%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET632+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:00:18 PM UTC 2025 % Result : Theorem 13.64s 13.86s % Output : Proof 13.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SET632+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 14:43:08 EDT 2025 % 0.13/0.34 % CPUTime : % 13.64/13.86 SZS status Theorem for theBenchmark.p % 13.64/13.86 SZS output start Proof for theBenchmark.p % 13.64/13.86 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 13.64/13.86 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (intersect B C) (Exists fun D => And (member D B) (member D C))) True % 13.64/13.86 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 13.64/13.86 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (disjoint B C) (Not (intersect B C))) True % 13.64/13.86 Clause #4 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True % 13.64/13.86 Clause #8 (by assumption #[]): Eq (Not (∀ (B C D : Iota), And (And (subset B C) (subset B D)) (disjoint C D) → Eq B empty_set)) True % 13.64/13.86 Clause #10 (by clausification #[2]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 13.64/13.86 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (member a empty_set) False % 13.64/13.86 Clause #23 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 13.64/13.86 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 13.64/13.86 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 13.64/13.86 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (D : Iota), member D a → member D a_1) True) % 13.64/13.86 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 13.64/13.86 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 1 a a_1 a_2) a → member (skS.0 1 a a_1 a_2) a_1)) True) % 13.64/13.86 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 13.64/13.86 Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a → member (skS.0 1 a a_1 a_2) a_1) False) % 13.64/13.86 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a) True) % 13.64/13.86 Clause #31 (by superposition #[29, 11]): ∀ (a : Iota), Or (Eq (subset empty_set a) True) (Eq True False) % 13.64/13.86 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (subset empty_set a) True % 13.64/13.86 Clause #36 (by clausification #[8]): Eq (∀ (B C D : Iota), And (And (subset B C) (subset B D)) (disjoint C D) → Eq B empty_set) False % 13.64/13.86 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 13.64/13.86 Eq % 13.64/13.86 (Not % 13.64/13.86 (∀ (C D : Iota), % 13.64/13.86 And (And (subset (skS.0 2 a) C) (subset (skS.0 2 a) D)) (disjoint C D) → Eq (skS.0 2 a) empty_set)) % 13.64/13.86 True % 13.64/13.86 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 13.64/13.86 Eq (∀ (C D : Iota), And (And (subset (skS.0 2 a) C) (subset (skS.0 2 a) D)) (disjoint C D) → Eq (skS.0 2 a) empty_set) % 13.64/13.86 False % 13.64/13.86 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 13.64/13.86 Eq % 13.64/13.86 (Not % 13.64/13.86 (∀ (D : Iota), % 13.64/13.86 And (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 2 a) D)) (disjoint (skS.0 3 a a_1) D) → % 13.64/13.86 Eq (skS.0 2 a) empty_set)) % 13.64/13.86 True % 13.64/13.86 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 13.64/13.86 Eq % 13.64/13.86 (∀ (D : Iota), % 13.64/13.86 And (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 2 a) D)) (disjoint (skS.0 3 a a_1) D) → % 13.64/13.86 Eq (skS.0 2 a) empty_set) % 13.64/13.86 False % 13.64/13.86 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 13.64/13.86 Eq % 13.64/13.86 (Not % 13.64/13.86 (And (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.64/13.86 (disjoint (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) → % 13.64/13.86 Eq (skS.0 2 a) empty_set)) % 13.64/13.86 True % 13.64/13.86 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 13.64/13.86 Eq % 13.64/13.86 (And (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.64/13.86 (disjoint (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) → % 13.64/13.86 Eq (skS.0 2 a) empty_set) % 13.64/13.86 False % 13.64/13.86 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 13.64/13.86 Eq % 13.64/13.86 (And (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.64/13.86 (disjoint (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.64/13.86 True % 13.64/13.86 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (Eq (skS.0 2 a) empty_set) False % 13.64/13.86 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (disjoint (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True % 13.71/13.89 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 2 a) (skS.0 4 a a_1 a_2))) True % 13.71/13.89 Clause #47 (by clausification #[44]): ∀ (a : Iota), Ne (skS.0 2 a) empty_set % 13.71/13.89 Clause #48 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (intersect a C) (Exists fun D => And (member D a) (member D C))) True % 13.71/13.89 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (Iff (intersect a a_1) (Exists fun D => And (member D a) (member D a_1))) True % 13.71/13.89 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) True) (Eq (Exists fun D => And (member D a) (member D a_1)) False) % 13.71/13.89 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (intersect a a_1) False) (Eq (Exists fun D => And (member D a) (member D a_1)) True) % 13.71/13.89 Clause #52 (by clausification #[50]): ∀ (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) % 13.71/13.89 Clause #53 (by clausification #[52]): ∀ (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)) % 13.71/13.89 Clause #55 (by superposition #[53, 29]): ∀ (a a_1 a_2 a_3 : Iota), % 13.71/13.89 Or (Eq (intersect a a_1) True) % 13.71/13.89 (Or (Eq (member (skS.0 1 a a_2 a_3) a_1) False) (Or (Eq (subset a a_2) True) (Eq False True))) % 13.71/13.89 Clause #56 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (member a_2 a → member a_2 a_1) True) % 13.71/13.89 Clause #57 (by clausification #[56]): ∀ (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)) % 13.71/13.89 Clause #62 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (disjoint a C) (Not (intersect a C))) True % 13.71/13.89 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Not (intersect a a_1))) True % 13.71/13.89 Clause #65 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Not (intersect a a_1)) True) % 13.71/13.89 Clause #67 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (intersect a a_1) False) % 13.71/13.89 Clause #68 (by superposition #[67, 45]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False) (Eq False True) % 13.71/13.89 Clause #70 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True % 13.71/13.89 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 13.71/13.89 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 13.71/13.89 Clause #74 (by clausification #[72]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 13.71/13.89 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 13.71/13.89 Clause #88 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 13.71/13.89 Or (Eq (intersect a a_1) False) (Eq (And (member (skS.0 5 a a_1 a_2) a) (member (skS.0 5 a a_1 a_2) a_1)) True) % 13.71/13.89 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a a_1) False) (Eq (member (skS.0 5 a a_1 a_2) a_1) True) % 13.71/13.89 Clause #93 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 13.71/13.89 Clause #94 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True % 13.71/13.89 Clause #95 (by superposition #[93, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 13.71/13.89 Or (Eq True False) (Or (Eq (member a (skS.0 2 a_1)) False) (Eq (member a (skS.0 4 a_1 a_2 a_3)) True)) % 13.71/13.89 Clause #100 (by superposition #[94, 57]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (member a (skS.0 2 a_1)) False) (Eq (member a (skS.0 3 a_1 a_2)) True)) % 13.71/13.89 Clause #104 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (skS.0 2 a_1)) False) (Eq (member a (skS.0 3 a_1 a_2)) True) % 13.71/13.89 Clause #108 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (intersect (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False % 13.71/13.89 Clause #109 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), % 13.71/13.89 Or (Eq (intersect a a_1) True) (Or (Eq (member (skS.0 1 a a_2 a_3) a_1) False) (Eq (subset a a_2) True)) % 13.71/13.93 Clause #110 (by superposition #[109, 29]): ∀ (a a_1 : Iota), % 13.71/13.93 Or (Eq (intersect a a) True) (Or (Eq (subset a a_1) True) (Or (Eq (subset a a_1) True) (Eq False True))) % 13.71/13.93 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), Or (Eq (intersect a a) True) (Or (Eq (subset a a_1) True) (Eq (subset a a_1) True)) % 13.71/13.93 Clause #112 (by eliminate duplicate literals #[111]): ∀ (a a_1 : Iota), Or (Eq (intersect a a) True) (Eq (subset a a_1) True) % 13.71/13.93 Clause #115 (by superposition #[112, 75]): ∀ (a a_1 : Iota), Or (Eq (intersect a a) True) (Or (Eq a a_1) (Or (Eq True False) (Eq (subset a_1 a) False))) % 13.71/13.93 Clause #116 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Eq (intersect a a) True) (Or (Eq a a_1) (Eq (subset a_1 a) False)) % 13.71/13.93 Clause #119 (by superposition #[116, 32]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Or (Eq a empty_set) (Eq False True)) % 13.71/13.93 Clause #123 (by clausification #[119]): ∀ (a : Iota), Or (Eq (intersect a a) True) (Eq a empty_set) % 13.71/13.93 Clause #124 (by superposition #[123, 89]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Or (Eq True False) (Eq (member (skS.0 5 a a a_1) a) True)) % 13.71/13.93 Clause #129 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member a (skS.0 2 a_1)) False) (Eq (member a (skS.0 4 a_1 a_2 a_3)) True) % 13.71/13.93 Clause #202 (by clausification #[124]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (member (skS.0 5 a a a_1) a) True) % 13.71/13.93 Clause #207 (by superposition #[202, 123]): ∀ (a a_1 a_2 : Iota), Or (Eq (member (skS.0 5 a a a_1) a) True) (Or (Eq (intersect a_2 a_2) True) (Eq a_2 a)) % 13.71/13.93 Clause #283 (by superposition #[207, 47]): ∀ (a a_1 a_2 : Iota), % 13.71/13.93 Or (Eq (member (skS.0 5 a a a_1) a) True) (Or (Eq (intersect (skS.0 2 a_2) (skS.0 2 a_2)) True) (Ne a empty_set)) % 13.71/13.93 Clause #744 (by destructive equality resolution #[283]): ∀ (a a_1 : Iota), % 13.71/13.93 Or (Eq (member (skS.0 5 empty_set empty_set a) empty_set) True) (Eq (intersect (skS.0 2 a_1) (skS.0 2 a_1)) True) % 13.71/13.93 Clause #745 (by superposition #[744, 11]): ∀ (a : Iota), Or (Eq (intersect (skS.0 2 a) (skS.0 2 a)) True) (Eq True False) % 13.71/13.93 Clause #788 (by clausification #[745]): ∀ (a : Iota), Eq (intersect (skS.0 2 a) (skS.0 2 a)) True % 13.71/13.93 Clause #789 (by superposition #[788, 89]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_1) (skS.0 2 a)) True) % 13.71/13.93 Clause #856 (by clausification #[789]): ∀ (a a_1 : Iota), Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_1) (skS.0 2 a)) True % 13.71/13.93 Clause #857 (by superposition #[856, 104]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) % 13.71/13.93 Clause #858 (by superposition #[856, 129]): ∀ (a a_1 a_2 a_3 : Iota), % 13.71/13.93 Or (Eq True False) (Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_1) (skS.0 4 a a_2 a_3)) True) % 13.71/13.93 Clause #1147 (by clausification #[857]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_1) (skS.0 3 a a_2)) True % 13.71/13.93 Clause #1152 (by superposition #[1147, 53]): ∀ (a a_1 a_2 a_3 : Iota), % 13.71/13.93 Or (Eq (intersect (skS.0 3 a a_1) a_2) True) % 13.71/13.93 (Or (Eq True False) (Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_3) a_2) False)) % 13.71/13.93 Clause #1768 (by clausification #[858]): ∀ (a a_1 a_2 a_3 : Iota), Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_1) (skS.0 4 a a_2 a_3)) True % 13.71/13.93 Clause #2557 (by clausification #[1152]): ∀ (a a_1 a_2 a_3 : Iota), % 13.71/13.93 Or (Eq (intersect (skS.0 3 a a_1) a_2) True) (Eq (member (skS.0 5 (skS.0 2 a) (skS.0 2 a) a_3) a_2) False) % 13.71/13.93 Clause #2560 (by superposition #[2557, 1768]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (intersect (skS.0 3 a a_1) (skS.0 4 a a_2 a_3)) True) (Eq False True) % 13.71/13.93 Clause #2655 (by clausification #[2560]): ∀ (a a_1 a_2 a_3 : Iota), Eq (intersect (skS.0 3 a a_1) (skS.0 4 a a_2 a_3)) True % 13.71/13.93 Clause #2656 (by superposition #[2655, 108]): Eq True False % 13.71/13.93 Clause #2676 (by clausification #[2656]): False % 13.71/13.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------