%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET620+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 5.07s 5.21s % Output : Proof 5.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET620+3 : TPTP v9.2.0. Released v2.2.0. % 0.11/0.13 % Command : duper %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 14:45:08 EDT 2025 % 0.12/0.34 % CPUTime : % 5.07/5.21 SZS status Theorem for theBenchmark.p % 5.07/5.21 SZS output start Proof for theBenchmark.p % 5.07/5.21 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True % 5.07/5.21 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Eq (difference B (intersection B C)) (difference B C)) True % 5.07/5.21 Clause #2 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (difference (union B C) D) (union (difference B D) (difference C D))) True % 5.07/5.21 Clause #7 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True % 5.07/5.21 Clause #8 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 5.07/5.21 Clause #13 (by assumption #[]): Eq (Not (∀ (B C : Iota), Eq (symmetric_difference B C) (difference (union B C) (intersection B C)))) True % 5.07/5.21 Clause #18 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 5.07/5.21 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 5.07/5.21 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 5.07/5.21 Clause #21 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True % 5.07/5.21 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True % 5.07/5.21 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a) % 5.07/5.21 Clause #32 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True % 5.07/5.21 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True % 5.07/5.21 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a)) % 5.07/5.21 Clause #36 (by superposition #[34, 23]): ∀ (a a_1 : Iota), Eq (union (difference a a_1) (difference a_1 a)) (symmetric_difference a_1 a) % 5.07/5.21 Clause #42 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (difference a (intersection a C)) (difference a C)) True % 5.07/5.21 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (Eq (difference a (intersection a a_1)) (difference a a_1)) True % 5.07/5.21 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (difference a (intersection a a_1)) (difference a a_1) % 5.07/5.21 Clause #49 (by superposition #[44, 20]): ∀ (a a_1 : Iota), Eq (difference a (intersection a_1 a)) (difference a a_1) % 5.07/5.21 Clause #66 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (difference (union a C) D) (union (difference a D) (difference C D))) True % 5.07/5.21 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Eq (difference (union a a_1) D) (union (difference a D) (difference a_1 D))) True % 5.07/5.21 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Eq (Eq (difference (union a a_1) a_2) (union (difference a a_2) (difference a_1 a_2))) True % 5.07/5.21 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (difference (union a a_1) a_2) (union (difference a a_2) (difference a_1 a_2)) % 5.07/5.21 Clause #76 (by superposition #[69, 23]): ∀ (a a_1 a_2 : Iota), Eq (union (difference a a_1) (difference a_2 a_1)) (difference (union a_2 a) a_1) % 5.07/5.21 Clause #111 (by superposition #[76, 49]): ∀ (a a_1 a_2 : Iota), % 5.07/5.21 Eq (union (difference a a_1) (difference a_2 (intersection a_1 a))) (difference (union a_2 a) (intersection a_1 a)) % 5.07/5.21 Clause #182 (by clausification #[13]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (difference (union B C) (intersection B C))) False % 5.07/5.21 Clause #183 (by clausification #[182]): ∀ (a : Iota), % 5.07/5.21 Eq % 5.07/5.21 (Not % 5.07/5.21 (∀ (C : Iota), % 5.07/5.21 Eq (symmetric_difference (skS.0 2 a) C) (difference (union (skS.0 2 a) C) (intersection (skS.0 2 a) C)))) % 5.07/5.21 True % 5.07/5.21 Clause #184 (by clausification #[183]): ∀ (a : Iota), % 5.07/5.21 Eq % 5.07/5.21 (∀ (C : Iota), % 5.07/5.21 Eq (symmetric_difference (skS.0 2 a) C) (difference (union (skS.0 2 a) C) (intersection (skS.0 2 a) C))) % 5.07/5.21 False % 5.07/5.21 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), % 5.07/5.21 Eq % 5.07/5.21 (Not % 5.07/5.21 (Eq (symmetric_difference (skS.0 2 a) (skS.0 3 a a_1)) % 5.07/5.22 (difference (union (skS.0 2 a) (skS.0 3 a a_1)) (intersection (skS.0 2 a) (skS.0 3 a a_1))))) % 5.07/5.22 True % 5.07/5.22 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), % 5.07/5.22 Eq % 5.07/5.22 (Eq (symmetric_difference (skS.0 2 a) (skS.0 3 a a_1)) % 5.07/5.22 (difference (union (skS.0 2 a) (skS.0 3 a a_1)) (intersection (skS.0 2 a) (skS.0 3 a a_1)))) % 5.07/5.22 False % 5.07/5.22 Clause #187 (by clausification #[186]): ∀ (a a_1 : Iota), % 5.07/5.22 Ne (symmetric_difference (skS.0 2 a) (skS.0 3 a a_1)) % 5.07/5.22 (difference (union (skS.0 2 a) (skS.0 3 a a_1)) (intersection (skS.0 2 a) (skS.0 3 a a_1))) % 5.07/5.22 Clause #280 (by superposition #[111, 44]): ∀ (a a_1 : Iota), Eq (union (difference a a_1) (difference a_1 a)) (difference (union a_1 a) (intersection a_1 a)) % 5.07/5.22 Clause #456 (by superposition #[280, 36]): ∀ (a a_1 : Iota), Eq (difference (union a a_1) (intersection a a_1)) (symmetric_difference a a_1) % 5.07/5.22 Clause #485 (by backward contextual literal cutting #[456, 187]): False % 5.07/5.22 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------