%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU628^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:02:05 PM UTC 2025 % Result : Theorem 4.18s 4.34s % Output : Proof 4.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU628^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n001.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 : Fri Oct 3 05:38:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.18/4.34 SZS status Theorem for theBenchmark.p % 4.18/4.34 SZS output start Proof for theBenchmark.p % 4.18/4.34 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True % 4.18/4.34 Clause #1 (by assumption #[]): Eq % 4.18/4.34 (Eq ubforcartprodlem1 % 4.18/4.34 (∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (binunion A B)))) % 4.18/4.34 True % 4.18/4.34 Clause #2 (by assumption #[]): Eq % 4.18/4.34 (Not % 4.18/4.34 (powersetI1 → % 4.18/4.34 ubforcartprodlem1 → % 4.18/4.34 ∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (powerset (binunion A B))))) % 4.18/4.34 True % 4.18/4.34 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A)) % 4.18/4.34 Clause #16 (by clausification #[1]): Eq ubforcartprodlem1 % 4.18/4.34 (∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (binunion A B))) % 4.18/4.34 Clause #34 (by clausification #[2]): Eq % 4.18/4.34 (powersetI1 → % 4.18/4.34 ubforcartprodlem1 → % 4.18/4.34 ∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (powerset (binunion A B)))) % 4.18/4.34 False % 4.18/4.34 Clause #35 (by clausification #[34]): Eq powersetI1 True % 4.18/4.34 Clause #36 (by clausification #[34]): Eq % 4.18/4.34 (ubforcartprodlem1 → % 4.18/4.34 ∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (powerset (binunion A B)))) % 4.18/4.34 False % 4.18/4.34 Clause #37 (by backward demodulation #[35, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A)) % 4.18/4.34 Clause #41 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True % 4.18/4.34 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True % 4.18/4.34 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True) % 4.18/4.34 Clause #48 (by clausification #[36]): Eq ubforcartprodlem1 True % 4.18/4.34 Clause #49 (by clausification #[36]): Eq % 4.18/4.34 (∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (powerset (binunion A B)))) % 4.18/4.34 False % 4.18/4.34 Clause #50 (by backward demodulation #[48, 16]): Eq True % 4.18/4.34 (∀ (A B Xx : Iota), % 4.18/4.34 in Xx A → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (binunion A B))) % 4.18/4.34 Clause #55 (by clausification #[50]): ∀ (a : Iota), % 4.18/4.34 Eq % 4.18/4.34 (∀ (B Xx : Iota), % 4.18/4.34 in Xx a → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy B → % 4.18/4.34 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (binunion a B))) % 4.18/4.34 True % 4.18/4.34 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 4.18/4.34 Eq % 4.18/4.34 (∀ (Xx : Iota), % 4.18/4.34 in Xx a → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy a_1 → % 4.18/4.34 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (binunion a a_1))) % 4.18/4.34 True % 4.18/4.34 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 4.18/4.34 Eq % 4.18/4.34 (in a a_1 → % 4.18/4.34 ∀ (Xy : Iota), % 4.18/4.34 in Xy a_2 → % 4.18/4.34 subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) % 4.18/4.34 (powerset (binunion a_1 a_2))) % 4.18/4.34 True % 4.18/4.34 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 4.18/4.34 Or (Eq (in a a_1) False) % 4.18/4.36 (Eq % 4.18/4.36 (∀ (Xy : Iota), % 4.18/4.36 in Xy a_2 → % 4.18/4.36 subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (binunion a_1 a_2))) % 4.18/4.36 True) % 4.18/4.36 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.36 Or (Eq (in a a_1) False) % 4.18/4.36 (Eq % 4.18/4.36 (in a_2 a_3 → % 4.18/4.36 subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_2 emptyset)) emptyset)) % 4.18/4.36 (powerset (binunion a_1 a_3))) % 4.18/4.36 True) % 4.18/4.36 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.36 Or (Eq (in a a_1) False) % 4.18/4.36 (Or (Eq (in a_2 a_3) False) % 4.18/4.36 (Eq % 4.18/4.36 (subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_2 emptyset)) emptyset)) % 4.18/4.36 (powerset (binunion a_1 a_3))) % 4.18/4.36 True)) % 4.18/4.36 Clause #61 (by clausification #[49]): ∀ (a : Iota), % 4.18/4.36 Eq % 4.18/4.36 (Not % 4.18/4.36 (∀ (B Xx : Iota), % 4.18/4.36 in Xx (skS.0 6 a) → % 4.18/4.36 ∀ (Xy : Iota), % 4.18/4.36 in Xy B → % 4.18/4.36 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) B))))) % 4.18/4.36 True % 4.18/4.36 Clause #62 (by clausification #[61]): ∀ (a : Iota), % 4.18/4.36 Eq % 4.18/4.36 (∀ (B Xx : Iota), % 4.18/4.36 in Xx (skS.0 6 a) → % 4.18/4.36 ∀ (Xy : Iota), % 4.18/4.36 in Xy B → % 4.18/4.36 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) B)))) % 4.18/4.36 False % 4.18/4.36 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 4.18/4.36 Eq % 4.18/4.36 (Not % 4.18/4.36 (∀ (Xx : Iota), % 4.18/4.36 in Xx (skS.0 6 a) → % 4.18/4.36 ∀ (Xy : Iota), % 4.18/4.36 in Xy (skS.0 7 a a_1) → % 4.18/4.36 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))) % 4.18/4.36 True % 4.18/4.36 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 4.18/4.36 Eq % 4.18/4.36 (∀ (Xx : Iota), % 4.18/4.36 in Xx (skS.0 6 a) → % 4.18/4.36 ∀ (Xy : Iota), % 4.18/4.36 in Xy (skS.0 7 a a_1) → % 4.18/4.36 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 4.18/4.36 False % 4.18/4.36 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 4.18/4.36 Eq % 4.18/4.36 (Not % 4.18/4.36 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) → % 4.18/4.36 ∀ (Xy : Iota), % 4.18/4.36 in Xy (skS.0 7 a a_1) → % 4.18/4.36 in % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))) % 4.18/4.36 True % 4.18/4.36 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 4.18/4.36 Eq % 4.18/4.36 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) → % 4.18/4.36 ∀ (Xy : Iota), % 4.18/4.36 in Xy (skS.0 7 a a_1) → % 4.18/4.36 in % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 4.18/4.36 False % 4.18/4.36 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 6 a)) True % 4.18/4.36 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 4.18/4.36 Eq % 4.18/4.36 (∀ (Xy : Iota), % 4.18/4.36 in Xy (skS.0 7 a a_1) → % 4.18/4.36 in % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) emptyset)) % 4.18/4.36 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 4.18/4.36 False % 4.18/4.36 Clause #69 (by superposition #[67, 60]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.18/4.36 Or (Eq True False) % 4.18/4.36 (Or (Eq (in a a_1) False) % 4.18/4.36 (Eq % 4.18/4.36 (subset % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) emptyset) % 4.18/4.36 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) emptyset)) % 4.18/4.36 (powerset (binunion (skS.0 6 a_2) a_1))) % 4.18/4.36 True)) % 4.18/4.36 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.18/4.36 Or (Eq (in a a_1) False) % 4.18/4.37 (Eq % 4.18/4.37 (subset % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) emptyset)) % 4.18/4.37 (powerset (binunion (skS.0 6 a_2) a_1))) % 4.18/4.37 True) % 4.18/4.37 Clause #72 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.37 Eq % 4.18/4.37 (Not % 4.18/4.37 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) → % 4.18/4.37 in % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset)) % 4.18/4.37 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))) % 4.18/4.37 True % 4.18/4.37 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.37 Eq % 4.18/4.37 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) → % 4.18/4.37 in % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset)) % 4.18/4.37 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 4.18/4.37 False % 4.18/4.37 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1)) True % 4.18/4.37 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.37 Eq % 4.18/4.37 (in % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset)) % 4.18/4.37 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 4.18/4.37 False % 4.18/4.37 Clause #77 (by superposition #[74, 70]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.18/4.37 Or (Eq True False) % 4.18/4.37 (Eq % 4.18/4.37 (subset % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset)) % 4.18/4.37 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))) % 4.18/4.37 True) % 4.18/4.37 Clause #87 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.18/4.37 Eq % 4.18/4.37 (subset % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset)) % 4.18/4.37 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))) % 4.18/4.37 True % 4.18/4.37 Clause #88 (by superposition #[87, 43]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.18/4.37 Or (Eq True False) % 4.18/4.37 (Eq % 4.18/4.37 (in % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset)) % 4.18/4.37 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))))) % 4.18/4.37 True) % 4.18/4.37 Clause #91 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.18/4.37 Eq % 4.18/4.37 (in % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 4.18/4.37 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset)) % 4.18/4.37 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))))) % 4.18/4.37 True % 4.18/4.37 Clause #95 (by superposition #[91, 75]): Eq True False % 4.18/4.37 Clause #96 (by clausification #[95]): False % 4.18/4.37 SZS output end Proof for theBenchmark.p 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