%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU588^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:01:59 PM UTC 2025 % Result : Theorem 4.47s 4.63s % Output : Proof 4.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU588^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.15 % Command : duper %s % 0.15/0.36 % Computer : n005.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Fri Oct 3 04:41:08 EDT 2025 % 0.15/0.37 % CPUTime : % 4.47/4.63 SZS status Theorem for theBenchmark.p % 4.47/4.63 SZS output start Proof for theBenchmark.p % 4.47/4.63 Clause #0 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 4.47/4.63 Clause #1 (by assumption #[]): Eq (Eq binunionIR (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B))) True % 4.47/4.63 Clause #2 (by assumption #[]): Eq (Not (subsetI2 → binunionIR → ∀ (A B : Iota), subset B (binunion A B))) True % 4.47/4.63 Clause #3 (by clausification #[0]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.47/4.63 Clause #22 (by clausification #[2]): Eq (subsetI2 → binunionIR → ∀ (A B : Iota), subset B (binunion A B)) False % 4.47/4.63 Clause #23 (by clausification #[22]): Eq subsetI2 True % 4.47/4.63 Clause #24 (by clausification #[22]): Eq (binunionIR → ∀ (A B : Iota), subset B (binunion A B)) False % 4.47/4.63 Clause #25 (by backward demodulation #[23, 3]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.47/4.63 Clause #28 (by clausification #[1]): Eq binunionIR (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) % 4.47/4.63 Clause #32 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 4.47/4.63 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 4.47/4.63 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 4.47/4.63 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 4.47/4.63 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 4.47/4.63 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1) False) % 4.47/4.63 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a) True) % 4.47/4.63 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a_1) False) % 4.47/4.63 Clause #39 (by clausification #[24]): Eq binunionIR True % 4.47/4.63 Clause #40 (by clausification #[24]): Eq (∀ (A B : Iota), subset B (binunion A B)) False % 4.47/4.63 Clause #41 (by backward demodulation #[39, 28]): Eq True (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) % 4.47/4.63 Clause #42 (by clausification #[40]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset B (binunion (skS.0 4 a) B))) True % 4.47/4.63 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B (binunion (skS.0 4 a) B)) False % 4.47/4.63 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 5 a a_1) (binunion (skS.0 4 a) (skS.0 5 a a_1)))) True % 4.47/4.63 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (subset (skS.0 5 a a_1) (binunion (skS.0 4 a) (skS.0 5 a a_1))) False % 4.47/4.63 Clause #46 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx B → in Xx (binunion a B)) True % 4.47/4.63 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a_1 a)) True % 4.47/4.63 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_2 a_1)) True % 4.47/4.63 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_2 a_1)) True) % 4.47/4.63 Clause #50 (by superposition #[49, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.63 Or (Eq (in (skS.0 3 a a_1 a_2) (binunion a_3 a)) True) (Or (Eq (subset a a_1) True) (Eq False True)) % 4.47/4.63 Clause #74 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 3 a a_1 a_2) (binunion a_3 a)) True) (Eq (subset a a_1) True) % 4.47/4.63 Clause #75 (by superposition #[74, 38]): ∀ (a a_1 : Iota), Or (Eq (subset a (binunion a_1 a)) True) (Or (Eq (subset a (binunion a_1 a)) True) (Eq True False)) % 4.47/4.63 Clause #77 (by clausification #[75]): ∀ (a a_1 : Iota), Or (Eq (subset a (binunion a_1 a)) True) (Eq (subset a (binunion a_1 a)) True) % 4.47/4.63 Clause #78 (by eliminate duplicate literals #[77]): ∀ (a a_1 : Iota), Eq (subset a (binunion a_1 a)) True % 4.47/4.63 Clause #79 (by superposition #[78, 45]): Eq True False % 4.47/4.63 Clause #80 (by clausification #[79]): False % 4.47/4.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------