%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU563^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 5.45s 5.70s % Output : Proof 5.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : SEU563^2 : TPTP v9.2.0. Released v3.7.0. % 0.02/0.10 % Command : duper %s % 0.09/0.29 % Computer : n012.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 300 % 0.09/0.29 % DateTime : Fri Oct 3 05:19:38 EDT 2025 % 0.09/0.30 % CPUTime : % 5.45/5.70 SZS status Theorem for theBenchmark.p % 5.45/5.70 SZS output start Proof for theBenchmark.p % 5.45/5.70 Clause #0 (by assumption #[]): Eq (Eq emptysetimpfalse (∀ (Xx : Iota), in Xx emptyset → False)) True % 5.45/5.70 Clause #2 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 5.45/5.70 Clause #3 (by assumption #[]): Eq (Not (emptysetimpfalse → subsetI2 → ∀ (A : Iota), subset emptyset A)) True % 5.45/5.70 Clause #4 (by clausification #[0]): Eq emptysetimpfalse (∀ (Xx : Iota), in Xx emptyset → False) % 5.45/5.70 Clause #18 (by clausification #[3]): Eq (emptysetimpfalse → subsetI2 → ∀ (A : Iota), subset emptyset A) False % 5.45/5.70 Clause #19 (by clausification #[18]): Eq emptysetimpfalse True % 5.45/5.70 Clause #20 (by clausification #[18]): Eq (subsetI2 → ∀ (A : Iota), subset emptyset A) False % 5.45/5.70 Clause #21 (by backward demodulation #[19, 4]): Eq True (∀ (Xx : Iota), in Xx emptyset → False) % 5.45/5.70 Clause #24 (by clausification #[21]): ∀ (a : Iota), Eq (in a emptyset → False) True % 5.45/5.70 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq False True) % 5.45/5.70 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (in a emptyset) False % 5.45/5.70 Clause #27 (by clausification #[20]): Eq subsetI2 True % 5.45/5.70 Clause #28 (by clausification #[20]): Eq (∀ (A : Iota), subset emptyset A) False % 5.45/5.70 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (Not (subset emptyset (skS.0 1 a))) True % 5.45/5.70 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (subset emptyset (skS.0 1 a)) False % 5.45/5.70 Clause #31 (by clausification #[2]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 5.45/5.70 Clause #32 (by forward demodulation #[31, 27]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 5.45/5.70 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 5.45/5.70 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 5.45/5.70 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 5.45/5.70 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 5.45/5.70 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) % 5.45/5.70 Clause #37 (by clausification #[36]): ∀ (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) % 5.45/5.70 Clause #38 (by clausification #[37]): ∀ (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) % 5.45/5.70 Clause #40 (by superposition #[38, 26]): ∀ (a : Iota), Or (Eq (subset emptyset a) True) (Eq True False) % 5.45/5.70 Clause #41 (by clausification #[40]): ∀ (a : Iota), Eq (subset emptyset a) True % 5.45/5.70 Clause #42 (by superposition #[41, 30]): Eq True False % 5.45/5.70 Clause #43 (by clausification #[42]): False % 5.45/5.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------