%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU626^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 3.99s 4.19s % Output : Proof 3.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU626^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n004.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 06:00:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.99/4.19 SZS status Theorem for theBenchmark.p % 3.99/4.19 SZS output start Proof for theBenchmark.p % 3.99/4.19 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True % 3.99/4.19 Clause #1 (by assumption #[]): Eq % 3.99/4.19 (Eq upairsubunion % 3.99/4.19 (∀ (A B Xx : Iota), % 3.99/4.19 in Xx A → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion A B))) % 3.99/4.19 True % 3.99/4.19 Clause #2 (by assumption #[]): Eq % 3.99/4.19 (Not % 3.99/4.19 (powersetI1 → % 3.99/4.19 upairsubunion → % 3.99/4.19 ∀ (A B Xx : Iota), % 3.99/4.19 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B)))) % 3.99/4.19 True % 3.99/4.19 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A)) % 3.99/4.19 Clause #16 (by clausification #[1]): Eq upairsubunion % 3.99/4.19 (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion A B)) % 3.99/4.19 Clause #34 (by clausification #[2]): Eq % 3.99/4.19 (powersetI1 → % 3.99/4.19 upairsubunion → % 3.99/4.19 ∀ (A B Xx : Iota), % 3.99/4.19 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B))) % 3.99/4.19 False % 3.99/4.19 Clause #35 (by clausification #[34]): Eq powersetI1 True % 3.99/4.19 Clause #36 (by clausification #[34]): Eq % 3.99/4.19 (upairsubunion → % 3.99/4.19 ∀ (A B Xx : Iota), % 3.99/4.19 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B))) % 3.99/4.19 False % 3.99/4.19 Clause #37 (by backward demodulation #[35, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A)) % 3.99/4.19 Clause #41 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True % 3.99/4.19 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True % 3.99/4.19 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True) % 3.99/4.19 Clause #48 (by clausification #[36]): Eq upairsubunion True % 3.99/4.19 Clause #49 (by clausification #[36]): Eq % 3.99/4.19 (∀ (A B Xx : Iota), % 3.99/4.19 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B))) % 3.99/4.19 False % 3.99/4.19 Clause #50 (by backward demodulation #[48, 16]): Eq True % 3.99/4.19 (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion A B)) % 3.99/4.19 Clause #54 (by clausification #[50]): ∀ (a : Iota), % 3.99/4.19 Eq (∀ (B Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion a B)) % 3.99/4.19 True % 3.99/4.19 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 3.99/4.19 Eq % 3.99/4.19 (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a_1 → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion a a_1)) % 3.99/4.19 True % 3.99/4.19 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 3.99/4.19 Eq (in a a_1 → ∀ (Xy : Iota), in Xy a_2 → subset (setadjoin a (setadjoin Xy emptyset)) (binunion a_1 a_2)) True % 3.99/4.19 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 3.99/4.19 Or (Eq (in a a_1) False) % 3.99/4.19 (Eq (∀ (Xy : Iota), in Xy a_2 → subset (setadjoin a (setadjoin Xy emptyset)) (binunion a_1 a_2)) True) % 3.99/4.19 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 3.99/4.19 Or (Eq (in a a_1) False) (Eq (in a_2 a_3 → subset (setadjoin a (setadjoin a_2 emptyset)) (binunion a_1 a_3)) True) % 3.99/4.19 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 3.99/4.19 Or (Eq (in a a_1) False) % 3.99/4.19 (Or (Eq (in a_2 a_3) False) (Eq (subset (setadjoin a (setadjoin a_2 emptyset)) (binunion a_1 a_3)) True)) % 3.99/4.19 Clause #60 (by clausification #[49]): ∀ (a : Iota), % 3.99/4.19 Eq % 3.99/4.19 (Not % 3.99/4.19 (∀ (B Xx : Iota), % 3.99/4.19 in Xx (skS.0 6 a) → % 3.99/4.19 ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) B)))) % 3.99/4.19 True % 3.99/4.19 Clause #61 (by clausification #[60]): ∀ (a : Iota), % 3.99/4.19 Eq % 3.99/4.19 (∀ (B Xx : Iota), % 3.99/4.19 in Xx (skS.0 6 a) → % 3.99/4.19 ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) B))) % 3.99/4.19 False % 3.99/4.19 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 3.99/4.19 Eq % 3.99/4.19 (Not % 3.99/4.19 (∀ (Xx : Iota), % 3.99/4.19 in Xx (skS.0 6 a) → % 3.99/4.19 ∀ (Xy : Iota), % 3.99/4.19 in Xy (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 3.99/4.21 True % 3.99/4.21 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (∀ (Xx : Iota), % 3.99/4.21 in Xx (skS.0 6 a) → % 3.99/4.21 ∀ (Xy : Iota), % 3.99/4.21 in Xy (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))) % 3.99/4.21 False % 3.99/4.21 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (Not % 3.99/4.21 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) → % 3.99/4.21 ∀ (Xy : Iota), % 3.99/4.21 in Xy (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) % 3.99/4.21 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 3.99/4.21 True % 3.99/4.21 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) → % 3.99/4.21 ∀ (Xy : Iota), % 3.99/4.21 in Xy (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))) % 3.99/4.21 False % 3.99/4.21 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 6 a)) True % 3.99/4.21 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (∀ (Xy : Iota), % 3.99/4.21 in Xy (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))) % 3.99/4.21 False % 3.99/4.21 Clause #68 (by superposition #[66, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.99/4.21 Or (Eq True False) % 3.99/4.21 (Or (Eq (in a a_1) False) % 3.99/4.21 (Eq (subset (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) (binunion (skS.0 6 a_2) a_1)) True)) % 3.99/4.21 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.99/4.21 Or (Eq (in a a_1) False) % 3.99/4.21 (Eq (subset (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) (binunion (skS.0 6 a_2) a_1)) True) % 3.99/4.21 Clause #71 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (Not % 3.99/4.21 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) % 3.99/4.21 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))) % 3.99/4.21 True % 3.99/4.21 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) → % 3.99/4.21 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) % 3.99/4.21 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))) % 3.99/4.21 False % 3.99/4.21 Clause #73 (by clausification #[72]): ∀ (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 % 3.99/4.21 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) % 3.99/4.21 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))) % 3.99/4.21 False % 3.99/4.21 Clause #76 (by superposition #[73, 69]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 3.99/4.21 Or (Eq True False) % 3.99/4.21 (Eq % 3.99/4.21 (subset (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) % 3.99/4.21 (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))) % 3.99/4.21 True) % 3.99/4.21 Clause #89 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (subset (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) % 3.99/4.21 (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))) % 3.99/4.21 True % 3.99/4.21 Clause #90 (by superposition #[89, 43]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 3.99/4.21 Or (Eq True False) % 3.99/4.21 (Eq % 3.99/4.21 (in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) % 3.99/4.21 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))) % 3.99/4.21 True) % 3.99/4.21 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 3.99/4.21 Eq % 3.99/4.21 (in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) % 3.99/4.21 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))) % 3.99/4.21 True % 3.99/4.21 Clause #92 (by superposition #[91, 74]): Eq True False % 3.99/4.21 Clause #96 (by clausification #[92]): False % 3.99/4.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------