%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET573+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 3.47s 3.67s % Output : Proof 3.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET573+3 : TPTP v9.2.0. Released v2.2.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n024.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 14:54:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.47/3.67 SZS status Theorem for theBenchmark.p % 3.47/3.67 SZS output start Proof for theBenchmark.p % 3.47/3.67 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 3.47/3.67 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (disjoint B C) (Not (intersect B C))) True % 3.47/3.67 Clause #3 (by assumption #[]): Eq (Not (∀ (B C D : Iota), And (member B C) (disjoint C D) → Not (member B D))) True % 3.47/3.67 Clause #7 (by clausification #[3]): Eq (∀ (B C D : Iota), And (member B C) (disjoint C D) → Not (member B D)) False % 3.47/3.67 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (C D : Iota), And (member (skS.0 0 a) C) (disjoint C D) → Not (member (skS.0 0 a) D))) True % 3.47/3.67 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (member (skS.0 0 a) C) (disjoint C D) → Not (member (skS.0 0 a) D)) False % 3.47/3.67 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 3.47/3.67 Eq % 3.47/3.67 (Not % 3.47/3.67 (∀ (D : Iota), % 3.47/3.67 And (member (skS.0 0 a) (skS.0 1 a a_1)) (disjoint (skS.0 1 a a_1) D) → Not (member (skS.0 0 a) D))) % 3.47/3.67 True % 3.47/3.67 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 3.47/3.67 Eq (∀ (D : Iota), And (member (skS.0 0 a) (skS.0 1 a a_1)) (disjoint (skS.0 1 a a_1) D) → Not (member (skS.0 0 a) D)) % 3.47/3.67 False % 3.47/3.67 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 3.47/3.67 Eq % 3.47/3.67 (Not % 3.47/3.67 (And (member (skS.0 0 a) (skS.0 1 a a_1)) (disjoint (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.47/3.67 Not (member (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 3.47/3.67 True % 3.47/3.67 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 3.47/3.67 Eq % 3.47/3.67 (And (member (skS.0 0 a) (skS.0 1 a a_1)) (disjoint (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.47/3.67 Not (member (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 3.47/3.67 False % 3.47/3.67 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Eq (And (member (skS.0 0 a) (skS.0 1 a a_1)) (disjoint (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 3.47/3.67 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Eq (Not (member (skS.0 0 a) (skS.0 2 a a_1 a_2))) False % 3.47/3.67 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (disjoint (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 3.47/3.67 Clause #17 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (member (skS.0 0 a) (skS.0 1 a a_1)) True % 3.47/3.67 Clause #18 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (disjoint a C) (Not (intersect a C))) True % 3.47/3.67 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Not (intersect a a_1))) True % 3.47/3.67 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Not (intersect a a_1)) True) % 3.47/3.67 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (intersect a a_1) False) % 3.47/3.67 Clause #24 (by superposition #[23, 16]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False) (Eq False True) % 3.47/3.67 Clause #27 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 3.47/3.67 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 3.47/3.67 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) True) (Eq (Exists fun D => And (member D a) (member D a_1)) False) % 3.47/3.67 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Eq (And (member a_2 a) (member a_2 a_1)) False) % 3.47/3.67 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) True) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) False)) % 3.47/3.67 Clause #36 (by superposition #[17, 32]): ∀ (a a_1 a_2 : Iota), % 3.47/3.67 Or (Eq (intersect (skS.0 1 a a_1) a_2) True) (Or (Eq (member (skS.0 0 a) a_2) False) (Eq False True)) % 3.47/3.67 Clause #37 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 3.47/3.67 Clause #39 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect (skS.0 1 a a_1) a_2) True) (Eq (member (skS.0 0 a) a_2) False) % 3.47/3.67 Clause #41 (by superposition #[39, 37]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (intersect (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True) (Eq False True) % 3.47/3.67 Clause #42 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 3.47/3.67 Clause #47 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), Eq (intersect (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True % 3.47/3.67 Clause #48 (by superposition #[47, 42]): Eq True False % 3.47/3.67 Clause #52 (by clausification #[48]): False % 3.47/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------