%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU577^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:01:57 PM UTC 2025 % Result : Theorem 3.68s 3.91s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU577^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n009.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 06:23:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.68/3.91 SZS status Theorem for theBenchmark.p % 3.68/3.91 SZS output start Proof for theBenchmark.p % 3.68/3.91 Clause #0 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True % 3.68/3.91 Clause #1 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 3.68/3.91 Clause #2 (by assumption #[]): Eq (Not (powersetE → subsetI1 → ∀ (A B : Iota), in B (powerset A) → subset B A)) True % 3.68/3.91 Clause #3 (by clausification #[2]): Eq (powersetE → subsetI1 → ∀ (A B : Iota), in B (powerset A) → subset B A) False % 3.68/3.91 Clause #4 (by clausification #[3]): Eq powersetE True % 3.68/3.91 Clause #5 (by clausification #[3]): Eq (subsetI1 → ∀ (A B : Iota), in B (powerset A) → subset B A) False % 3.68/3.91 Clause #6 (by clausification #[5]): Eq subsetI1 True % 3.68/3.91 Clause #7 (by clausification #[5]): Eq (∀ (A B : Iota), in B (powerset A) → subset B A) False % 3.68/3.91 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in B (powerset (skS.0 0 a)) → subset B (skS.0 0 a))) True % 3.68/3.91 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), in B (powerset (skS.0 0 a)) → subset B (skS.0 0 a)) False % 3.68/3.91 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → subset (skS.0 1 a a_1) (skS.0 0 a))) True % 3.68/3.91 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → subset (skS.0 1 a a_1) (skS.0 0 a)) False % 3.68/3.91 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True % 3.68/3.91 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) False % 3.68/3.91 Clause #14 (by clausification #[1]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.68/3.91 Clause #15 (by forward demodulation #[14, 6]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.68/3.91 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 3.68/3.91 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 3.68/3.91 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) % 3.68/3.91 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 3.68/3.91 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) % 3.68/3.91 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) % 3.68/3.91 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) % 3.68/3.91 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) % 3.68/3.91 Clause #23 (by clausification #[0]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 3.68/3.91 Clause #24 (by forward demodulation #[23, 4]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 3.68/3.91 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True % 3.68/3.91 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True % 3.68/3.91 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True % 3.68/3.91 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.68/3.91 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 3.68/3.91 Clause #30 (by superposition #[29, 12]): ∀ (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)) % 3.68/3.91 Clause #35 (by clausification #[30]): ∀ (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) % 3.68/3.91 Clause #36 (by superposition #[35, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 3.68/3.92 Or (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True) % 3.68/3.92 (Or (Eq (subset (skS.0 1 a a_1) a_2) True) (Eq False True)) % 3.68/3.92 Clause #39 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 3.68/3.92 Or (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True) (Eq (subset (skS.0 1 a a_1) a_2) True) % 3.68/3.92 Clause #40 (by superposition #[39, 22]): ∀ (a a_1 : Iota), % 3.68/3.92 Or (Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) True) (Or (Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) True) (Eq True False)) % 3.68/3.92 Clause #46 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) True) (Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) True) % 3.68/3.92 Clause #47 (by eliminate duplicate literals #[46]): ∀ (a a_1 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) True % 3.68/3.92 Clause #48 (by superposition #[47, 13]): Eq True False % 3.68/3.92 Clause #49 (by clausification #[48]): False % 3.68/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------