%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU169+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:01:02 PM UTC 2025 % Result : Theorem 4.68s 4.88s % Output : Proof 4.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU169+1 : TPTP v9.2.0. Released v3.3.0. % 0.13/0.14 % Command : duper %s % 0.15/0.35 % Computer : n002.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 04:10:08 EDT 2025 % 0.15/0.35 % CPUTime : % 4.68/4.88 SZS status Theorem for theBenchmark.p % 4.68/4.88 SZS output start Proof for theBenchmark.p % 4.68/4.88 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True % 4.68/4.88 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), And (Not (empty A) → Iff (element B A) (in B A)) (empty A → Iff (element B A) (empty B))) True % 4.68/4.88 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 4.68/4.88 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Not (empty (powerset A))) True % 4.68/4.88 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), element B (powerset A) → ∀ (C : Iota), in C B → in C A)) True % 4.68/4.88 Clause #16 (by clausification #[6]): ∀ (a : Iota), Eq (Not (empty (powerset a))) True % 4.68/4.88 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (empty (powerset a)) False % 4.68/4.88 Clause #37 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True % 4.68/4.88 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True % 4.68/4.88 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) % 4.68/4.88 Clause #50 (by clausification #[8]): Eq (∀ (A B : Iota), element B (powerset A) → ∀ (C : Iota), in C B → in C A) False % 4.68/4.88 Clause #51 (by clausification #[50]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), element B (powerset (skS.0 4 a)) → ∀ (C : Iota), in C B → in C (skS.0 4 a))) True % 4.68/4.88 Clause #52 (by clausification #[51]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset (skS.0 4 a)) → ∀ (C : Iota), in C B → in C (skS.0 4 a)) False % 4.68/4.88 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 4.68/4.88 Eq (Not (element (skS.0 5 a a_1) (powerset (skS.0 4 a)) → ∀ (C : Iota), in C (skS.0 5 a a_1) → in C (skS.0 4 a))) True % 4.68/4.88 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 4.68/4.88 Eq (element (skS.0 5 a a_1) (powerset (skS.0 4 a)) → ∀ (C : Iota), in C (skS.0 5 a a_1) → in C (skS.0 4 a)) False % 4.68/4.88 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (element (skS.0 5 a a_1) (powerset (skS.0 4 a))) True % 4.68/4.88 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), in C (skS.0 5 a a_1) → in C (skS.0 4 a)) False % 4.68/4.88 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) → in (skS.0 6 a a_1 a_2) (skS.0 4 a))) True % 4.68/4.88 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) → in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False % 4.68/4.88 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True % 4.68/4.88 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False % 4.68/4.88 Clause #64 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 4.68/4.88 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 4.68/4.88 Clause #67 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 4.68/4.88 Clause #74 (by clausification #[2]): ∀ (a : Iota), % 4.68/4.88 Eq (∀ (B : Iota), And (Not (empty a) → Iff (element B a) (in B a)) (empty a → Iff (element B a) (empty B))) True % 4.68/4.88 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 4.68/4.88 Eq (And (Not (empty a) → Iff (element a_1 a) (in a_1 a)) (empty a → Iff (element a_1 a) (empty a_1))) True % 4.68/4.88 Clause #77 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (Not (empty a) → Iff (element a_1 a) (in a_1 a)) True % 4.68/4.88 Clause #85 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (Not (empty a)) False) (Eq (Iff (element a_1 a) (in a_1 a)) True) % 4.68/4.88 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Eq (Iff (element a a_1) (in a a_1)) True) (Eq (empty a_1) True) % 4.68/4.88 Clause #88 (by clausification #[86]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Or (Eq (element a_1 a) False) (Eq (in a_1 a) True)) % 4.68/4.89 Clause #101 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 4.68/4.89 Clause #102 (by clausification #[101]): ∀ (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)) % 4.68/4.89 Clause #119 (by superposition #[88, 55]): ∀ (a a_1 : Iota), % 4.68/4.89 Or (Eq (empty (powerset (skS.0 4 a))) True) (Or (Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True) (Eq False True)) % 4.68/4.89 Clause #131 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1)) % 4.68/4.89 Clause #132 (by clausification #[131]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True) % 4.68/4.89 Clause #134 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) False) (Eq (subset a_2 a_1) True)) % 4.68/4.89 Clause #174 (by destructive equality resolution #[134]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (subset a a_1) True) % 4.68/4.89 Clause #260 (by clausification #[119]): ∀ (a a_1 : Iota), Or (Eq (empty (powerset (skS.0 4 a))) True) (Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True) % 4.68/4.89 Clause #261 (by forward demodulation #[260, 17]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True) % 4.68/4.89 Clause #262 (by clausification #[261]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True % 4.68/4.89 Clause #263 (by superposition #[262, 174]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (subset (skS.0 5 a a_1) (skS.0 4 a)) True) % 4.68/4.89 Clause #285 (by clausification #[263]): ∀ (a a_1 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 4 a)) True % 4.68/4.89 Clause #286 (by superposition #[285, 102]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1)) True)) % 4.68/4.89 Clause #308 (by clausification #[286]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1)) True) % 4.68/4.89 Clause #309 (by superposition #[308, 59]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True) (Eq False True) % 4.68/4.89 Clause #314 (by clausification #[309]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True % 4.68/4.89 Clause #315 (by superposition #[314, 60]): Eq True False % 4.68/4.89 Clause #330 (by clausification #[315]): False % 4.68/4.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------