%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET618+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:00:16 PM UTC 2025 % Result : Theorem 3.42s 3.65s % Output : Proof 3.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET618+3 : TPTP v9.2.0. Released v2.2.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.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 : Thu Oct 2 14:58:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.42/3.65 SZS status Theorem for theBenchmark.p % 3.42/3.65 SZS output start Proof for theBenchmark.p % 3.42/3.65 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True % 3.42/3.65 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Eq (union B B) B) True % 3.42/3.65 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Eq (difference B B) empty_set) True % 3.42/3.65 Clause #11 (by assumption #[]): Eq (Not (∀ (B : Iota), Eq (symmetric_difference B B) empty_set)) True % 3.42/3.65 Clause #15 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (difference a a) empty_set) True % 3.42/3.65 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (difference a a) empty_set % 3.42/3.65 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (Eq (union a a) a) True % 3.42/3.65 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (union a a) a % 3.42/3.65 Clause #19 (by clausification #[11]): Eq (∀ (B : Iota), Eq (symmetric_difference B B) empty_set) False % 3.42/3.65 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (Eq (symmetric_difference (skS.0 0 a) (skS.0 0 a)) empty_set)) True % 3.42/3.65 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (Eq (symmetric_difference (skS.0 0 a) (skS.0 0 a)) empty_set) False % 3.42/3.65 Clause #22 (by clausification #[21]): ∀ (a : Iota), Ne (symmetric_difference (skS.0 0 a) (skS.0 0 a)) empty_set % 3.42/3.65 Clause #23 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True % 3.42/3.65 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True % 3.42/3.65 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a)) % 3.42/3.65 Clause #27 (by superposition #[25, 16]): ∀ (a : Iota), Eq (symmetric_difference a a) (union empty_set empty_set) % 3.42/3.65 Clause #28 (by forward demodulation #[27, 18]): ∀ (a : Iota), Eq (symmetric_difference a a) empty_set % 3.42/3.65 Clause #30 (by backward contextual literal cutting #[28, 22]): False % 3.42/3.65 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------