%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET900+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:00:39 PM UTC 2025 % Result : Theorem 4.69s 4.93s % Output : Proof 4.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET900+1 : TPTP v9.2.0. Released v3.2.0. % 0.12/0.14 % Command : duper %s % 0.14/0.35 % Computer : n011.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 : Thu Oct 2 14:45:38 EDT 2025 % 0.14/0.36 % CPUTime : % 4.69/4.93 SZS status Theorem for theBenchmark.p % 4.69/4.93 SZS output start Proof for theBenchmark.p % 4.69/4.93 Clause #4 (by assumption #[]): Eq % 4.69/4.93 (Not % 4.69/4.93 (∀ (A B : Iota), Not (And (And (Ne A (singleton B)) (Ne A empty_set)) (∀ (C : Iota), Not (And (in C A) (Ne C B)))))) % 4.69/4.93 True % 4.69/4.93 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (And (Ne A (singleton B)) (Ne A empty_set)) (∀ (C : Iota), Not (And (in C A) (Ne C B))))) % 4.69/4.93 True % 4.69/4.93 Clause #14 (by clausification #[5]): ∀ (a : Iota), % 4.69/4.93 Eq (∀ (B : Iota), Not (And (And (Ne a (singleton B)) (Ne a empty_set)) (∀ (C : Iota), Not (And (in C a) (Ne C B))))) % 4.69/4.93 True % 4.69/4.93 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), % 4.69/4.93 Eq (Not (And (And (Ne a (singleton a_1)) (Ne a empty_set)) (∀ (C : Iota), Not (And (in C a) (Ne C a_1))))) True % 4.69/4.93 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 4.69/4.93 Eq (And (And (Ne a (singleton a_1)) (Ne a empty_set)) (∀ (C : Iota), Not (And (in C a) (Ne C a_1)))) False % 4.69/4.93 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 4.69/4.93 Or (Eq (And (Ne a (singleton a_1)) (Ne a empty_set)) False) (Eq (∀ (C : Iota), Not (And (in C a) (Ne C a_1))) False) % 4.69/4.93 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 4.69/4.93 Or (Eq (∀ (C : Iota), Not (And (in C a) (Ne C a_1))) False) % 4.69/4.93 (Or (Eq (Ne a (singleton a_1)) False) (Eq (Ne a empty_set) False)) % 4.69/4.93 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 4.69/4.93 Or (Eq (Ne a (singleton a_1)) False) % 4.69/4.93 (Or (Eq (Ne a empty_set) False) (Eq (Not (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)))) True)) % 4.69/4.93 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 4.69/4.93 Or (Eq (Ne a empty_set) False) % 4.69/4.93 (Or (Eq (Not (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)))) True) (Eq a (singleton a_1))) % 4.69/4.93 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 4.69/4.93 Or (Eq (Not (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)))) True) % 4.69/4.93 (Or (Eq a (singleton a_1)) (Eq a empty_set)) % 4.69/4.93 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 4.69/4.93 Or (Eq a (singleton a_1)) % 4.69/4.93 (Or (Eq a empty_set) (Eq (Not (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1))) False)) % 4.69/4.93 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.69/4.93 Or (Eq a (singleton a_1)) % 4.69/4.93 (Or (Eq a empty_set) (Eq (And (in (skS.0 2 a a_1 a_2) a) (Ne (skS.0 2 a a_1 a_2) a_1)) True)) % 4.69/4.93 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq a empty_set) (Eq (Ne (skS.0 2 a a_1 a_2) a_1) True)) % 4.69/4.93 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq a empty_set) (Eq (in (skS.0 2 a a_1 a_2) a) True)) % 4.69/4.93 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq a empty_set) (Ne (skS.0 2 a a_1 a_2) a_1)) % 4.69/4.93 Clause #27 (by clausification #[4]): Eq (∀ (A B : Iota), Not (And (And (Ne A (singleton B)) (Ne A empty_set)) (∀ (C : Iota), Not (And (in C A) (Ne C B))))) % 4.69/4.93 False % 4.69/4.93 Clause #28 (by clausification #[27]): ∀ (a : Iota), % 4.69/4.93 Eq % 4.69/4.93 (Not % 4.69/4.93 (∀ (B : Iota), % 4.69/4.93 Not % 4.69/4.93 (And (And (Ne (skS.0 3 a) (singleton B)) (Ne (skS.0 3 a) empty_set)) % 4.69/4.93 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C B)))))) % 4.69/4.93 True % 4.69/4.93 Clause #29 (by clausification #[28]): ∀ (a : Iota), % 4.69/4.93 Eq % 4.69/4.93 (∀ (B : Iota), % 4.69/4.93 Not % 4.69/4.93 (And (And (Ne (skS.0 3 a) (singleton B)) (Ne (skS.0 3 a) empty_set)) % 4.69/4.93 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C B))))) % 4.69/4.93 False % 4.69/4.93 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 4.69/4.93 Eq % 4.69/4.93 (Not % 4.69/4.93 (Not % 4.69/4.93 (And (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set)) % 4.69/4.93 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1))))))) % 4.69/4.93 True % 4.69/4.93 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.69/4.93 Eq % 4.69/4.93 (Not % 4.69/4.93 (And (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set)) % 4.69/4.93 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1)))))) % 4.69/4.93 False % 4.69/4.93 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 4.69/4.93 Eq % 4.69/4.93 (And (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set)) % 4.69/4.94 (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1))))) % 4.69/4.94 True % 4.69/4.94 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Not (And (in C (skS.0 3 a)) (Ne C (skS.0 4 a a_1)))) True % 4.69/4.94 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (And (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Ne (skS.0 3 a) empty_set)) True % 4.69/4.94 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Not (And (in a (skS.0 3 a_1)) (Ne a (skS.0 4 a_1 a_2)))) True % 4.69/4.94 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (And (in a (skS.0 3 a_1)) (Ne a (skS.0 4 a_1 a_2))) False % 4.69/4.94 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 3 a_1)) False) (Eq (Ne a (skS.0 4 a_1 a_2)) False) % 4.69/4.94 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 3 a_1)) False) (Eq a (skS.0 4 a_1 a_2)) % 4.69/4.94 Clause #43 (by superposition #[25, 38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.69/4.94 Or (Eq (skS.0 2 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) % 4.69/4.94 (Or (Eq (skS.0 3 a) (singleton a_1)) (Or (Eq (skS.0 3 a) empty_set) (Eq False True))) % 4.69/4.94 Clause #55 (by clausification #[34]): ∀ (a : Iota), Eq (Ne (skS.0 3 a) empty_set) True % 4.69/4.94 Clause #56 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 3 a) (singleton (skS.0 4 a a_1))) True % 4.69/4.94 Clause #57 (by clausification #[55]): ∀ (a : Iota), Ne (skS.0 3 a) empty_set % 4.69/4.94 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Ne (skS.0 3 a) (singleton (skS.0 4 a a_1)) % 4.69/4.94 Clause #241 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.69/4.94 Or (Eq (skS.0 2 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) (Or (Eq (skS.0 3 a) (singleton a_1)) (Eq (skS.0 3 a) empty_set)) % 4.69/4.94 Clause #242 (by forward contextual literal cutting #[241, 57]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 2 (skS.0 3 a) a_1 a_2) (skS.0 4 a a_3)) (Eq (skS.0 3 a) (singleton a_1)) % 4.69/4.94 Clause #244 (by superposition #[242, 26]): ∀ (a a_1 a_2 : Iota), % 4.69/4.94 Or (Eq (skS.0 3 a) (singleton a_1)) % 4.69/4.94 (Or (Eq (skS.0 3 a) (singleton a_1)) (Or (Eq (skS.0 3 a) empty_set) (Ne (skS.0 4 a a_2) a_1))) % 4.69/4.94 Clause #349 (by eliminate duplicate literals #[244]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 3 a) (singleton a_1)) (Or (Eq (skS.0 3 a) empty_set) (Ne (skS.0 4 a a_2) a_1)) % 4.69/4.94 Clause #350 (by destructive equality resolution #[349]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a) (singleton (skS.0 4 a a_1))) (Eq (skS.0 3 a) empty_set) % 4.69/4.94 Clause #351 (by forward contextual literal cutting #[350, 58]): ∀ (a : Iota), Eq (skS.0 3 a) empty_set % 4.69/4.94 Clause #352 (by forward contextual literal cutting #[351, 57]): False % 4.69/4.94 SZS output end Proof for theBenchmark.p 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