%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU562^2 : TPTP v9.2.0. Released v3.7.0. % 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 08:01:55 PM UTC 2025 % Result : Theorem 5.07s 5.28s % Output : Proof 5.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU562^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % 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 04:36:23 EDT 2025 % 0.13/0.34 % CPUTime : % 5.07/5.28 SZS status Theorem for theBenchmark.p % 5.07/5.28 SZS output start Proof for theBenchmark.p % 5.07/5.28 Clause #1 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 5.07/5.28 Clause #2 (by assumption #[]): Eq (Not (subsetI1 → ∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 5.07/5.28 Clause #3 (by clausification #[2]): Eq (subsetI1 → ∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) False % 5.07/5.28 Clause #4 (by clausification #[3]): Eq subsetI1 True % 5.07/5.28 Clause #5 (by clausification #[3]): Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) False % 5.07/5.28 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx B) → subset (skS.0 0 a) B)) True % 5.07/5.28 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx B) → subset (skS.0 0 a) B) False % 5.07/5.28 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 5.07/5.28 Eq (Not ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) → subset (skS.0 0 a) (skS.0 1 a a_1))) True % 5.07/5.28 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 5.07/5.28 Eq ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) → subset (skS.0 0 a) (skS.0 1 a a_1)) False % 5.07/5.28 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) True % 5.07/5.28 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) False % 5.07/5.28 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 0 a_1) → in a (skS.0 1 a_1 a_2)) True % 5.07/5.28 Clause #13 (by clausification #[12]): ∀ (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) % 5.07/5.28 Clause #14 (by clausification #[1]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 5.07/5.28 Clause #15 (by forward demodulation #[14, 4]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 5.07/5.28 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 5.07/5.28 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 5.07/5.28 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 5.07/5.28 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 5.07/5.28 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 5.07/5.28 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 5.07/5.28 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a) True) % 5.07/5.28 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False) % 5.07/5.28 Clause #23 (by superposition #[21, 13]): ∀ (a a_1 a_2 a_3 : Iota), % 5.07/5.28 Or (Eq (subset (skS.0 0 a) a_1) True) % 5.07/5.28 (Or (Eq True False) (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True)) % 5.07/5.28 Clause #61 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 5.07/5.28 Or (Eq (subset (skS.0 0 a) a_1) True) (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) % 5.07/5.28 Clause #62 (by superposition #[61, 22]): ∀ (a a_1 : Iota), % 5.07/5.28 Or (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)) % 5.07/5.28 Clause #378 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.07/5.28 Clause #379 (by eliminate duplicate literals #[378]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 5.07/5.28 Clause #380 (by superposition #[379, 11]): Eq True False % 5.07/5.28 Clause #383 (by clausification #[380]): False % 5.07/5.28 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------