TSTP Solution File: SEU189+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU189+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 3.79s 4.01s
% Output : Proof 3.87s
% 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 : SEU189+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 01:06:17 EDT 2023
% 0.16/0.34 % CPUTime :
% 3.79/4.01 SZS status Theorem for theBenchmark.p
% 3.79/4.01 SZS output start Proof for theBenchmark.p
% 3.79/4.01 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), empty A → And (empty (relation_dom A)) (relation (relation_dom A))) True
% 3.79/4.01 Clause #11 (by assumption #[]): Eq (∀ (A : Iota), empty A → And (empty (relation_rng A)) (relation (relation_rng A))) True
% 3.79/4.01 Clause #17 (by assumption #[]): Eq (empty empty_set) True
% 3.79/4.01 Clause #18 (by assumption #[]): Eq (∀ (A : Iota), empty A → Eq A empty_set) True
% 3.79/4.01 Clause #19 (by assumption #[]): Eq (Not (∀ (A : Iota), relation A → Iff (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set))) True
% 3.79/4.01 Clause #21 (by assumption #[]): Eq (∀ (A : Iota), relation A → Or (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set) → Eq A empty_set) True
% 3.79/4.01 Clause #45 (by clausification #[18]): ∀ (a : Iota), Eq (empty a → Eq a empty_set) True
% 3.79/4.01 Clause #46 (by clausification #[45]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (Eq a empty_set) True)
% 3.79/4.01 Clause #47 (by clausification #[46]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq a empty_set)
% 3.79/4.01 Clause #63 (by clausification #[21]): ∀ (a : Iota), Eq (relation a → Or (Eq (relation_dom a) empty_set) (Eq (relation_rng a) empty_set) → Eq a empty_set) True
% 3.79/4.01 Clause #64 (by clausification #[63]): ∀ (a : Iota),
% 3.79/4.01 Or (Eq (relation a) False)
% 3.79/4.01 (Eq (Or (Eq (relation_dom a) empty_set) (Eq (relation_rng a) empty_set) → Eq a empty_set) True)
% 3.79/4.01 Clause #65 (by clausification #[64]): ∀ (a : Iota),
% 3.79/4.01 Or (Eq (relation a) False)
% 3.79/4.01 (Or (Eq (Or (Eq (relation_dom a) empty_set) (Eq (relation_rng a) empty_set)) False) (Eq (Eq a empty_set) True))
% 3.79/4.01 Clause #66 (by clausification #[65]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq (relation_rng a) empty_set) False))
% 3.79/4.01 Clause #67 (by clausification #[65]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq (relation_dom a) empty_set) False))
% 3.79/4.01 Clause #68 (by clausification #[66]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq (relation_rng a) empty_set) False) (Eq a empty_set))
% 3.79/4.01 Clause #69 (by clausification #[68]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq a empty_set) (Ne (relation_rng a) empty_set))
% 3.79/4.01 Clause #93 (by clausification #[11]): ∀ (a : Iota), Eq (empty a → And (empty (relation_rng a)) (relation (relation_rng a))) True
% 3.79/4.01 Clause #94 (by clausification #[93]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (And (empty (relation_rng a)) (relation (relation_rng a))) True)
% 3.79/4.01 Clause #96 (by clausification #[94]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (empty (relation_rng a)) True)
% 3.79/4.01 Clause #102 (by superposition #[96, 17]): Or (Eq (empty (relation_rng empty_set)) True) (Eq False True)
% 3.79/4.01 Clause #103 (by clausification #[10]): ∀ (a : Iota), Eq (empty a → And (empty (relation_dom a)) (relation (relation_dom a))) True
% 3.79/4.01 Clause #104 (by clausification #[103]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (And (empty (relation_dom a)) (relation (relation_dom a))) True)
% 3.79/4.01 Clause #106 (by clausification #[104]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (empty (relation_dom a)) True)
% 3.79/4.01 Clause #112 (by clausification #[102]): Eq (empty (relation_rng empty_set)) True
% 3.79/4.01 Clause #114 (by superposition #[112, 47]): Or (Eq True False) (Eq (relation_rng empty_set) empty_set)
% 3.79/4.01 Clause #118 (by clausification #[114]): Eq (relation_rng empty_set) empty_set
% 3.79/4.01 Clause #124 (by superposition #[106, 17]): Or (Eq (empty (relation_dom empty_set)) True) (Eq False True)
% 3.79/4.01 Clause #125 (by clausification #[124]): Eq (empty (relation_dom empty_set)) True
% 3.79/4.01 Clause #127 (by superposition #[125, 47]): Or (Eq True False) (Eq (relation_dom empty_set) empty_set)
% 3.79/4.01 Clause #132 (by clausification #[127]): Eq (relation_dom empty_set) empty_set
% 3.79/4.01 Clause #145 (by clausification #[19]): Eq (∀ (A : Iota), relation A → Iff (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set)) False
% 3.79/4.01 Clause #146 (by clausification #[145]): ∀ (a : Iota),
% 3.79/4.01 Eq
% 3.79/4.01 (Not
% 3.79/4.01 (relation (skS.0 5 a) → Iff (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set)))
% 3.79/4.01 True
% 3.79/4.01 Clause #147 (by clausification #[146]): ∀ (a : Iota),
% 3.87/4.03 Eq (relation (skS.0 5 a) → Iff (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set))
% 3.87/4.03 False
% 3.87/4.03 Clause #148 (by clausification #[147]): ∀ (a : Iota), Eq (relation (skS.0 5 a)) True
% 3.87/4.03 Clause #149 (by clausification #[147]): ∀ (a : Iota), Eq (Iff (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set)) False
% 3.87/4.03 Clause #152 (by superposition #[148, 69]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (skS.0 5 a) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set))
% 3.87/4.03 Clause #173 (by clausification #[67]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq (relation_dom a) empty_set) False) (Eq a empty_set))
% 3.87/4.03 Clause #174 (by clausification #[173]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq a empty_set) (Ne (relation_dom a) empty_set))
% 3.87/4.03 Clause #177 (by superposition #[174, 148]): ∀ (a : Iota), Or (Eq (skS.0 5 a) empty_set) (Or (Ne (relation_dom (skS.0 5 a)) empty_set) (Eq False True))
% 3.87/4.03 Clause #186 (by clausification #[177]): ∀ (a : Iota), Or (Eq (skS.0 5 a) empty_set) (Ne (relation_dom (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #195 (by clausification #[152]): ∀ (a : Iota), Or (Eq (skS.0 5 a) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #206 (by clausification #[149]): ∀ (a : Iota),
% 3.87/4.03 Or (Eq (Eq (relation_dom (skS.0 5 a)) empty_set) False) (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) False)
% 3.87/4.03 Clause #207 (by clausification #[149]): ∀ (a : Iota), Or (Eq (Eq (relation_dom (skS.0 5 a)) empty_set) True) (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) True)
% 3.87/4.03 Clause #208 (by clausification #[206]): ∀ (a : Iota), Or (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) False) (Ne (relation_dom (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #209 (by clausification #[208]): ∀ (a : Iota), Or (Ne (relation_dom (skS.0 5 a)) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #210 (by clausification #[207]): ∀ (a : Iota), Or (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) True) (Eq (relation_dom (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #211 (by clausification #[210]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #212 (by superposition #[211, 195]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 5 a)) empty_set) (Or (Eq (skS.0 5 a) empty_set) (Ne empty_set empty_set))
% 3.87/4.03 Clause #214 (by eliminate resolved literals #[212]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (skS.0 5 a) empty_set)
% 3.87/4.03 Clause #215 (by forward contextual literal cutting #[214, 186]): ∀ (a : Iota), Eq (skS.0 5 a) empty_set
% 3.87/4.03 Clause #220 (by backward demodulation #[215, 209]): ∀ (a : Iota), Or (Ne (relation_dom empty_set) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #223 (by forward demodulation #[220, 132]): ∀ (a : Iota), Or (Ne empty_set empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set)
% 3.87/4.03 Clause #224 (by eliminate resolved literals #[223]): ∀ (a : Iota), Ne (relation_rng (skS.0 5 a)) empty_set
% 3.87/4.03 Clause #225 (by forward demodulation #[224, 215]): Ne (relation_rng empty_set) empty_set
% 3.87/4.03 Clause #226 (by forward demodulation #[225, 118]): Ne empty_set empty_set
% 3.87/4.03 Clause #227 (by eliminate resolved literals #[226]): False
% 3.87/4.03 SZS output end Proof for theBenchmark.p
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