%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU566^2 : TPTP v9.2.0. Released v3.7.0. % 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 08:01:55 PM UTC 2025 % Result : Theorem 3.53s 3.75s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU566^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n002.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 06:09:23 EDT 2025 % 0.12/0.34 % CPUTime : % 3.53/3.75 SZS status Theorem for theBenchmark.p % 3.53/3.75 SZS output start Proof for theBenchmark.p % 3.53/3.75 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 3.53/3.75 Clause #1 (by assumption #[]): Eq (Not (subsetE → ∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → Not (subset A B))) True % 3.53/3.75 Clause #2 (by clausification #[1]): Eq (subsetE → ∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → Not (subset A B)) False % 3.53/3.75 Clause #3 (by clausification #[2]): Eq subsetE True % 3.53/3.75 Clause #4 (by clausification #[2]): Eq (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → Not (subset A B)) False % 3.53/3.75 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx B) → Not (subset (skS.0 0 a) B))) True % 3.53/3.75 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx B) → Not (subset (skS.0 0 a) B)) False % 3.53/3.75 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.53/3.75 Eq (Not (∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (skS.0 1 a a_1)) → Not (subset (skS.0 0 a) (skS.0 1 a a_1)))) % 3.53/3.75 True % 3.53/3.75 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 3.53/3.75 Eq (∀ (Xx : Iota), in Xx (skS.0 0 a) → Not (in Xx (skS.0 1 a a_1)) → Not (subset (skS.0 0 a) (skS.0 1 a a_1))) False % 3.53/3.75 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.53/3.75 Eq % 3.53/3.75 (Not % 3.53/3.75 (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → % 3.53/3.75 Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) → Not (subset (skS.0 0 a) (skS.0 1 a a_1)))) % 3.53/3.75 True % 3.53/3.75 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.53/3.75 Eq % 3.53/3.75 (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → % 3.53/3.75 Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) → Not (subset (skS.0 0 a) (skS.0 1 a a_1))) % 3.53/3.75 False % 3.53/3.75 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 3.53/3.75 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 (subset (skS.0 0 a) (skS.0 1 a a_1))) False % 3.53/3.75 Clause #13 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.53/3.75 Clause #14 (by forward demodulation #[13, 3]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.53/3.75 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 3.53/3.75 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 3.53/3.75 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 3.53/3.75 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.53/3.75 Clause #19 (by clausification #[18]): ∀ (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)) % 3.53/3.75 Clause #20 (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 % 3.53/3.75 Clause #21 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (skS.0 1 a a_1))) False % 3.53/3.75 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 3.53/3.75 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 3.53/3.75 Clause #24 (by superposition #[23, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a (skS.0 1 a_1 a_2)) True)) % 3.53/3.75 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a (skS.0 1 a_1 a_2)) True) % 3.53/3.75 Clause #26 (by superposition #[25, 11]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True) (Eq False True) % 3.53/3.75 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True % 3.53/3.75 Clause #28 (by superposition #[27, 22]): Eq True False % 3.53/3.75 Clause #29 (by clausification #[28]): False % 3.53/3.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------