%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET575+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:00:09 PM UTC 2025 % Result : Theorem 3.69s 3.87s % Output : Proof 3.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET575+3 : TPTP v9.2.0. Released v2.2.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n024.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 13:55:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.69/3.87 SZS status Theorem for theBenchmark.p % 3.69/3.87 SZS output start Proof for theBenchmark.p % 3.69/3.87 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 3.69/3.87 Clause #2 (by assumption #[]): Eq (Not (∀ (B C : Iota), intersect B C → Exists fun D => And (member D B) (member D C))) True % 3.69/3.87 Clause #6 (by clausification #[2]): Eq (∀ (B C : Iota), intersect B C → Exists fun D => And (member D B) (member D C)) False % 3.69/3.87 Clause #7 (by clausification #[6]): ∀ (a : Iota), % 3.69/3.87 Eq (Not (∀ (C : Iota), intersect (skS.0 0 a) C → Exists fun D => And (member D (skS.0 0 a)) (member D C))) True % 3.69/3.87 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (C : Iota), intersect (skS.0 0 a) C → Exists fun D => And (member D (skS.0 0 a)) (member D C)) False % 3.69/3.87 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 3.69/3.87 Eq % 3.69/3.87 (Not % 3.69/3.87 (intersect (skS.0 0 a) (skS.0 1 a a_1) → Exists fun D => And (member D (skS.0 0 a)) (member D (skS.0 1 a a_1)))) % 3.69/3.87 True % 3.69/3.87 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 3.69/3.87 Eq (intersect (skS.0 0 a) (skS.0 1 a a_1) → Exists fun D => And (member D (skS.0 0 a)) (member D (skS.0 1 a a_1))) % 3.69/3.87 False % 3.69/3.87 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True % 3.69/3.87 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Exists fun D => And (member D (skS.0 0 a)) (member D (skS.0 1 a a_1))) False % 3.69/3.87 Clause #14 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 3.69/3.87 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 3.69/3.87 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 3.69/3.87 Clause #20 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.69/3.87 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 2 a a_1 a_2) a) (member (skS.0 2 a a_1 a_2) a_1)) True) % 3.69/3.87 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 2 a a_1 a_2) a_1) True) % 3.69/3.87 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 2 a a_1 a_2) a) True) % 3.69/3.87 Clause #23 (by superposition #[21, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True) (Eq False True) % 3.69/3.87 Clause #24 (by superposition #[22, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) (Eq False True) % 3.69/3.87 Clause #25 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (And (member a (skS.0 0 a_1)) (member a (skS.0 1 a_1 a_2))) False % 3.69/3.87 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (skS.0 0 a_1)) False) (Eq (member a (skS.0 1 a_1 a_2)) False) % 3.69/3.87 Clause #31 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True % 3.69/3.87 Clause #32 (by superposition #[31, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.87 Or (Eq True False) (Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_3)) False) % 3.69/3.87 Clause #39 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True % 3.69/3.87 Clause #41 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_3)) False % 3.69/3.87 Clause #42 (by superposition #[41, 39]): Eq False True % 3.69/3.87 Clause #43 (by clausification #[42]): False % 3.69/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------