TSTP Solution File: SEU188+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU188+1 : TPTP v8.1.2. Released v3.3.0.
% 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 16:40:42 EDT 2023
% Result : Theorem 4.04s 4.33s
% Output : Proof 4.04s
% 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 : SEU188+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 14:10:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.04/4.33 SZS status Theorem for theBenchmark.p
% 4.04/4.33 SZS output start Proof for theBenchmark.p
% 4.04/4.33 Clause #8 (by assumption #[]): Eq (empty empty_set) True
% 4.04/4.33 Clause #13 (by assumption #[]): Eq (∀ (A : Iota), And (Not (empty A)) (relation A) → Not (empty (relation_dom A))) True
% 4.04/4.33 Clause #14 (by assumption #[]): Eq (∀ (A : Iota), And (Not (empty A)) (relation A) → Not (empty (relation_rng A))) True
% 4.04/4.33 Clause #23 (by assumption #[]): Eq (∀ (A : Iota), relation A → (∀ (B C : Iota), Not (in (ordered_pair B C) A)) → Eq A empty_set) True
% 4.04/4.33 Clause #24 (by assumption #[]): Eq
% 4.04/4.33 (Not (∀ (A : Iota), relation A → Or (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set) → Eq A empty_set))
% 4.04/4.33 True
% 4.04/4.33 Clause #26 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (in A B) (empty B))) True
% 4.04/4.33 Clause #41 (by clausification #[14]): ∀ (a : Iota), Eq (And (Not (empty a)) (relation a) → Not (empty (relation_rng a))) True
% 4.04/4.33 Clause #42 (by clausification #[41]): ∀ (a : Iota), Or (Eq (And (Not (empty a)) (relation a)) False) (Eq (Not (empty (relation_rng a))) True)
% 4.04/4.33 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (Not (empty (relation_rng a))) True) (Or (Eq (Not (empty a)) False) (Eq (relation a) False))
% 4.04/4.33 Clause #44 (by clausification #[43]): ∀ (a : Iota), Or (Eq (Not (empty a)) False) (Or (Eq (relation a) False) (Eq (empty (relation_rng a)) False))
% 4.04/4.33 Clause #45 (by clausification #[44]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (empty (relation_rng a)) False) (Eq (empty a) True))
% 4.04/4.33 Clause #47 (by clausification #[13]): ∀ (a : Iota), Eq (And (Not (empty a)) (relation a) → Not (empty (relation_dom a))) True
% 4.04/4.33 Clause #48 (by clausification #[47]): ∀ (a : Iota), Or (Eq (And (Not (empty a)) (relation a)) False) (Eq (Not (empty (relation_dom a))) True)
% 4.04/4.33 Clause #49 (by clausification #[48]): ∀ (a : Iota), Or (Eq (Not (empty (relation_dom a))) True) (Or (Eq (Not (empty a)) False) (Eq (relation a) False))
% 4.04/4.33 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (Not (empty a)) False) (Or (Eq (relation a) False) (Eq (empty (relation_dom a)) False))
% 4.04/4.33 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (empty (relation_dom a)) False) (Eq (empty a) True))
% 4.04/4.33 Clause #67 (by clausification #[23]): ∀ (a : Iota), Eq (relation a → (∀ (B C : Iota), Not (in (ordered_pair B C) a)) → Eq a empty_set) True
% 4.04/4.33 Clause #68 (by clausification #[67]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq ((∀ (B C : Iota), Not (in (ordered_pair B C) a)) → Eq a empty_set) True)
% 4.04/4.33 Clause #69 (by clausification #[68]): ∀ (a : Iota),
% 4.04/4.33 Or (Eq (relation a) False) (Or (Eq (∀ (B C : Iota), Not (in (ordered_pair B C) a)) False) (Eq (Eq a empty_set) True))
% 4.04/4.33 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 4.04/4.33 Or (Eq (relation a) False)
% 4.04/4.33 (Or (Eq (Eq a empty_set) True) (Eq (Not (∀ (C : Iota), Not (in (ordered_pair (skS.0 2 a a_1) C) a))) True))
% 4.04/4.33 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 4.04/4.33 Or (Eq (relation a) False)
% 4.04/4.33 (Or (Eq (Not (∀ (C : Iota), Not (in (ordered_pair (skS.0 2 a a_1) C) a))) True) (Eq a empty_set))
% 4.04/4.33 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota),
% 4.04/4.33 Or (Eq (relation a) False)
% 4.04/4.33 (Or (Eq a empty_set) (Eq (∀ (C : Iota), Not (in (ordered_pair (skS.0 2 a a_1) C) a)) False))
% 4.04/4.33 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.33 Or (Eq (relation a) False)
% 4.04/4.33 (Or (Eq a empty_set) (Eq (Not (Not (in (ordered_pair (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) a))) True))
% 4.04/4.33 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.33 Or (Eq (relation a) False)
% 4.04/4.33 (Or (Eq a empty_set) (Eq (Not (in (ordered_pair (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) a)) False))
% 4.04/4.33 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.33 Or (Eq (relation a) False) (Or (Eq a empty_set) (Eq (in (ordered_pair (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) a) True))
% 4.04/4.33 Clause #99 (by clausification #[24]): Eq (∀ (A : Iota), relation A → Or (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set) → Eq A empty_set)
% 4.04/4.33 False
% 4.04/4.33 Clause #100 (by clausification #[99]): ∀ (a : Iota),
% 4.04/4.33 Eq
% 4.04/4.33 (Not
% 4.04/4.33 (relation (skS.0 6 a) →
% 4.04/4.35 Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) →
% 4.04/4.35 Eq (skS.0 6 a) empty_set))
% 4.04/4.35 True
% 4.04/4.35 Clause #101 (by clausification #[100]): ∀ (a : Iota),
% 4.04/4.35 Eq
% 4.04/4.35 (relation (skS.0 6 a) →
% 4.04/4.35 Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) → Eq (skS.0 6 a) empty_set)
% 4.04/4.35 False
% 4.04/4.35 Clause #102 (by clausification #[101]): ∀ (a : Iota), Eq (relation (skS.0 6 a)) True
% 4.04/4.35 Clause #103 (by clausification #[101]): ∀ (a : Iota),
% 4.04/4.35 Eq (Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) → Eq (skS.0 6 a) empty_set)
% 4.04/4.35 False
% 4.04/4.35 Clause #104 (by superposition #[102, 45]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (relation_rng (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True))
% 4.04/4.35 Clause #105 (by superposition #[102, 51]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (relation_dom (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True))
% 4.04/4.35 Clause #106 (by superposition #[102, 75]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.35 Or (Eq True False)
% 4.04/4.35 (Or (Eq (skS.0 6 a) empty_set)
% 4.04/4.35 (Eq (in (ordered_pair (skS.0 2 (skS.0 6 a) a_1) (skS.0 3 (skS.0 6 a) a_1 a_2)) (skS.0 6 a)) True))
% 4.04/4.35 Clause #207 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (in a B) (empty B))) True
% 4.04/4.35 Clause #208 (by clausification #[207]): ∀ (a a_1 : Iota), Eq (Not (And (in a a_1) (empty a_1))) True
% 4.04/4.35 Clause #209 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (And (in a a_1) (empty a_1)) False
% 4.04/4.35 Clause #210 (by clausification #[209]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (empty a_1) False)
% 4.04/4.35 Clause #214 (by clausification #[103]): ∀ (a : Iota), Eq (Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set)) True
% 4.04/4.35 Clause #215 (by clausification #[103]): ∀ (a : Iota), Eq (Eq (skS.0 6 a) empty_set) False
% 4.04/4.35 Clause #216 (by clausification #[214]): ∀ (a : Iota), Or (Eq (Eq (relation_dom (skS.0 6 a)) empty_set) True) (Eq (Eq (relation_rng (skS.0 6 a)) empty_set) True)
% 4.04/4.35 Clause #217 (by clausification #[216]): ∀ (a : Iota), Or (Eq (Eq (relation_rng (skS.0 6 a)) empty_set) True) (Eq (relation_dom (skS.0 6 a)) empty_set)
% 4.04/4.35 Clause #218 (by clausification #[217]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set)
% 4.04/4.35 Clause #226 (by clausification #[215]): ∀ (a : Iota), Ne (skS.0 6 a) empty_set
% 4.04/4.35 Clause #311 (by clausification #[104]): ∀ (a : Iota), Or (Eq (empty (relation_rng (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True)
% 4.04/4.35 Clause #336 (by clausification #[105]): ∀ (a : Iota), Or (Eq (empty (relation_dom (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True)
% 4.04/4.35 Clause #366 (by clausification #[106]): ∀ (a a_1 a_2 : Iota),
% 4.04/4.35 Or (Eq (skS.0 6 a) empty_set)
% 4.04/4.35 (Eq (in (ordered_pair (skS.0 2 (skS.0 6 a) a_1) (skS.0 3 (skS.0 6 a) a_1 a_2)) (skS.0 6 a)) True)
% 4.04/4.35 Clause #367 (by forward contextual literal cutting #[366, 226]): ∀ (a a_1 a_2 : Iota), Eq (in (ordered_pair (skS.0 2 (skS.0 6 a) a_1) (skS.0 3 (skS.0 6 a) a_1 a_2)) (skS.0 6 a)) True
% 4.04/4.35 Clause #370 (by superposition #[367, 210]): ∀ (a : Iota), Or (Eq True False) (Eq (empty (skS.0 6 a)) False)
% 4.04/4.35 Clause #371 (by clausification #[370]): ∀ (a : Iota), Eq (empty (skS.0 6 a)) False
% 4.04/4.35 Clause #372 (by backward demodulation #[371, 311]): ∀ (a : Iota), Or (Eq (empty (relation_rng (skS.0 6 a))) False) (Eq False True)
% 4.04/4.35 Clause #373 (by backward demodulation #[371, 336]): ∀ (a : Iota), Or (Eq (empty (relation_dom (skS.0 6 a))) False) (Eq False True)
% 4.04/4.35 Clause #374 (by clausification #[373]): ∀ (a : Iota), Eq (empty (relation_dom (skS.0 6 a))) False
% 4.04/4.35 Clause #375 (by superposition #[374, 218]): ∀ (a : Iota), Or (Eq (relation_rng (skS.0 6 a)) empty_set) (Eq (empty empty_set) False)
% 4.04/4.35 Clause #376 (by forward demodulation #[375, 8]): ∀ (a : Iota), Or (Eq (relation_rng (skS.0 6 a)) empty_set) (Eq True False)
% 4.04/4.35 Clause #377 (by clausification #[376]): ∀ (a : Iota), Eq (relation_rng (skS.0 6 a)) empty_set
% 4.04/4.35 Clause #379 (by clausification #[372]): ∀ (a : Iota), Eq (empty (relation_rng (skS.0 6 a))) False
% 4.04/4.35 Clause #380 (by forward demodulation #[379, 377]): Eq (empty empty_set) False
% 4.04/4.35 Clause #381 (by superposition #[380, 8]): Eq False True
% 4.04/4.35 Clause #383 (by clausification #[381]): False
% 4.04/4.35 SZS output end Proof for theBenchmark.p
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