (function a)) (transfinite_sequence a)) False)
% 7.04/7.27 (Eq (Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) True)
% 7.04/7.27 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota),
% 7.04/7.27 Or (Eq (Iff (transfinite_sequence_of a a_1) (subset (relation_rng a) a_1)) True)
% 7.04/7.27 (Or (Eq (And (relation a) (function a)) False) (Eq (transfinite_sequence a) False))
% 7.04/7.27 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota),
% 7.04/7.27 Or (Eq (And (relation a) (function a)) False)
% 7.04/7.27 (Or (Eq (transfinite_sequence a) False)
% 7.04/7.27 (Or (Eq (transfinite_sequence_of a a_1) True) (Eq (subset (relation_rng a) a_1) False)))
% 7.04/7.27 Clause #158 (by clausification #[156]): ∀ (a a_1 : Iota),
% 7.04/7.27 Or (Eq (transfinite_sequence a) False)
% 7.04/7.27 (Or (Eq (transfinite_sequence_of a a_1) True)
% 7.04/7.27 (Or (Eq (subset (relation_rng a) a_1) False) (Or (Eq (relation a) False) (Eq (function a) False))))
% 7.04/7.27 Clause #160 (by clausification #[39]): Eq (∀ (A : Iota), And (relation A) (function A) → ordinal (relation_dom A) → transfinite_sequence_of A (relation_rng A))
% 7.04/7.27 False
% 7.04/7.27 Clause #161 (by clausification #[160]): ∀ (a : Iota),
% 7.04/7.27 Eq
% 7.04/7.27 (Not
% 7.04/7.27 (And (relation (skS.0 5 a)) (function (skS.0 5 a)) →
% 7.04/7.27 ordinal (relation_dom (skS.0 5 a)) → transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))))
% 7.04/7.27 True
% 7.04/7.27 Clause #162 (by clausification #[161]): ∀ (a : Iota),
% 7.04/7.27 Eq
% 7.04/7.27 (And (relation (skS.0 5 a)) (function (skS.0 5 a)) →
% 7.04/7.27 ordinal (relation_dom (skS.0 5 a)) → transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a)))
% 7.04/7.27 False
% 7.04/7.27 Clause #163 (by clausification #[162]): ∀ (a : Iota), Eq (And (relation (skS.0 5 a)) (function (skS.0 5 a))) True
% 7.04/7.27 Clause #164 (by clausification #[162]): ∀ (a : Iota),
% 7.04/7.27 Eq (ordinal (relation_dom (skS.0 5 a)) → transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) False
% 7.04/7.27 Clause #165 (by clausification #[163]): ∀ (a : Iota), Eq (function (skS.0 5 a)) True
% 7.04/7.27 Clause #166 (by clausification #[163]): ∀ (a : Iota), Eq (relation (skS.0 5 a)) True
% 7.04/7.27 Clause #171 (by superposition #[166, 135]): ∀ (a : Iota),
% 7.04/7.29 Or (Eq True False)
% 7.04/7.29 (Or (Eq (function (skS.0 5 a)) False)
% 7.04/7.29 (Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False)))
% 7.04/7.29 Clause #493 (by clausification #[164]): ∀ (a : Iota), Eq (ordinal (relation_dom (skS.0 5 a))) True
% 7.04/7.29 Clause #494 (by clausification #[164]): ∀ (a : Iota), Eq (transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) False
% 7.04/7.29 Clause #548 (by clausification #[171]): ∀ (a : Iota),
% 7.04/7.29 Or (Eq (function (skS.0 5 a)) False)
% 7.04/7.29 (Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False))
% 7.04/7.29 Clause #549 (by forward demodulation #[548, 165]): ∀ (a : Iota),
% 7.04/7.29 Or (Eq True False) (Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False))
% 7.04/7.29 Clause #550 (by clausification #[549]): ∀ (a : Iota), Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq (ordinal (relation_dom (skS.0 5 a))) False)
% 7.04/7.29 Clause #551 (by superposition #[550, 493]): ∀ (a : Iota), Or (Eq (transfinite_sequence (skS.0 5 a)) True) (Eq False True)
% 7.04/7.29 Clause #552 (by clausification #[551]): ∀ (a : Iota), Eq (transfinite_sequence (skS.0 5 a)) True
% 7.04/7.29 Clause #554 (by superposition #[552, 158]): ∀ (a a_1 : Iota),
% 7.04/7.29 Or (Eq True False)
% 7.04/7.29 (Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True)
% 7.04/7.29 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False)
% 7.04/7.29 (Or (Eq (relation (skS.0 5 a)) False) (Eq (function (skS.0 5 a)) False))))
% 7.04/7.29 Clause #849 (by clausification #[554]): ∀ (a a_1 : Iota),
% 7.04/7.29 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True)
% 7.04/7.29 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False)
% 7.04/7.29 (Or (Eq (relation (skS.0 5 a)) False) (Eq (function (skS.0 5 a)) False)))
% 7.04/7.29 Clause #850 (by forward demodulation #[849, 166]): ∀ (a a_1 : Iota),
% 7.04/7.29 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True)
% 7.04/7.29 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) (Or (Eq True False) (Eq (function (skS.0 5 a)) False)))
% 7.04/7.29 Clause #851 (by clausification #[850]): ∀ (a a_1 : Iota),
% 7.04/7.29 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True)
% 7.04/7.29 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) (Eq (function (skS.0 5 a)) False))
% 7.04/7.29 Clause #852 (by forward demodulation #[851, 165]): ∀ (a a_1 : Iota),
% 7.04/7.29 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True)
% 7.04/7.29 (Or (Eq (subset (relation_rng (skS.0 5 a)) a_1) False) (Eq True False))
% 7.04/7.29 Clause #853 (by clausification #[852]): ∀ (a a_1 : Iota),
% 7.04/7.29 Or (Eq (transfinite_sequence_of (skS.0 5 a) a_1) True) (Eq (subset (relation_rng (skS.0 5 a)) a_1) False)
% 7.04/7.29 Clause #854 (by superposition #[853, 65]): ∀ (a : Iota), Or (Eq (transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) True) (Eq False True)
% 7.04/7.29 Clause #926 (by clausification #[854]): ∀ (a : Iota), Eq (transfinite_sequence_of (skS.0 5 a) (relation_rng (skS.0 5 a))) True
% 7.04/7.29 Clause #927 (by superposition #[926, 494]): Eq True False
% 7.04/7.29 Clause #932 (by clausification #[927]): False
% 7.04/7.29 SZS output end Proof for theBenchmark.p
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