%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET175+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 07:59:46 PM UTC 2025 % Result : Theorem 51.47s 51.68s % Output : Proof 51.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET175+3 : TPTP v9.2.0. Released v2.2.0. % 0.08/0.15 % Command : duper %s % 0.13/0.36 % Computer : n022.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Thu Oct 2 13:56:08 EDT 2025 % 0.13/0.36 % CPUTime : % 51.47/51.68 SZS status Theorem for theBenchmark.p % 51.47/51.68 SZS output start Proof for theBenchmark.p % 51.47/51.68 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (union B C)) (Or (member D B) (member D C))) True % 51.47/51.68 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (intersection B C)) (And (member D B) (member D C))) True % 51.47/51.68 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True % 51.47/51.68 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True % 51.47/51.68 Clause #4 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 51.47/51.68 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 51.47/51.68 Clause #8 (by assumption #[]): Eq (Not (∀ (B C : Iota), Eq (union B (intersection B C)) B)) True % 51.47/51.68 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True % 51.47/51.68 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True % 51.47/51.68 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a) % 51.47/51.68 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 51.47/51.68 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 51.47/51.68 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 51.47/51.68 Clause #16 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 51.47/51.68 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 51.47/51.68 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 51.47/51.68 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 51.47/51.68 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 0 a a_1 a_2) a → member (skS.0 0 a a_1 a_2) a_1)) True) % 51.47/51.68 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 51.47/51.68 Or (Eq (subset a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a → member (skS.0 0 a a_1 a_2) a_1) False) % 51.47/51.68 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a) True) % 51.47/51.68 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a_1) False) % 51.47/51.68 Clause #27 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (union a C)) (Or (member D a) (member D C))) True % 51.47/51.68 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (union a a_1)) (Or (member D a) (member D a_1))) True % 51.47/51.68 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (union a_1 a_2)) (Or (member a a_1) (member a a_2))) True % 51.47/51.68 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (Or (member a a_1) (member a a_2)) False) % 51.47/51.68 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) False) (Eq (Or (member a a_1) (member a a_2)) True) % 51.47/51.68 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (member a a_2) False) % 51.47/51.68 Clause #34 (by superposition #[32, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 51.47/51.68 Or (Eq (member (skS.0 0 a a_1 a_2) (union a_3 a)) True) (Or (Eq (subset a a_1) True) (Eq False True)) % 51.47/51.68 Clause #37 (by clausification #[8]): Eq (∀ (B C : Iota), Eq (union B (intersection B C)) B) False % 51.47/51.68 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), Eq (union (skS.0 1 a) (intersection (skS.0 1 a) C)) (skS.0 1 a))) True % 51.47/51.68 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union (skS.0 1 a) (intersection (skS.0 1 a) C)) (skS.0 1 a)) False % 51.47/51.68 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (Eq (union (skS.0 1 a) (intersection (skS.0 1 a) (skS.0 2 a a_1))) (skS.0 1 a))) True % 51.47/51.68 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Eq (union (skS.0 1 a) (intersection (skS.0 1 a) (skS.0 2 a a_1))) (skS.0 1 a)) False % 51.47/51.71 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Ne (union (skS.0 1 a) (intersection (skS.0 1 a) (skS.0 2 a a_1))) (skS.0 1 a) % 51.47/51.71 Clause #43 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) False) (Or (Eq (member a a_1) True) (Eq (member a a_2) True)) % 51.47/51.71 Clause #44 (by superposition #[43, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 51.47/51.71 Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a) True) % 51.47/51.71 (Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a_1) True) % 51.47/51.71 (Or (Eq (subset (union a a_1) a_2) True) (Eq False True))) % 51.47/51.71 Clause #47 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (intersection a C)) (And (member D a) (member D C))) True % 51.47/51.71 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (intersection a a_1)) (And (member D a) (member D a_1))) True % 51.47/51.71 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (intersection a_1 a_2)) (And (member a a_1) (member a a_2))) True % 51.47/51.71 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) True) (Eq (And (member a a_1) (member a a_2)) False) % 51.47/51.71 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (And (member a a_1) (member a a_2)) True) % 51.47/51.71 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 51.47/51.71 Or (Eq (member a (intersection a_1 a_2)) True) (Or (Eq (member a a_1) False) (Eq (member a a_2) False)) % 51.47/51.71 Clause #53 (by superposition #[52, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 51.47/51.71 Or (Eq (member (skS.0 0 a a_1 a_2) (intersection a a_3)) True) % 51.47/51.71 (Or (Eq (member (skS.0 0 a a_1 a_2) a_3) False) (Or (Eq (subset a a_1) True) (Eq False True))) % 51.47/51.71 Clause #54 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (member a a_2) True) % 51.47/51.71 Clause #56 (by superposition #[54, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 51.47/51.71 Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) a_1) True) % 51.47/51.71 (Or (Eq (subset (intersection a a_1) a_2) True) (Eq False True)) % 51.47/51.71 Clause #58 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True % 51.47/51.71 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 51.47/51.71 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 51.47/51.71 Clause #62 (by clausification #[60]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 51.47/51.71 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 51.47/51.71 Clause #85 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member (skS.0 0 a a_1 a_2) (union a_3 a)) True) (Eq (subset a a_1) True) % 51.47/51.71 Clause #86 (by superposition #[85, 23]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a_1 a)) True) (Or (Eq (subset a (union a_1 a)) True) (Eq True False)) % 51.47/51.71 Clause #91 (by clausification #[86]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a_1 a)) True) (Eq (subset a (union a_1 a)) True) % 51.47/51.71 Clause #92 (by eliminate duplicate literals #[91]): ∀ (a a_1 : Iota), Eq (subset a (union a_1 a)) True % 51.47/51.71 Clause #95 (by superposition #[92, 12]): ∀ (a a_1 : Iota), Eq (subset a (union a a_1)) True % 51.47/51.71 Clause #97 (by superposition #[95, 63]): ∀ (a a_1 : Iota), Or (Eq a (union a a_1)) (Or (Eq True False) (Eq (subset (union a a_1) a) False)) % 51.47/51.71 Clause #99 (by clausification #[97]): ∀ (a a_1 : Iota), Or (Eq a (union a a_1)) (Eq (subset (union a a_1) a) False) % 51.47/51.71 Clause #114 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 51.47/51.71 Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a) True) % 51.47/51.71 (Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a_1) True) (Eq (subset (union a a_1) a_2) True)) % 51.47/51.71 Clause #115 (by superposition #[114, 54]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 51.47/51.71 Or (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_2) True) % 51.47/51.71 (Or (Eq (subset (union (intersection a a_1) a_2) a_3) True) % 51.54/51.73 (Or (Eq True False) (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_1) True))) % 51.54/51.73 Clause #168 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (member (skS.0 0 a a_1 a_2) (intersection a a_3)) True) % 51.54/51.73 (Or (Eq (member (skS.0 0 a a_1 a_2) a_3) False) (Eq (subset a a_1) True)) % 51.54/51.73 Clause #173 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) a_1) True) (Eq (subset (intersection a a_1) a_2) True) % 51.54/51.73 Clause #176 (by superposition #[173, 23]): ∀ (a a_1 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) a_1) True) (Or (Eq (subset (intersection a a_1) a_1) True) (Eq True False)) % 51.54/51.73 Clause #177 (by superposition #[173, 168]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) a_2) True) % 51.54/51.73 (Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection (intersection a a_1) a_1)) True) % 51.54/51.73 (Or (Eq True False) (Eq (subset (intersection a a_1) a_2) True))) % 51.54/51.73 Clause #186 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (subset (intersection a a_1) a_1) True) (Eq (subset (intersection a a_1) a_1) True) % 51.54/51.73 Clause #187 (by eliminate duplicate literals #[186]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) a_1) True % 51.54/51.73 Clause #189 (by superposition #[187, 63]): ∀ (a a_1 : Iota), Or (Eq (intersection a a_1) a_1) (Or (Eq True False) (Eq (subset a_1 (intersection a a_1)) False)) % 51.54/51.73 Clause #193 (by clausification #[189]): ∀ (a a_1 : Iota), Or (Eq (intersection a a_1) a_1) (Eq (subset a_1 (intersection a a_1)) False) % 51.54/51.73 Clause #670 (by clausification #[115]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 51.54/51.73 Or (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_2) True) % 51.54/51.73 (Or (Eq (subset (union (intersection a a_1) a_2) a_3) True) % 51.54/51.73 (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_1) True)) % 51.54/51.73 Clause #719 (by superposition #[670, 15]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 51.54/51.73 Or (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_2) True) % 51.54/51.73 (Or (Eq (subset (union (intersection a a_1) a_2) a_3) True) % 51.54/51.73 (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a) True)) % 51.54/51.73 Clause #816 (by superposition #[719, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 51.54/51.73 Or (Eq (member (skS.0 0 (union a (intersection a_1 a_2)) a_3 a_4) a) True) % 51.54/51.73 (Or (Eq (subset (union a (intersection a_1 a_2)) a_3) True) % 51.54/51.73 (Eq (member (skS.0 0 (union a (intersection a_1 a_2)) a_3 a_4) a_1) True)) % 51.54/51.73 Clause #1325 (by equality factoring #[816]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (subset (union a (intersection a a_1)) a_2) True) % 51.54/51.73 (Or (Ne True True) (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True)) % 51.54/51.73 Clause #2834 (by clausification #[177]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) a_2) True) % 51.54/51.73 (Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection (intersection a a_1) a_1)) True) % 51.54/51.73 (Eq (subset (intersection a a_1) a_2) True)) % 51.54/51.73 Clause #2835 (by eliminate duplicate literals #[2834]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) a_2) True) % 51.54/51.73 (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection (intersection a a_1) a_1)) True) % 51.54/51.73 Clause #2836 (by forward demodulation #[2835, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) a_2) True) % 51.54/51.73 (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection a_1 (intersection a a_1))) True) % 51.54/51.73 Clause #2868 (by superposition #[2836, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) a_2) True) % 51.54/51.73 (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection a (intersection a a_1))) True) % 51.54/51.73 Clause #3417 (by superposition #[2868, 23]): ∀ (a a_1 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True) % 51.54/51.73 (Or (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True) (Eq True False)) % 51.54/51.73 Clause #6045 (by clausification #[3417]): ∀ (a a_1 : Iota), % 51.54/51.73 Or (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True) % 51.54/51.73 (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True) % 51.60/51.83 Clause #6046 (by eliminate duplicate literals #[6045]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True % 51.60/51.83 Clause #6047 (by superposition #[6046, 193]): ∀ (a a_1 : Iota), Or (Eq (intersection a (intersection a a_1)) (intersection a a_1)) (Eq True False) % 51.60/51.83 Clause #6123 (by clausification #[6047]): ∀ (a a_1 : Iota), Eq (intersection a (intersection a a_1)) (intersection a a_1) % 51.60/51.83 Clause #6167 (by superposition #[6123, 15]): ∀ (a a_1 : Iota), Eq (intersection a (intersection a_1 a)) (intersection a_1 a) % 51.60/51.83 Clause #10409 (by clausification #[1325]): ∀ (a a_1 a_2 a_3 : Iota), % 51.60/51.83 Or (Eq (subset (union a (intersection a a_1)) a_2) True) % 51.60/51.83 (Or (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True) (Or (Eq True False) (Eq True False))) % 51.60/51.83 Clause #10411 (by clausification #[10409]): ∀ (a a_1 a_2 a_3 : Iota), % 51.60/51.83 Or (Eq (subset (union a (intersection a a_1)) a_2) True) % 51.60/51.83 (Or (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True) (Eq True False)) % 51.60/51.83 Clause #10412 (by clausification #[10411]): ∀ (a a_1 a_2 a_3 : Iota), % 51.60/51.83 Or (Eq (subset (union a (intersection a a_1)) a_2) True) % 51.60/51.83 (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True) % 51.60/51.83 Clause #10431 (by superposition #[10412, 23]): ∀ (a a_1 : Iota), % 51.60/51.83 Or (Eq (subset (union a (intersection a a_1)) a) True) % 51.60/51.83 (Or (Eq (subset (union a (intersection a a_1)) a) True) (Eq True False)) % 51.60/51.83 Clause #10489 (by clausification #[10431]): ∀ (a a_1 : Iota), % 51.60/51.83 Or (Eq (subset (union a (intersection a a_1)) a) True) (Eq (subset (union a (intersection a a_1)) a) True) % 51.60/51.83 Clause #10490 (by eliminate duplicate literals #[10489]): ∀ (a a_1 : Iota), Eq (subset (union a (intersection a a_1)) a) True % 51.60/51.83 Clause #10509 (by superposition #[10490, 6167]): ∀ (a a_1 : Iota), Eq (subset (union a (intersection a_1 a)) a) True % 51.60/51.83 Clause #10517 (by superposition #[10509, 99]): ∀ (a a_1 : Iota), Or (Eq a (union a (intersection a_1 a))) (Eq True False) % 51.60/51.83 Clause #10537 (by clausification #[10517]): ∀ (a a_1 : Iota), Eq a (union a (intersection a_1 a)) % 51.60/51.83 Clause #10618 (by superposition #[10537, 15]): ∀ (a a_1 : Iota), Eq a (union a (intersection a a_1)) % 51.60/51.83 Clause #10629 (by backward contextual literal cutting #[10618, 42]): False % 51.60/51.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------