TSTP Solution File: SEU623^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU623^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n006.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 16:43:03 EDT 2023
% Result : Theorem 3.79s 3.95s
% Output : Proof 3.79s
% 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 : SEU623^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:01:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.79/3.95 SZS status Theorem for theBenchmark.p
% 3.79/3.95 SZS output start Proof for theBenchmark.p
% 3.79/3.95 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True
% 3.79/3.95 Clause #2 (by assumption #[]): Eq (Eq binunionLsub (∀ (A B : Iota), subset A (binunion A B))) True
% 3.79/3.95 Clause #3 (by assumption #[]): Eq (Eq singletoninpowerset (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A))) True
% 3.79/3.95 Clause #4 (by assumption #[]): Eq
% 3.79/3.95 (Not
% 3.79/3.95 (subsetE →
% 3.79/3.95 powersetsubset →
% 3.79/3.95 binunionLsub →
% 3.79/3.95 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))))
% 3.79/3.95 True
% 3.79/3.95 Clause #5 (by clausification #[2]): Eq binunionLsub (∀ (A B : Iota), subset A (binunion A B))
% 3.79/3.95 Clause #7 (by clausify Prop equality #[5]): Or (Eq binunionLsub False) (Eq (∀ (A B : Iota), subset A (binunion A B)) True)
% 3.79/3.95 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq binunionLsub False) (Eq (∀ (B : Iota), subset a (binunion a B)) True)
% 3.79/3.95 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq binunionLsub False) (Eq (subset a (binunion a a_1)) True)
% 3.79/3.95 Clause #19 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 3.79/3.95 Clause #45 (by clausification #[3]): Eq singletoninpowerset (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A))
% 3.79/3.95 Clause #58 (by clausification #[4]): Eq
% 3.79/3.95 (subsetE →
% 3.79/3.95 powersetsubset →
% 3.79/3.95 binunionLsub →
% 3.79/3.95 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B)))
% 3.79/3.95 False
% 3.79/3.95 Clause #59 (by clausification #[58]): Eq subsetE True
% 3.79/3.95 Clause #60 (by clausification #[58]): Eq
% 3.79/3.95 (powersetsubset →
% 3.79/3.95 binunionLsub →
% 3.79/3.95 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B)))
% 3.79/3.95 False
% 3.79/3.95 Clause #61 (by backward demodulation #[59, 19]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 3.79/3.95 Clause #67 (by clausification #[61]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True
% 3.79/3.95 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True
% 3.79/3.95 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True
% 3.79/3.95 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True)
% 3.79/3.95 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True))
% 3.79/3.95 Clause #74 (by clausification #[60]): Eq
% 3.79/3.95 (binunionLsub →
% 3.79/3.95 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B)))
% 3.79/3.95 False
% 3.79/3.95 Clause #82 (by clausification #[74]): Eq binunionLsub True
% 3.79/3.95 Clause #83 (by clausification #[74]): Eq (singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) False
% 3.79/3.95 Clause #85 (by backward demodulation #[82, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (subset a (binunion a a_1)) True)
% 3.79/3.95 Clause #87 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (subset a (binunion a a_1)) True
% 3.79/3.95 Clause #88 (by superposition #[87, 71]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a a_1) False) (Eq (in a (binunion a_1 a_2)) True))
% 3.79/3.95 Clause #94 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_1 a_2)) True)
% 3.79/3.95 Clause #99 (by clausification #[83]): Eq singletoninpowerset True
% 3.79/3.95 Clause #100 (by clausification #[83]): Eq (∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) False
% 3.79/3.95 Clause #101 (by backward demodulation #[99, 45]): Eq True (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A))
% 3.79/3.95 Clause #105 (by clausification #[101]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx a → in (setadjoin Xx emptyset) (powerset a)) True
% 3.79/3.95 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (in a a_1 → in (setadjoin a emptyset) (powerset a_1)) True
% 3.79/3.95 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (in (setadjoin a emptyset) (powerset a_1)) True)
% 3.79/3.96 Clause #108 (by clausification #[100]): ∀ (a : Iota),
% 3.79/3.96 Eq (Not (∀ (B Xx : Iota), in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) B)))) True
% 3.79/3.96 Clause #109 (by clausification #[108]): ∀ (a : Iota),
% 3.79/3.96 Eq (∀ (B Xx : Iota), in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) B))) False
% 3.79/3.96 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota),
% 3.79/3.96 Eq
% 3.79/3.96 (Not
% 3.79/3.96 (∀ (Xx : Iota),
% 3.79/3.96 in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1)))))
% 3.79/3.96 True
% 3.79/3.96 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota),
% 3.79/3.96 Eq (∀ (Xx : Iota), in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1))))
% 3.79/3.96 False
% 3.79/3.96 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota),
% 3.79/3.96 Eq
% 3.79/3.96 (Not
% 3.79/3.96 (in (skS.0 11 a a_1 a_2) (skS.0 9 a) →
% 3.79/3.96 in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1)))))
% 3.79/3.96 True
% 3.79/3.96 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota),
% 3.79/3.96 Eq
% 3.79/3.96 (in (skS.0 11 a a_1 a_2) (skS.0 9 a) →
% 3.79/3.96 in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1))))
% 3.79/3.96 False
% 3.79/3.96 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 11 a a_1 a_2) (skS.0 9 a)) True
% 3.79/3.96 Clause #115 (by clausification #[113]): ∀ (a a_1 a_2 : Iota),
% 3.79/3.96 Eq (in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1)))) False
% 3.79/3.96 Clause #116 (by superposition #[114, 94]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 11 a a_1 a_2) (binunion (skS.0 9 a) a_3)) True)
% 3.79/3.96 Clause #139 (by clausification #[116]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 11 a a_1 a_2) (binunion (skS.0 9 a) a_3)) True
% 3.79/3.96 Clause #141 (by superposition #[139, 107]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.79/3.96 Or (Eq True False) (Eq (in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) a_3))) True)
% 3.79/3.96 Clause #159 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) a_3))) True
% 3.79/3.96 Clause #160 (by superposition #[159, 115]): Eq True False
% 3.79/3.96 Clause #163 (by clausification #[160]): False
% 3.79/3.96 SZS output end Proof for theBenchmark.p
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