%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU623^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 : Fri Oct 3 08:02:04 PM UTC 2025 % Result : Theorem 4.07s 4.23s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SEU623^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n014.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 05:05:08 EDT 2025 % 0.12/0.34 % CPUTime : % 4.07/4.23 SZS status Theorem for theBenchmark.p % 4.07/4.23 SZS output start Proof for theBenchmark.p % 4.07/4.23 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 4.07/4.23 Clause #2 (by assumption #[]): Eq (Eq binunionLsub (∀ (A B : Iota), subset A (binunion A B))) True % 4.07/4.23 Clause #3 (by assumption #[]): Eq (Eq singletoninpowerset (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A))) True % 4.07/4.23 Clause #4 (by assumption #[]): Eq % 4.07/4.23 (Not % 4.07/4.23 (subsetE → % 4.07/4.23 powersetsubset → % 4.07/4.23 binunionLsub → % 4.07/4.23 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B)))) % 4.07/4.23 True % 4.07/4.23 Clause #5 (by clausification #[2]): Eq binunionLsub (∀ (A B : Iota), subset A (binunion A B)) % 4.07/4.23 Clause #7 (by clausify Prop equality #[5]): Or (Eq binunionLsub False) (Eq (∀ (A B : Iota), subset A (binunion A B)) True) % 4.07/4.23 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq binunionLsub False) (Eq (∀ (B : Iota), subset a (binunion a B)) True) % 4.07/4.23 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq binunionLsub False) (Eq (subset a (binunion a a_1)) True) % 4.07/4.23 Clause #19 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 4.07/4.23 Clause #45 (by clausification #[3]): Eq singletoninpowerset (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A)) % 4.07/4.23 Clause #58 (by clausification #[4]): Eq % 4.07/4.23 (subsetE → % 4.07/4.23 powersetsubset → % 4.07/4.23 binunionLsub → % 4.07/4.23 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) % 4.07/4.23 False % 4.07/4.23 Clause #59 (by clausification #[58]): Eq subsetE True % 4.07/4.23 Clause #60 (by clausification #[58]): Eq % 4.07/4.23 (powersetsubset → % 4.07/4.23 binunionLsub → % 4.07/4.23 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) % 4.07/4.23 False % 4.07/4.23 Clause #61 (by backward demodulation #[59, 19]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 4.07/4.23 Clause #67 (by clausification #[61]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 4.07/4.23 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 4.07/4.23 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 % 4.07/4.23 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) % 4.07/4.23 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)) % 4.07/4.23 Clause #74 (by clausification #[60]): Eq % 4.07/4.23 (binunionLsub → % 4.07/4.23 singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) % 4.07/4.23 False % 4.07/4.23 Clause #82 (by clausification #[74]): Eq binunionLsub True % 4.07/4.23 Clause #83 (by clausification #[74]): Eq (singletoninpowerset → ∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) False % 4.07/4.23 Clause #85 (by backward demodulation #[82, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (subset a (binunion a a_1)) True) % 4.07/4.24 Clause #87 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (subset a (binunion a a_1)) True % 4.07/4.24 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)) % 4.07/4.24 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) % 4.07/4.24 Clause #99 (by clausification #[83]): Eq singletoninpowerset True % 4.07/4.24 Clause #100 (by clausification #[83]): Eq (∀ (A B Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset (binunion A B))) False % 4.07/4.24 Clause #101 (by backward demodulation #[99, 45]): Eq True (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A)) % 4.07/4.24 Clause #105 (by clausification #[101]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx a → in (setadjoin Xx emptyset) (powerset a)) True % 4.07/4.24 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (in a a_1 → in (setadjoin a emptyset) (powerset a_1)) True % 4.07/4.24 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) % 4.07/4.25 Clause #108 (by clausification #[100]): ∀ (a : Iota), % 4.07/4.25 Eq (Not (∀ (B Xx : Iota), in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) B)))) True % 4.07/4.25 Clause #109 (by clausification #[108]): ∀ (a : Iota), % 4.07/4.25 Eq (∀ (B Xx : Iota), in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) B))) False % 4.07/4.25 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota), % 4.07/4.25 Eq % 4.07/4.25 (Not % 4.07/4.25 (∀ (Xx : Iota), % 4.07/4.25 in Xx (skS.0 9 a) → in (setadjoin Xx emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1))))) % 4.07/4.25 True % 4.07/4.25 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), % 4.07/4.25 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)))) % 4.07/4.25 False % 4.07/4.25 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), % 4.07/4.25 Eq % 4.07/4.25 (Not % 4.07/4.25 (in (skS.0 11 a a_1 a_2) (skS.0 9 a) → % 4.07/4.25 in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1))))) % 4.07/4.25 True % 4.07/4.25 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), % 4.07/4.25 Eq % 4.07/4.25 (in (skS.0 11 a a_1 a_2) (skS.0 9 a) → % 4.07/4.25 in (setadjoin (skS.0 11 a a_1 a_2) emptyset) (powerset (binunion (skS.0 9 a) (skS.0 10 a a_1)))) % 4.07/4.25 False % 4.07/4.25 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 % 4.07/4.25 Clause #115 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), % 4.07/4.25 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 % 4.07/4.25 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) % 4.07/4.25 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 % 4.07/4.25 Clause #141 (by superposition #[139, 107]): ∀ (a a_1 a_2 a_3 : Iota), % 4.07/4.25 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) % 4.07/4.25 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 % 4.07/4.25 Clause #160 (by superposition #[159, 115]): Eq True False % 4.07/4.25 Clause #163 (by clausification #[160]): False % 4.07/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------