%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET625+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:00:17 PM UTC 2025 % Result : Theorem 4.20s 4.38s % Output : Proof 4.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET625+3 : TPTP v9.2.0. Released v2.2.0. % 0.06/0.14 % Command : duper %s % 0.14/0.35 % Computer : n023.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 13:38:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.20/4.38 SZS status Theorem for theBenchmark.p % 4.20/4.38 SZS output start Proof for theBenchmark.p % 4.20/4.38 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 4.20/4.38 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 4.20/4.38 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), intersect B C → intersect C B) True % 4.20/4.38 Clause #4 (by assumption #[]): Eq (Not (∀ (B C D : Iota), And (intersect B C) (subset C D) → intersect B D)) True % 4.20/4.38 Clause #6 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), intersect a C → intersect C a) True % 4.20/4.38 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (intersect a a_1 → intersect a_1 a) True % 4.20/4.38 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (intersect a_1 a) True) % 4.20/4.38 Clause #9 (by clausification #[4]): Eq (∀ (B C D : Iota), And (intersect B C) (subset C D) → intersect B D) False % 4.20/4.38 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (C D : Iota), And (intersect (skS.0 0 a) C) (subset C D) → intersect (skS.0 0 a) D)) True % 4.20/4.38 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (intersect (skS.0 0 a) C) (subset C D) → intersect (skS.0 0 a) D) False % 4.20/4.38 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (D : Iota), And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) D) → intersect (skS.0 0 a) D)) % 4.20/4.38 True % 4.20/4.38 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq (∀ (D : Iota), And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) D) → intersect (skS.0 0 a) D) % 4.20/4.38 False % 4.20/4.38 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.20/4.38 intersect (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.20/4.38 True % 4.20/4.38 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.20/4.38 intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 4.20/4.38 False % 4.20/4.38 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (And (intersect (skS.0 0 a) (skS.0 1 a a_1)) (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 4.20/4.38 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 4.20/4.38 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.20/4.38 Clause #19 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 0 a) (skS.0 1 a a_1)) True % 4.20/4.38 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 4.20/4.38 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 4.20/4.38 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (D : Iota), member D a → member D a_1) True) % 4.20/4.38 Clause #28 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (member a_2 a → member a_2 a_1) True) % 4.20/4.38 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) True)) % 4.20/4.38 Clause #30 (by superposition #[29, 18]): ∀ (a a_1 a_2 a_3 : Iota), % 4.20/4.38 Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Or (Eq (member a (skS.0 2 a_1 a_2 a_3)) True) (Eq False True)) % 4.20/4.38 Clause #32 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 4.20/4.38 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 4.20/4.38 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) True) (Eq (Exists fun D => And (member D a) (member D a_1)) False) % 4.20/4.38 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 4.20/4.40 Clause #36 (by clausification #[34]): ∀ (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) % 4.20/4.40 Clause #37 (by clausification #[36]): ∀ (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)) % 4.20/4.40 Clause #40 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.20/4.40 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 4 a a_1 a_2) a) (member (skS.0 4 a a_1 a_2) a_1)) True) % 4.20/4.40 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 4 a a_1 a_2) a_1) True) % 4.20/4.40 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 4 a a_1 a_2) a) True) % 4.20/4.40 Clause #43 (by superposition #[19, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (intersect (skS.0 1 a a_1) (skS.0 0 a)) True) % 4.20/4.40 Clause #48 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (intersect (skS.0 1 a a_1) (skS.0 0 a)) True % 4.20/4.40 Clause #50 (by superposition #[48, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) % 4.20/4.40 Clause #51 (by superposition #[48, 42]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) % 4.20/4.40 Clause #58 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Eq (member a (skS.0 2 a_1 a_2 a_3)) True) % 4.20/4.40 Clause #80 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True % 4.20/4.40 Clause #81 (by superposition #[80, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.20/4.40 Or (Eq (intersect (skS.0 0 a) a_1) True) % 4.20/4.40 (Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_2) (skS.0 0 a) a_3) a_1) False)) % 4.20/4.40 Clause #89 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True % 4.20/4.40 Clause #90 (by superposition #[89, 58]): ∀ (a a_1 a_2 a_3 : Iota), % 4.20/4.40 Or (Eq True False) (Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 2 a a_1 a_3)) True) % 4.20/4.40 Clause #95 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), % 4.20/4.40 Or (Eq (intersect (skS.0 0 a) a_1) True) (Eq (member (skS.0 4 (skS.0 1 a a_2) (skS.0 0 a) a_3) a_1) False) % 4.20/4.40 Clause #115 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), Eq (member (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 2 a a_1 a_3)) True % 4.20/4.40 Clause #116 (by superposition #[115, 95]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False) % 4.20/4.40 Clause #120 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 4.20/4.40 Clause #121 (by superposition #[120, 17]): Eq True False % 4.20/4.40 Clause #131 (by clausification #[121]): False % 4.20/4.40 SZS output end Proof for theBenchmark.p 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