%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU354+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:01:26 PM UTC 2025 % Result : Theorem 164.04s 164.18s % Output : Proof 164.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU354+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:34:08 EDT 2025 % 0.13/0.34 % CPUTime : % 164.04/164.18 SZS status Theorem for theBenchmark.p % 164.04/164.18 SZS output start Proof for theBenchmark.p % 164.04/164.18 Clause #16 (by assumption #[]): Eq (∀ (A B : Iota), element B A → Iff (proper_element B A) (Ne B (union A))) True % 164.04/164.18 Clause #29 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 164.04/164.18 Clause #32 (by assumption #[]): Eq (∀ (A B : Iota), Iff (element A (powerset B)) (subset A B)) True % 164.04/164.18 Clause #35 (by assumption #[]): Eq (Not (∀ (A B : Iota), element B (powerset A) → Iff (proper_element B (powerset A)) (Ne B A))) True % 164.04/164.18 Clause #39 (by assumption #[]): Eq (∀ (A : Iota), Eq (union (powerset A)) A) True % 164.04/164.18 Clause #52 (by clausification #[29]): ∀ (a : Iota), Eq (Iota → subset a a) True % 164.04/164.18 Clause #53 (by clausification #[52]): ∀ (a : Iota), Iota → Eq (subset a a) True % 164.04/164.18 Clause #83 (by clausification #[39]): ∀ (a : Iota), Eq (Eq (union (powerset a)) a) True % 164.04/164.18 Clause #84 (by clausification #[83]): ∀ (a : Iota), Eq (union (powerset a)) a % 164.04/164.18 Clause #125 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (element a (powerset B)) (subset a B)) True % 164.04/164.18 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Eq (Iff (element a (powerset a_1)) (subset a a_1)) True % 164.04/164.18 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) True) (Eq (subset a a_1) False) % 164.04/164.18 Clause #129 (by superposition #[127, 53]): ∀ (a : Iota), Or (Eq (element a (powerset a)) True) (Eq False True) % 164.04/164.18 Clause #130 (by clausification #[129]): ∀ (a : Iota), Eq (element a (powerset a)) True % 164.04/164.18 Clause #222 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (B : Iota), element B a → Iff (proper_element B a) (Ne B (union a))) True % 164.04/164.18 Clause #223 (by clausification #[222]): ∀ (a a_1 : Iota), Eq (element a a_1 → Iff (proper_element a a_1) (Ne a (union a_1))) True % 164.04/164.18 Clause #224 (by clausification #[223]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Iff (proper_element a a_1) (Ne a (union a_1))) True) % 164.04/164.18 Clause #225 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (proper_element a a_1) True) (Eq (Ne a (union a_1)) False)) % 164.04/164.18 Clause #226 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (proper_element a a_1) False) (Eq (Ne a (union a_1)) True)) % 164.04/164.18 Clause #227 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (proper_element a a_1) True) (Eq a (union a_1))) % 164.04/164.18 Clause #339 (by clausification #[35]): Eq (∀ (A B : Iota), element B (powerset A) → Iff (proper_element B (powerset A)) (Ne B A)) False % 164.04/164.18 Clause #340 (by clausification #[339]): ∀ (a : Iota), % 164.04/164.18 Eq % 164.04/164.18 (Not % 164.04/164.18 (∀ (B : Iota), % 164.04/164.18 element B (powerset (skS.0 5 a)) → Iff (proper_element B (powerset (skS.0 5 a))) (Ne B (skS.0 5 a)))) % 164.04/164.18 True % 164.04/164.18 Clause #341 (by clausification #[340]): ∀ (a : Iota), % 164.04/164.18 Eq (∀ (B : Iota), element B (powerset (skS.0 5 a)) → Iff (proper_element B (powerset (skS.0 5 a))) (Ne B (skS.0 5 a))) % 164.04/164.18 False % 164.04/164.18 Clause #342 (by clausification #[341]): ∀ (a a_1 : Iota), % 164.04/164.18 Eq % 164.04/164.18 (Not % 164.04/164.18 (element (skS.0 6 a a_1) (powerset (skS.0 5 a)) → % 164.04/164.18 Iff (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) (Ne (skS.0 6 a a_1) (skS.0 5 a)))) % 164.04/164.18 True % 164.04/164.18 Clause #343 (by clausification #[342]): ∀ (a a_1 : Iota), % 164.04/164.18 Eq % 164.04/164.18 (element (skS.0 6 a a_1) (powerset (skS.0 5 a)) → % 164.04/164.18 Iff (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) (Ne (skS.0 6 a a_1) (skS.0 5 a))) % 164.04/164.18 False % 164.04/164.18 Clause #344 (by clausification #[343]): ∀ (a a_1 : Iota), Eq (element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True % 164.04/164.18 Clause #345 (by clausification #[343]): ∀ (a a_1 : Iota), % 164.04/164.18 Eq (Iff (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) (Ne (skS.0 6 a a_1) (skS.0 5 a))) False % 164.04/164.18 Clause #348 (by superposition #[344, 227]): ∀ (a a_1 : Iota), % 164.04/164.18 Or (Eq True False) % 164.04/164.18 (Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True) % 164.04/164.18 (Eq (skS.0 6 a a_1) (union (powerset (skS.0 5 a))))) % 164.04/164.18 Clause #743 (by clausification #[226]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (proper_element a a_1) False) (Ne a (union a_1))) % 164.04/164.18 Clause #744 (by destructive equality resolution #[743]): ∀ (a : Iota), Or (Eq (element (union a) a) False) (Eq (proper_element (union a) a) False) % 164.23/164.43 Clause #747 (by superposition #[744, 84]): ∀ (a : Iota), Or (Eq (element a (powerset a)) False) (Eq (proper_element a (powerset a)) False) % 164.23/164.43 Clause #750 (by forward demodulation #[747, 130]): ∀ (a : Iota), Or (Eq True False) (Eq (proper_element a (powerset a)) False) % 164.23/164.43 Clause #751 (by clausification #[750]): ∀ (a : Iota), Eq (proper_element a (powerset a)) False % 164.23/164.43 Clause #1350 (by clausification #[345]): ∀ (a a_1 : Iota), % 164.23/164.43 Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) False) (Eq (Ne (skS.0 6 a a_1) (skS.0 5 a)) False) % 164.23/164.43 Clause #1351 (by clausification #[345]): ∀ (a a_1 : Iota), % 164.23/164.43 Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True) (Eq (Ne (skS.0 6 a a_1) (skS.0 5 a)) True) % 164.23/164.43 Clause #1352 (by clausification #[1350]): ∀ (a a_1 : Iota), Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) False) (Eq (skS.0 6 a a_1) (skS.0 5 a)) % 164.23/164.43 Clause #1407 (by clausification #[348]): ∀ (a a_1 : Iota), % 164.23/164.43 Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True) % 164.23/164.43 (Eq (skS.0 6 a a_1) (union (powerset (skS.0 5 a)))) % 164.23/164.43 Clause #1408 (by forward demodulation #[1407, 84]): ∀ (a a_1 : Iota), Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True) (Eq (skS.0 6 a a_1) (skS.0 5 a)) % 164.23/164.43 Clause #34936 (by clausification #[1351]): ∀ (a a_1 : Iota), Or (Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True) (Ne (skS.0 6 a a_1) (skS.0 5 a)) % 164.23/164.43 Clause #34937 (by forward contextual literal cutting #[34936, 1408]): ∀ (a a_1 : Iota), Eq (proper_element (skS.0 6 a a_1) (powerset (skS.0 5 a))) True % 164.23/164.43 Clause #34938 (by superposition #[34937, 1352]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 6 a a_1) (skS.0 5 a)) % 164.23/164.43 Clause #34967 (by clausification #[34938]): ∀ (a a_1 : Iota), Eq (skS.0 6 a a_1) (skS.0 5 a) % 164.23/164.43 Clause #34974 (by backward demodulation #[34967, 34937]): ∀ (a : Iota), Eq (proper_element (skS.0 5 a) (powerset (skS.0 5 a))) True % 164.23/164.43 Clause #34975 (by superposition #[34974, 751]): Eq True False % 164.23/164.43 Clause #34994 (by clausification #[34975]): False % 164.23/164.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------