%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET633+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:00:19 PM UTC 2025 % Result : Theorem 7.99s 8.21s % Output : Proof 8.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET633+3 : TPTP v9.2.0. Released v2.2.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 14:40:53 EDT 2025 % 0.12/0.34 % CPUTime : % 7.99/8.21 SZS status Theorem for theBenchmark.p % 7.99/8.21 SZS output start Proof for theBenchmark.p % 7.99/8.21 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True % 7.99/8.21 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), And (subset B C) (subset D C) → subset (union B D) C) True % 7.99/8.21 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (symmetric_difference C B)) True % 7.99/8.21 Clause #8 (by assumption #[]): Eq % 7.99/8.21 (Not % 7.99/8.21 (∀ (B C D : Iota), % 7.99/8.21 And (subset (difference B C) D) (subset (difference C B) D) → subset (symmetric_difference B C) D)) % 7.99/8.21 True % 7.99/8.21 Clause #10 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (subset a C) (subset D C) → subset (union a D) C) True % 7.99/8.21 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), And (subset a a_1) (subset D a_1) → subset (union a D) a_1) True % 7.99/8.21 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_2 a_1) → subset (union a a_2) a_1) True % 7.99/8.21 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_2 a_1)) False) (Eq (subset (union a a_2) a_1) True) % 7.99/8.21 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (union a a_1) a_2) True) (Or (Eq (subset a a_2) False) (Eq (subset a_1 a_2) False)) % 7.99/8.21 Clause #16 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (symmetric_difference C a)) True % 7.99/8.21 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (symmetric_difference a_1 a)) True % 7.99/8.21 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (symmetric_difference a_1 a) % 7.99/8.21 Clause #22 (by clausification #[8]): Eq (∀ (B C D : Iota), And (subset (difference B C) D) (subset (difference C B) D) → subset (symmetric_difference B C) D) % 7.99/8.21 False % 7.99/8.21 Clause #23 (by clausification #[22]): ∀ (a : Iota), % 7.99/8.21 Eq % 7.99/8.21 (Not % 7.99/8.21 (∀ (C D : Iota), % 7.99/8.21 And (subset (difference (skS.0 0 a) C) D) (subset (difference C (skS.0 0 a)) D) → % 7.99/8.21 subset (symmetric_difference (skS.0 0 a) C) D)) % 7.99/8.21 True % 7.99/8.21 Clause #24 (by clausification #[23]): ∀ (a : Iota), % 7.99/8.21 Eq % 7.99/8.21 (∀ (C D : Iota), % 7.99/8.21 And (subset (difference (skS.0 0 a) C) D) (subset (difference C (skS.0 0 a)) D) → % 7.99/8.21 subset (symmetric_difference (skS.0 0 a) C) D) % 7.99/8.21 False % 7.99/8.21 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 7.99/8.21 Eq % 7.99/8.21 (Not % 7.99/8.21 (∀ (D : Iota), % 7.99/8.21 And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) D) (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) D) → % 7.99/8.21 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) D)) % 7.99/8.21 True % 7.99/8.21 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), % 7.99/8.21 Eq % 7.99/8.21 (∀ (D : Iota), % 7.99/8.21 And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) D) (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) D) → % 7.99/8.21 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) D) % 7.99/8.21 False % 7.99/8.21 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 7.99/8.21 Eq % 7.99/8.21 (Not % 7.99/8.21 (And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) % 7.99/8.21 (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) → % 7.99/8.21 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))) % 7.99/8.21 True % 7.99/8.21 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 7.99/8.21 Eq % 7.99/8.21 (And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) % 7.99/8.21 (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) → % 7.99/8.21 subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) % 7.99/8.21 False % 7.99/8.21 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 7.99/8.21 Eq % 7.99/8.21 (And (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) % 7.99/8.21 (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2))) % 7.99/8.21 True % 7.99/8.21 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) False % 7.99/8.21 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (subset (difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) True % 8.08/8.24 Clause #32 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) True % 8.08/8.24 Clause #33 (by superposition #[31, 14]): ∀ (a a_1 a_2 a_3 : Iota), % 8.08/8.24 Or (Eq (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) a_2) (skS.0 2 a a_1 a_3)) True) % 8.08/8.24 (Or (Eq True False) (Eq (subset a_2 (skS.0 2 a a_1 a_3)) False)) % 8.08/8.24 Clause #34 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True % 8.08/8.24 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True % 8.08/8.24 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a)) % 8.08/8.24 Clause #141 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 8.08/8.24 Or (Eq (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) a_2) (skS.0 2 a a_1 a_3)) True) % 8.08/8.24 (Eq (subset a_2 (skS.0 2 a a_1 a_3)) False) % 8.08/8.24 Clause #143 (by superposition #[141, 32]): ∀ (a a_1 a_2 : Iota), % 8.08/8.24 Or % 8.08/8.24 (Eq % 8.08/8.24 (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) (difference (skS.0 0 a) (skS.0 1 a a_1))) % 8.08/8.24 (skS.0 2 a a_1 a_2)) % 8.08/8.24 True) % 8.08/8.24 (Eq False True) % 8.08/8.24 Clause #2269 (by clausification #[143]): ∀ (a a_1 a_2 : Iota), % 8.08/8.24 Eq % 8.08/8.24 (subset (union (difference (skS.0 1 a a_1) (skS.0 0 a)) (difference (skS.0 0 a) (skS.0 1 a a_1))) % 8.08/8.24 (skS.0 2 a a_1 a_2)) % 8.08/8.24 True % 8.08/8.24 Clause #2270 (by forward demodulation #[2269, 36]): ∀ (a a_1 a_2 : Iota), Eq (subset (symmetric_difference (skS.0 1 a a_1) (skS.0 0 a)) (skS.0 2 a a_1 a_2)) True % 8.08/8.24 Clause #2271 (by forward demodulation #[2270, 18]): ∀ (a a_1 a_2 : Iota), Eq (subset (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) True % 8.08/8.24 Clause #2272 (by superposition #[2271, 30]): Eq True False % 8.08/8.24 Clause #2293 (by clausification #[2272]): False % 8.08/8.24 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------