%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET639+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 08:00:19 PM UTC 2025 % Result : Theorem 5.13s 5.29s % Output : Proof 5.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET639+3 : TPTP v9.2.0. Released v2.2.0. % 0.12/0.14 % Command : duper %s % 0.14/0.36 % Computer : n003.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 14:27:23 EDT 2025 % 0.14/0.36 % CPUTime : % 5.13/5.29 SZS status Theorem for theBenchmark.p % 5.13/5.29 SZS output start Proof for theBenchmark.p % 5.13/5.29 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), subset B C → Eq (intersection B C) B) True % 5.13/5.29 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 5.13/5.29 Clause #9 (by assumption #[]): Eq (Not (∀ (B C : Iota), And (subset B C) (Eq (intersection C B) empty_set) → Eq B empty_set)) True % 5.13/5.29 Clause #13 (by clausification #[9]): Eq (∀ (B C : Iota), And (subset B C) (Eq (intersection C B) empty_set) → Eq B empty_set) False % 5.13/5.29 Clause #14 (by clausification #[13]): ∀ (a : Iota), % 5.13/5.29 Eq % 5.13/5.29 (Not % 5.13/5.29 (∀ (C : Iota), And (subset (skS.0 0 a) C) (Eq (intersection C (skS.0 0 a)) empty_set) → Eq (skS.0 0 a) empty_set)) % 5.13/5.29 True % 5.13/5.29 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 5.13/5.29 Eq (∀ (C : Iota), And (subset (skS.0 0 a) C) (Eq (intersection C (skS.0 0 a)) empty_set) → Eq (skS.0 0 a) empty_set) % 5.13/5.29 False % 5.13/5.29 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 5.13/5.29 Eq % 5.13/5.29 (Not % 5.13/5.29 (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (Eq (intersection (skS.0 1 a a_1) (skS.0 0 a)) empty_set) → % 5.13/5.29 Eq (skS.0 0 a) empty_set)) % 5.13/5.29 True % 5.13/5.29 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 5.13/5.29 Eq % 5.13/5.29 (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (Eq (intersection (skS.0 1 a a_1) (skS.0 0 a)) empty_set) → % 5.13/5.29 Eq (skS.0 0 a) empty_set) % 5.13/5.29 False % 5.13/5.29 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 5.13/5.29 Eq (And (subset (skS.0 0 a) (skS.0 1 a a_1)) (Eq (intersection (skS.0 1 a a_1) (skS.0 0 a)) empty_set)) True % 5.13/5.29 Clause #19 (by clausification #[17]): ∀ (a : Iota), Eq (Eq (skS.0 0 a) empty_set) False % 5.13/5.29 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Eq (intersection (skS.0 1 a a_1) (skS.0 0 a)) empty_set) True % 5.13/5.29 Clause #21 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 5.13/5.29 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (intersection (skS.0 1 a a_1) (skS.0 0 a)) empty_set % 5.13/5.29 Clause #23 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), subset a C → Eq (intersection a C) a) True % 5.13/5.29 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (intersection a a_1) a) True % 5.13/5.29 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (intersection a a_1) a) True) % 5.13/5.29 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (intersection a a_1) a) % 5.13/5.29 Clause #47 (by clausification #[19]): ∀ (a : Iota), Ne (skS.0 0 a) empty_set % 5.13/5.29 Clause #79 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 5.13/5.29 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 5.13/5.29 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 5.13/5.29 Clause #82 (by superposition #[81, 22]): ∀ (a a_1 : Iota), Eq (intersection (skS.0 0 a) (skS.0 1 a a_1)) empty_set % 5.13/5.29 Clause #102 (by superposition #[21, 26]): ∀ (a a_1 : Iota), Or (Eq (intersection (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) (Eq False True) % 5.13/5.29 Clause #261 (by clausification #[102]): ∀ (a a_1 : Iota), Eq (intersection (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a) % 5.13/5.29 Clause #262 (by superposition #[261, 82]): ∀ (a : Iota), Eq (skS.0 0 a) empty_set % 5.13/5.29 Clause #271 (by forward contextual literal cutting #[262, 47]): False % 5.13/5.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------