TSTP Solution File: SEU219+3 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU219+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 16:40:52 EDT 2023
% Result : Theorem 61.27s 61.59s
% Output : Proof 61.47s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU219+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n028.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 : Wed Aug 23 18:30:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 61.27/61.59 SZS status Theorem for theBenchmark.p
% 61.27/61.59 SZS output start Proof for theBenchmark.p
% 61.27/61.59 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), And (relation A) (function A) → one_to_one A → Eq (function_inverse A) (relation_inverse A)) True
% 61.27/61.59 Clause #32 (by assumption #[]): Eq
% 61.27/61.59 (∀ (A : Iota),
% 61.27/61.59 relation A →
% 61.27/61.59 And (Eq (relation_rng A) (relation_dom (relation_inverse A)))
% 61.27/61.59 (Eq (relation_dom A) (relation_rng (relation_inverse A))))
% 61.27/61.59 True
% 61.27/61.59 Clause #35 (by assumption #[]): Eq
% 61.27/61.59 (Not
% 61.27/61.59 (∀ (A : Iota),
% 61.27/61.59 And (relation A) (function A) →
% 61.27/61.59 one_to_one A →
% 61.27/61.59 And (Eq (relation_rng A) (relation_dom (function_inverse A)))
% 61.27/61.59 (Eq (relation_dom A) (relation_rng (function_inverse A)))))
% 61.27/61.59 True
% 61.27/61.59 Clause #93 (by clausification #[4]): ∀ (a : Iota), Eq (And (relation a) (function a) → one_to_one a → Eq (function_inverse a) (relation_inverse a)) True
% 61.27/61.59 Clause #94 (by clausification #[93]): ∀ (a : Iota),
% 61.27/61.59 Or (Eq (And (relation a) (function a)) False) (Eq (one_to_one a → Eq (function_inverse a) (relation_inverse a)) True)
% 61.27/61.59 Clause #95 (by clausification #[94]): ∀ (a : Iota),
% 61.27/61.59 Or (Eq (one_to_one a → Eq (function_inverse a) (relation_inverse a)) True)
% 61.27/61.59 (Or (Eq (relation a) False) (Eq (function a) False))
% 61.27/61.59 Clause #96 (by clausification #[95]): ∀ (a : Iota),
% 61.27/61.59 Or (Eq (relation a) False)
% 61.27/61.59 (Or (Eq (function a) False) (Or (Eq (one_to_one a) False) (Eq (Eq (function_inverse a) (relation_inverse a)) True)))
% 61.27/61.59 Clause #97 (by clausification #[96]): ∀ (a : Iota),
% 61.27/61.59 Or (Eq (relation a) False)
% 61.27/61.59 (Or (Eq (function a) False) (Or (Eq (one_to_one a) False) (Eq (function_inverse a) (relation_inverse a))))
% 61.27/61.59 Clause #359 (by clausification #[32]): ∀ (a : Iota),
% 61.27/61.59 Eq
% 61.27/61.59 (relation a →
% 61.27/61.59 And (Eq (relation_rng a) (relation_dom (relation_inverse a)))
% 61.27/61.59 (Eq (relation_dom a) (relation_rng (relation_inverse a))))
% 61.27/61.59 True
% 61.27/61.59 Clause #360 (by clausification #[359]): ∀ (a : Iota),
% 61.27/61.59 Or (Eq (relation a) False)
% 61.27/61.59 (Eq
% 61.27/61.59 (And (Eq (relation_rng a) (relation_dom (relation_inverse a)))
% 61.27/61.59 (Eq (relation_dom a) (relation_rng (relation_inverse a))))
% 61.27/61.59 True)
% 61.27/61.59 Clause #361 (by clausification #[360]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (Eq (relation_dom a) (relation_rng (relation_inverse a))) True)
% 61.27/61.59 Clause #362 (by clausification #[360]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (Eq (relation_rng a) (relation_dom (relation_inverse a))) True)
% 61.27/61.59 Clause #363 (by clausification #[361]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (relation_dom a) (relation_rng (relation_inverse a)))
% 61.27/61.59 Clause #404 (by clausification #[35]): Eq
% 61.27/61.59 (∀ (A : Iota),
% 61.27/61.59 And (relation A) (function A) →
% 61.27/61.59 one_to_one A →
% 61.27/61.59 And (Eq (relation_rng A) (relation_dom (function_inverse A)))
% 61.27/61.59 (Eq (relation_dom A) (relation_rng (function_inverse A))))
% 61.27/61.59 False
% 61.27/61.59 Clause #405 (by clausification #[404]): ∀ (a : Iota),
% 61.27/61.59 Eq
% 61.27/61.59 (Not
% 61.27/61.59 (And (relation (skS.0 11 a)) (function (skS.0 11 a)) →
% 61.27/61.59 one_to_one (skS.0 11 a) →
% 61.27/61.59 And (Eq (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a))))
% 61.27/61.59 (Eq (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a))))))
% 61.27/61.59 True
% 61.27/61.59 Clause #406 (by clausification #[405]): ∀ (a : Iota),
% 61.27/61.59 Eq
% 61.27/61.59 (And (relation (skS.0 11 a)) (function (skS.0 11 a)) →
% 61.27/61.59 one_to_one (skS.0 11 a) →
% 61.27/61.59 And (Eq (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a))))
% 61.27/61.59 (Eq (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a)))))
% 61.27/61.59 False
% 61.27/61.59 Clause #407 (by clausification #[406]): ∀ (a : Iota), Eq (And (relation (skS.0 11 a)) (function (skS.0 11 a))) True
% 61.27/61.59 Clause #408 (by clausification #[406]): ∀ (a : Iota),
% 61.27/61.59 Eq
% 61.27/61.59 (one_to_one (skS.0 11 a) →
% 61.27/61.59 And (Eq (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a))))
% 61.27/61.59 (Eq (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a)))))
% 61.27/61.59 False
% 61.27/61.59 Clause #409 (by clausification #[407]): ∀ (a : Iota), Eq (function (skS.0 11 a)) True
% 61.27/61.59 Clause #410 (by clausification #[407]): ∀ (a : Iota), Eq (relation (skS.0 11 a)) True
% 61.47/61.63 Clause #416 (by superposition #[410, 97]): ∀ (a : Iota),
% 61.47/61.63 Or (Eq True False)
% 61.47/61.63 (Or (Eq (function (skS.0 11 a)) False)
% 61.47/61.63 (Or (Eq (one_to_one (skS.0 11 a)) False) (Eq (function_inverse (skS.0 11 a)) (relation_inverse (skS.0 11 a)))))
% 61.47/61.63 Clause #420 (by superposition #[410, 363]): ∀ (a : Iota), Or (Eq True False) (Eq (relation_dom (skS.0 11 a)) (relation_rng (relation_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #526 (by clausification #[362]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (relation_rng a) (relation_dom (relation_inverse a)))
% 61.47/61.63 Clause #533 (by superposition #[526, 410]): ∀ (a : Iota), Or (Eq (relation_rng (skS.0 11 a)) (relation_dom (relation_inverse (skS.0 11 a)))) (Eq False True)
% 61.47/61.63 Clause #1268 (by clausification #[420]): ∀ (a : Iota), Eq (relation_dom (skS.0 11 a)) (relation_rng (relation_inverse (skS.0 11 a)))
% 61.47/61.63 Clause #1281 (by clausification #[533]): ∀ (a : Iota), Eq (relation_rng (skS.0 11 a)) (relation_dom (relation_inverse (skS.0 11 a)))
% 61.47/61.63 Clause #1543 (by clausification #[408]): ∀ (a : Iota), Eq (one_to_one (skS.0 11 a)) True
% 61.47/61.63 Clause #1544 (by clausification #[408]): ∀ (a : Iota),
% 61.47/61.63 Eq
% 61.47/61.63 (And (Eq (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a))))
% 61.47/61.63 (Eq (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a)))))
% 61.47/61.63 False
% 61.47/61.63 Clause #1579 (by clausification #[416]): ∀ (a : Iota),
% 61.47/61.63 Or (Eq (function (skS.0 11 a)) False)
% 61.47/61.63 (Or (Eq (one_to_one (skS.0 11 a)) False) (Eq (function_inverse (skS.0 11 a)) (relation_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #1580 (by forward demodulation #[1579, 409]): ∀ (a : Iota),
% 61.47/61.63 Or (Eq True False)
% 61.47/61.63 (Or (Eq (one_to_one (skS.0 11 a)) False) (Eq (function_inverse (skS.0 11 a)) (relation_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #1581 (by clausification #[1580]): ∀ (a : Iota),
% 61.47/61.63 Or (Eq (one_to_one (skS.0 11 a)) False) (Eq (function_inverse (skS.0 11 a)) (relation_inverse (skS.0 11 a)))
% 61.47/61.63 Clause #1582 (by superposition #[1581, 1543]): ∀ (a : Iota), Or (Eq (function_inverse (skS.0 11 a)) (relation_inverse (skS.0 11 a))) (Eq False True)
% 61.47/61.63 Clause #1623 (by clausification #[1582]): ∀ (a : Iota), Eq (function_inverse (skS.0 11 a)) (relation_inverse (skS.0 11 a))
% 61.47/61.63 Clause #6685 (by clausification #[1544]): ∀ (a : Iota),
% 61.47/61.63 Or (Eq (Eq (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a)))) False)
% 61.47/61.63 (Eq (Eq (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a)))) False)
% 61.47/61.63 Clause #6686 (by clausification #[6685]): ∀ (a : Iota),
% 61.47/61.63 Or (Eq (Eq (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a)))) False)
% 61.47/61.63 (Ne (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #6687 (by clausification #[6686]): ∀ (a : Iota),
% 61.47/61.63 Or (Ne (relation_rng (skS.0 11 a)) (relation_dom (function_inverse (skS.0 11 a))))
% 61.47/61.63 (Ne (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #6688 (by forward demodulation #[6687, 1623]): ∀ (a : Iota),
% 61.47/61.63 Or (Ne (relation_rng (skS.0 11 a)) (relation_dom (relation_inverse (skS.0 11 a))))
% 61.47/61.63 (Ne (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #6689 (by forward demodulation #[6688, 1281]): ∀ (a : Iota),
% 61.47/61.63 Or (Ne (relation_rng (skS.0 11 a)) (relation_rng (skS.0 11 a)))
% 61.47/61.63 (Ne (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a))))
% 61.47/61.63 Clause #6690 (by eliminate resolved literals #[6689]): ∀ (a : Iota), Ne (relation_dom (skS.0 11 a)) (relation_rng (function_inverse (skS.0 11 a)))
% 61.47/61.63 Clause #6691 (by forward demodulation #[6690, 1623]): ∀ (a : Iota), Ne (relation_dom (skS.0 11 a)) (relation_rng (relation_inverse (skS.0 11 a)))
% 61.47/61.63 Clause #6692 (by forward demodulation #[6691, 1268]): ∀ (a : Iota), Ne (relation_dom (skS.0 11 a)) (relation_dom (skS.0 11 a))
% 61.47/61.63 Clause #6693 (by eliminate resolved literals #[6692]): False
% 61.47/61.63 SZS output end Proof for theBenchmark.p
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