%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET576+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:00:10 PM UTC 2025 % Result : Theorem 4.27s 4.48s % Output : Proof 4.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET576+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 14:25:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.27/4.48 SZS status Theorem for theBenchmark.p % 4.27/4.48 SZS output start Proof for theBenchmark.p % 4.27/4.48 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 4.27/4.48 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (disjoint B C) (Not (intersect B C))) True % 4.27/4.48 Clause #3 (by assumption #[]): Eq (Not (∀ (B C : Iota), (∀ (D : Iota), member D B → Not (member D C)) → disjoint B C)) True % 4.27/4.48 Clause #7 (by clausification #[3]): Eq (∀ (B C : Iota), (∀ (D : Iota), member D B → Not (member D C)) → disjoint B C) False % 4.27/4.48 Clause #8 (by clausification #[7]): ∀ (a : Iota), % 4.27/4.48 Eq (Not (∀ (C : Iota), (∀ (D : Iota), member D (skS.0 0 a) → Not (member D C)) → disjoint (skS.0 0 a) C)) True % 4.27/4.48 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C : Iota), (∀ (D : Iota), member D (skS.0 0 a) → Not (member D C)) → disjoint (skS.0 0 a) C) False % 4.27/4.48 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.27/4.48 Eq % 4.27/4.48 (Not ((∀ (D : Iota), member D (skS.0 0 a) → Not (member D (skS.0 1 a a_1))) → disjoint (skS.0 0 a) (skS.0 1 a a_1))) % 4.27/4.48 True % 4.27/4.48 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.27/4.48 Eq ((∀ (D : Iota), member D (skS.0 0 a) → Not (member D (skS.0 1 a a_1))) → disjoint (skS.0 0 a) (skS.0 1 a a_1)) % 4.27/4.48 False % 4.27/4.48 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), member D (skS.0 0 a) → Not (member D (skS.0 1 a a_1))) True % 4.27/4.48 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 0 a) (skS.0 1 a a_1)) False % 4.27/4.48 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (member a (skS.0 0 a_1) → Not (member a (skS.0 1 a_1 a_2))) True % 4.27/4.48 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (skS.0 0 a_1)) False) (Eq (Not (member a (skS.0 1 a_1 a_2))) True) % 4.27/4.48 Clause #16 (by clausification #[15]): ∀ (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) % 4.27/4.48 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (disjoint a C) (Not (intersect a C))) True % 4.27/4.48 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Not (intersect a a_1))) True % 4.27/4.48 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Not (intersect a a_1)) False) % 4.27/4.48 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (intersect a a_1) True) % 4.27/4.48 Clause #25 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 4.27/4.48 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 4.27/4.48 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 4.27/4.48 Clause #31 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 4.27/4.48 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) % 4.27/4.48 Clause #32 (by clausification #[31]): ∀ (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) % 4.27/4.48 Clause #33 (by clausification #[31]): ∀ (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) % 4.27/4.48 Clause #34 (by superposition #[13, 21]): ∀ (a a_1 : Iota), Or (Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 4.27/4.48 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True % 4.27/4.48 Clause #37 (by superposition #[35, 32]): ∀ (a a_1 a_2 : Iota), 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_1)) True) % 4.27/4.48 Clause #38 (by superposition #[35, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 4.27/4.48 Clause #43 (by clausification #[37]): ∀ (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 % 4.27/4.48 Clause #48 (by clausification #[38]): ∀ (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 % 4.27/4.49 Clause #49 (by superposition #[48, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 4.27/4.49 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) % 4.27/4.49 Clause #53 (by clausification #[49]): ∀ (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 % 4.27/4.49 Clause #54 (by superposition #[53, 43]): Eq False True % 4.27/4.49 Clause #58 (by clausification #[54]): False % 4.27/4.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------