%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET617+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 4.04s 4.24s % Output : Proof 4.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.15 % Problem : SET617+3 : TPTP v9.2.0. Released v2.2.0. % 0.08/0.16 % Command : duper %s % 0.13/0.37 % Computer : n022.cluster.edu % 0.13/0.37 % Model : x86_64 x86_64 % 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.37 % Memory : 8042.1875MB % 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.37 % CPULimit : 300 % 0.13/0.37 % WCLimit : 300 % 0.13/0.37 % DateTime : Thu Oct 2 14:29:23 EDT 2025 % 0.13/0.38 % CPUTime : % 4.04/4.24 SZS status Theorem for theBenchmark.p % 4.04/4.24 SZS output start Proof for theBenchmark.p % 4.04/4.24 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True % 4.04/4.24 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Eq (union B empty_set) B) True % 4.04/4.24 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Eq (difference B empty_set) B) True % 4.04/4.24 Clause #3 (by assumption #[]): Eq (∀ (B : Iota), Eq (difference empty_set B) empty_set) True % 4.04/4.24 Clause #6 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True % 4.04/4.24 Clause #12 (by assumption #[]): Eq (Not (∀ (B : Iota), And (Eq (symmetric_difference B empty_set) B) (Eq (symmetric_difference empty_set B) B))) True % 4.04/4.24 Clause #16 (by clausification #[3]): ∀ (a : Iota), Eq (Eq (difference empty_set a) empty_set) True % 4.04/4.24 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (difference empty_set a) empty_set % 4.04/4.24 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (difference a empty_set) a) True % 4.04/4.24 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (difference a empty_set) a % 4.04/4.24 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (Eq (union a empty_set) a) True % 4.04/4.24 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (union a empty_set) a % 4.04/4.24 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True % 4.04/4.24 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True % 4.04/4.24 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a)) % 4.04/4.24 Clause #27 (by superposition #[24, 19]): ∀ (a : Iota), Eq (symmetric_difference a empty_set) (union a (difference empty_set a)) % 4.04/4.24 Clause #28 (by superposition #[24, 17]): ∀ (a : Iota), Eq (symmetric_difference empty_set a) (union empty_set (difference a empty_set)) % 4.04/4.24 Clause #29 (by forward demodulation #[28, 19]): ∀ (a : Iota), Eq (symmetric_difference empty_set a) (union empty_set a) % 4.04/4.24 Clause #31 (by forward demodulation #[27, 17]): ∀ (a : Iota), Eq (symmetric_difference a empty_set) (union a empty_set) % 4.04/4.24 Clause #32 (by superposition #[31, 21]): ∀ (a : Iota), Eq (symmetric_difference a empty_set) a % 4.04/4.24 Clause #51 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True % 4.04/4.24 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True % 4.04/4.24 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a) % 4.04/4.24 Clause #55 (by superposition #[53, 21]): ∀ (a : Iota), Eq (union empty_set a) a % 4.04/4.24 Clause #57 (by superposition #[55, 29]): ∀ (a : Iota), Eq (symmetric_difference empty_set a) a % 4.04/4.24 Clause #95 (by clausification #[12]): Eq (∀ (B : Iota), And (Eq (symmetric_difference B empty_set) B) (Eq (symmetric_difference empty_set B) B)) False % 4.04/4.24 Clause #96 (by clausification #[95]): ∀ (a : Iota), % 4.04/4.24 Eq % 4.04/4.24 (Not % 4.04/4.24 (And (Eq (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a)) % 4.04/4.24 (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)))) % 4.04/4.24 True % 4.04/4.24 Clause #97 (by clausification #[96]): ∀ (a : Iota), % 4.04/4.24 Eq % 4.04/4.24 (And (Eq (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a)) % 4.04/4.24 (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a))) % 4.04/4.24 False % 4.04/4.24 Clause #98 (by clausification #[97]): ∀ (a : Iota), % 4.04/4.24 Or (Eq (Eq (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a)) False) % 4.04/4.24 (Eq (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)) False) % 4.04/4.24 Clause #99 (by clausification #[98]): ∀ (a : Iota), % 4.04/4.24 Or (Eq (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)) False) % 4.04/4.24 (Ne (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a)) % 4.04/4.24 Clause #100 (by clausification #[99]): ∀ (a : Iota), % 4.04/4.24 Or (Ne (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a)) % 4.04/4.24 (Ne (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)) % 4.04/4.24 Clause #101 (by forward demodulation #[100, 32]): ∀ (a : Iota), Or (Ne (skS.0 3 a) (skS.0 3 a)) (Ne (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)) % 4.04/4.24 Clause #102 (by eliminate resolved literals #[101]): ∀ (a : Iota), Ne (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a) % 4.04/4.24 Clause #103 (by forward demodulation #[102, 57]): ∀ (a : Iota), Ne (skS.0 3 a) (skS.0 3 a) % 4.04/4.24 Clause #104 (by eliminate resolved literals #[103]): False % 4.04/4.24 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------