%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET932+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:00:43 PM UTC 2025 % Result : Theorem 12.52s 12.72s % Output : Proof 12.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET932+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.12 % Command : duper %s % 0.11/0.32 % Computer : n009.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 2 13:32:23 EDT 2025 % 0.11/0.33 % CPUTime : % 12.52/12.72 SZS status Theorem for theBenchmark.p % 12.52/12.72 SZS output start Proof for theBenchmark.p % 12.52/12.72 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True % 12.52/12.72 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 12.52/12.72 Clause #6 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True % 12.52/12.72 Clause #7 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset A B → subset (powerset A) (powerset B))) True % 12.52/12.72 Clause #18 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True % 12.52/12.72 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True % 12.52/12.72 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 12.52/12.72 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True) % 12.52/12.72 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False)) % 12.52/12.72 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True % 12.52/12.72 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True % 12.52/12.72 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) % 12.52/12.72 Clause #33 (by clausification #[7]): Eq (∀ (A B : Iota), subset A B → subset (powerset A) (powerset B)) False % 12.52/12.72 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (skS.0 3 a) B → subset (powerset (skS.0 3 a)) (powerset B))) True % 12.52/12.72 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (skS.0 3 a) B → subset (powerset (skS.0 3 a)) (powerset B)) False % 12.52/12.72 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 12.52/12.72 Eq (Not (subset (skS.0 3 a) (skS.0 4 a a_1) → subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1)))) True % 12.52/12.72 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 12.52/12.72 Eq (subset (skS.0 3 a) (skS.0 4 a a_1) → subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) False % 12.52/12.72 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True % 12.52/12.72 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) False % 12.52/12.72 Clause #42 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 12.52/12.72 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 12.52/12.72 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 12.52/12.72 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 12.52/12.72 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1)) True) % 12.52/12.72 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1) False) % 12.52/12.72 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a) True) % 12.52/12.72 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a_1) False) % 12.52/12.72 Clause #56 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1)) % 12.52/12.72 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True) % 12.52/12.72 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) True) (Eq (subset a_2 a_1) False)) % 12.52/12.72 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) False) (Eq (subset a_2 a_1) True)) % 12.52/12.74 Clause #60 (by destructive equality resolution #[58]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (subset a a_1) False) % 12.52/12.74 Clause #66 (by destructive equality resolution #[59]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (subset a a_1) True) % 12.52/12.74 Clause #68 (by superposition #[66, 48]): ∀ (a a_1 a_2 : Iota), % 12.52/12.74 Or (Eq (subset (skS.0 5 (powerset a) a_1 a_2) a) True) (Or (Eq (subset (powerset a) a_1) True) (Eq False True)) % 12.52/12.74 Clause #93 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (skS.0 5 (powerset a) a_1 a_2) a) True) (Eq (subset (powerset a) a_1) True) % 12.52/12.74 Clause #94 (by superposition #[93, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 12.52/12.74 Or (Eq (subset (powerset a) a_1) True) % 12.52/12.74 (Or (Eq (subset (skS.0 5 (powerset a) a_1 a_2) a_3) True) (Or (Eq True False) (Eq (subset a a_3) False))) % 12.52/12.74 Clause #114 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 12.52/12.74 Or (Eq (subset (powerset a) a_1) True) % 12.52/12.74 (Or (Eq (subset (skS.0 5 (powerset a) a_1 a_2) a_3) True) (Eq (subset a a_3) False)) % 12.52/12.74 Clause #115 (by superposition #[114, 38]): ∀ (a a_1 a_2 a_3 : Iota), % 12.52/12.74 Or (Eq (subset (powerset (skS.0 3 a)) a_1) True) % 12.52/12.74 (Or (Eq (subset (skS.0 5 (powerset (skS.0 3 a)) a_1 a_2) (skS.0 4 a a_3)) True) (Eq False True)) % 12.52/12.74 Clause #981 (by clausification #[115]): ∀ (a a_1 a_2 a_3 : Iota), % 12.52/12.74 Or (Eq (subset (powerset (skS.0 3 a)) a_1) True) % 12.52/12.74 (Eq (subset (skS.0 5 (powerset (skS.0 3 a)) a_1 a_2) (skS.0 4 a a_3)) True) % 12.52/12.74 Clause #984 (by superposition #[981, 60]): ∀ (a a_1 a_2 a_3 : Iota), % 12.52/12.74 Or (Eq (subset (powerset (skS.0 3 a)) a_1) True) % 12.52/12.74 (Or (Eq (in (skS.0 5 (powerset (skS.0 3 a)) a_1 a_2) (powerset (skS.0 4 a a_3))) True) (Eq True False)) % 12.52/12.74 Clause #1203 (by clausification #[984]): ∀ (a a_1 a_2 a_3 : Iota), % 12.52/12.74 Or (Eq (subset (powerset (skS.0 3 a)) a_1) True) % 12.52/12.74 (Eq (in (skS.0 5 (powerset (skS.0 3 a)) a_1 a_2) (powerset (skS.0 4 a a_3))) True) % 12.52/12.74 Clause #1205 (by superposition #[1203, 49]): ∀ (a a_1 : Iota), % 12.52/12.74 Or (Eq (subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) True) % 12.52/12.74 (Or (Eq (subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) True) (Eq True False)) % 12.52/12.74 Clause #1225 (by clausification #[1205]): ∀ (a a_1 : Iota), % 12.52/12.74 Or (Eq (subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) True) % 12.52/12.74 (Eq (subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) True) % 12.52/12.74 Clause #1226 (by eliminate duplicate literals #[1225]): ∀ (a a_1 : Iota), Eq (subset (powerset (skS.0 3 a)) (powerset (skS.0 4 a a_1))) True % 12.52/12.74 Clause #1227 (by superposition #[1226, 39]): Eq True False % 12.52/12.74 Clause #1254 (by clausification #[1227]): False % 12.52/12.74 SZS output end Proof for theBenchmark.p 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