%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU823^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:02:31 PM UTC 2025 % Result : Theorem 3.71s 3.89s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU823^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.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 06:01:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.71/3.89 SZS status Theorem for theBenchmark.p % 3.71/3.89 SZS output start Proof for theBenchmark.p % 3.71/3.89 Clause #3 (by assumption #[]): Eq (Eq ordinalTransSet (∀ (X : Iota), ordinal X → ∀ (Xx A : Iota), in A X → in Xx A → in Xx X)) True % 3.71/3.89 Clause #4 (by assumption #[]): Eq (Eq ordinalIrrefl (∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → Not (in A A))) True % 3.71/3.89 Clause #5 (by assumption #[]): Eq (Not (ordinalTransSet → ordinalIrrefl → ∀ (X : Iota), ordinal X → ∀ (A : Iota), in X A → Not (in A X))) True % 3.71/3.89 Clause #13 (by clausification #[5]): Eq (ordinalTransSet → ordinalIrrefl → ∀ (X : Iota), ordinal X → ∀ (A : Iota), in X A → Not (in A X)) False % 3.71/3.89 Clause #14 (by clausification #[13]): Eq ordinalTransSet True % 3.71/3.89 Clause #15 (by clausification #[13]): Eq (ordinalIrrefl → ∀ (X : Iota), ordinal X → ∀ (A : Iota), in X A → Not (in A X)) False % 3.71/3.89 Clause #16 (by clausification #[15]): Eq ordinalIrrefl True % 3.71/3.89 Clause #17 (by clausification #[15]): Eq (∀ (X : Iota), ordinal X → ∀ (A : Iota), in X A → Not (in A X)) False % 3.71/3.89 Clause #20 (by clausification #[17]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 0 a) → ∀ (A : Iota), in (skS.0 0 a) A → Not (in A (skS.0 0 a)))) True % 3.71/3.89 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (ordinal (skS.0 0 a) → ∀ (A : Iota), in (skS.0 0 a) A → Not (in A (skS.0 0 a))) False % 3.71/3.89 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq (ordinal (skS.0 0 a)) True % 3.71/3.89 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (A : Iota), in (skS.0 0 a) A → Not (in A (skS.0 0 a))) False % 3.71/3.89 Clause #27 (by clausification #[4]): Eq ordinalIrrefl (∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → Not (in A A)) % 3.71/3.89 Clause #28 (by forward demodulation #[27, 16]): Eq True (∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → Not (in A A)) % 3.71/3.89 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (ordinal a → ∀ (A : Iota), in A a → Not (in A A)) True % 3.71/3.89 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (∀ (A : Iota), in A a → Not (in A A)) True) % 3.71/3.89 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (ordinal a) False) (Eq (in a_1 a → Not (in a_1 a_1)) True) % 3.71/3.89 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (ordinal a) False) (Or (Eq (in a_1 a) False) (Eq (Not (in a_1 a_1)) True)) % 3.71/3.89 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (ordinal a) False) (Or (Eq (in a_1 a) False) (Eq (in a_1 a_1) False)) % 3.71/3.89 Clause #34 (by superposition #[33, 22]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (in a a) False) (Eq False True)) % 3.71/3.89 Clause #35 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 0 a) (skS.0 1 a a_1) → Not (in (skS.0 1 a a_1) (skS.0 0 a)))) True % 3.71/3.89 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1) → Not (in (skS.0 1 a a_1) (skS.0 0 a))) False % 3.71/3.89 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True % 3.71/3.89 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 1 a a_1) (skS.0 0 a))) False % 3.71/3.89 Clause #39 (by clausification #[3]): Eq ordinalTransSet (∀ (X : Iota), ordinal X → ∀ (Xx A : Iota), in A X → in Xx A → in Xx X) % 3.71/3.89 Clause #40 (by forward demodulation #[39, 14]): Eq True (∀ (X : Iota), ordinal X → ∀ (Xx A : Iota), in A X → in Xx A → in Xx X) % 3.71/3.89 Clause #41 (by clausification #[40]): ∀ (a : Iota), Eq (ordinal a → ∀ (Xx A : Iota), in A a → in Xx A → in Xx a) True % 3.71/3.89 Clause #42 (by clausification #[41]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (∀ (Xx A : Iota), in A a → in Xx A → in Xx a) True) % 3.71/3.89 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (ordinal a) False) (Eq (∀ (A : Iota), in A a → in a_1 A → in a_1 a) True) % 3.71/3.89 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (ordinal a) False) (Eq (in a_1 a → in a_2 a_1 → in a_2 a) True) % 3.71/3.89 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (ordinal a) False) (Or (Eq (in a_1 a) False) (Eq (in a_2 a_1 → in a_2 a) True)) % 3.71/3.89 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 3.71/3.90 Or (Eq (ordinal a) False) (Or (Eq (in a_1 a) False) (Or (Eq (in a_2 a_1) False) (Eq (in a_2 a) True))) % 3.71/3.90 Clause #47 (by superposition #[46, 22]): ∀ (a a_1 a_2 : Iota), % 3.71/3.90 Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (in a_2 a) False) (Or (Eq (in a_2 (skS.0 0 a_1)) True) (Eq False True))) % 3.71/3.90 Clause #50 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a a) False) % 3.71/3.90 Clause #56 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (skS.0 0 a)) True % 3.71/3.90 Clause #79 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 (skS.0 0 a_1)) True)) % 3.71/3.90 Clause #80 (by superposition #[79, 56]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Or (Eq (in a (skS.0 0 a_1)) True) (Eq False True)) % 3.71/3.90 Clause #83 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Eq (in a (skS.0 0 a_1)) True) % 3.71/3.90 Clause #84 (by superposition #[83, 37]): ∀ (a : Iota), Or (Eq (in (skS.0 0 a) (skS.0 0 a)) True) (Eq False True) % 3.71/3.90 Clause #87 (by clausification #[84]): ∀ (a : Iota), Eq (in (skS.0 0 a) (skS.0 0 a)) True % 3.71/3.90 Clause #88 (by superposition #[87, 50]): Or (Eq True False) (Eq True False) % 3.71/3.90 Clause #90 (by clausification #[88]): Eq True False % 3.71/3.90 Clause #91 (by clausification #[90]): False % 3.71/3.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------