%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU606^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:02:01 PM UTC 2025 % Result : Theorem 4.23s 4.43s % Output : Proof 4.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU606^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n029.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 06:02:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.23/4.43 SZS status Theorem for theBenchmark.p % 4.23/4.43 SZS output start Proof for theBenchmark.p % 4.23/4.43 Clause #0 (by assumption #[]): Eq (Eq setminusERneg (∀ (A B Xx : Iota), Not (in Xx (setminus A B)) → in Xx A → in Xx B)) True % 4.23/4.43 Clause #1 (by assumption #[]): Eq (Not (setminusERneg → ∀ (A B Xx : Iota), Not (in Xx (setminus A B)) → Not (in Xx B) → Not (in Xx A))) True % 4.23/4.43 Clause #2 (by clausification #[1]): Eq (setminusERneg → ∀ (A B Xx : Iota), Not (in Xx (setminus A B)) → Not (in Xx B) → Not (in Xx A)) False % 4.23/4.43 Clause #3 (by clausification #[2]): Eq setminusERneg True % 4.23/4.43 Clause #4 (by clausification #[2]): Eq (∀ (A B Xx : Iota), Not (in Xx (setminus A B)) → Not (in Xx B) → Not (in Xx A)) False % 4.23/4.43 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 4.23/4.43 Eq (Not (∀ (B Xx : Iota), Not (in Xx (setminus (skS.0 0 a) B)) → Not (in Xx B) → Not (in Xx (skS.0 0 a)))) True % 4.23/4.43 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), Not (in Xx (setminus (skS.0 0 a) B)) → Not (in Xx B) → Not (in Xx (skS.0 0 a))) False % 4.23/4.43 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.23/4.43 Eq % 4.23/4.43 (Not % 4.23/4.43 (∀ (Xx : Iota), % 4.23/4.43 Not (in Xx (setminus (skS.0 0 a) (skS.0 1 a a_1))) → Not (in Xx (skS.0 1 a a_1)) → Not (in Xx (skS.0 0 a)))) % 4.23/4.43 True % 4.23/4.43 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.23/4.43 Eq % 4.23/4.43 (∀ (Xx : Iota), % 4.23/4.43 Not (in Xx (setminus (skS.0 0 a) (skS.0 1 a a_1))) → Not (in Xx (skS.0 1 a a_1)) → Not (in Xx (skS.0 0 a))) % 4.23/4.43 False % 4.23/4.43 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.23/4.43 Eq % 4.23/4.43 (Not % 4.23/4.43 (Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) → % 4.23/4.43 Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) → Not (in (skS.0 2 a a_1 a_2) (skS.0 0 a)))) % 4.23/4.43 True % 4.23/4.43 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.23/4.43 Eq % 4.23/4.43 (Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) → % 4.23/4.43 Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) → Not (in (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 4.23/4.43 False % 4.23/4.43 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1)))) True % 4.23/4.43 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) → Not (in (skS.0 2 a a_1 a_2) (skS.0 0 a))) False % 4.23/4.43 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) (skS.0 1 a a_1))) False % 4.23/4.43 Clause #14 (by clausification #[0]): Eq setminusERneg (∀ (A B Xx : Iota), Not (in Xx (setminus A B)) → in Xx A → in Xx B) % 4.23/4.43 Clause #15 (by forward demodulation #[14, 3]): Eq True (∀ (A B Xx : Iota), Not (in Xx (setminus A B)) → in Xx A → in Xx B) % 4.23/4.43 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), Not (in Xx (setminus a B)) → in Xx a → in Xx B) True % 4.23/4.43 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), Not (in Xx (setminus a a_1)) → in Xx a → in Xx a_1) True % 4.23/4.43 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (Not (in a (setminus a_1 a_2)) → in a a_1 → in a a_2) True % 4.23/4.43 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (in a (setminus a_1 a_2))) False) (Eq (in a a_1 → in a a_2) True) % 4.23/4.43 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1 → in a a_2) True) (Eq (in a (setminus a_1 a_2)) True) % 4.23/4.43 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) True) (Or (Eq (in a a_1) False) (Eq (in a a_2) True)) % 4.23/4.43 Clause #22 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) True % 4.23/4.43 Clause #23 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 2 a a_1 a_2) (skS.0 0 a))) False % 4.23/4.43 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 4.23/4.43 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 4.23/4.43 Clause #26 (by superposition #[25, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.23/4.43 Or (Eq (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) a_3)) True) % 4.23/4.43 (Or (Eq True False) (Eq (in (skS.0 2 a a_1 a_2) a_3) True)) % 4.29/4.44 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), % 4.29/4.44 Or (Eq (in (skS.0 2 a a_1 a_2) (setminus (skS.0 0 a) a_3)) True) (Eq (in (skS.0 2 a a_1 a_2) a_3) True) % 4.29/4.44 Clause #28 (by superposition #[27, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq True False) % 4.29/4.44 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 4.29/4.44 Clause #31 (by superposition #[30, 24]): Eq True False % 4.29/4.44 Clause #33 (by clausification #[31]): False % 4.29/4.44 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------