%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET947+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:00:44 PM UTC 2025 % Result : Theorem 6.62s 6.82s % Output : Proof 6.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET947+1 : TPTP v9.2.0. Released v3.2.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n011.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 13:50:08 EDT 2025 % 0.14/0.35 % CPUTime : % 6.62/6.82 SZS status Theorem for theBenchmark.p % 6.62/6.82 SZS output start Proof for theBenchmark.p % 6.62/6.82 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True % 6.62/6.82 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 6.62/6.82 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), in A B → subset A (union B)) True % 6.62/6.82 Clause #7 (by assumption #[]): Eq (Not (∀ (A : Iota), subset A (powerset (union A)))) True % 6.62/6.82 Clause #14 (by clausification #[7]): Eq (∀ (A : Iota), subset A (powerset (union A))) False % 6.62/6.82 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (Not (subset (skS.0 2 a) (powerset (union (skS.0 2 a))))) True % 6.62/6.82 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (subset (skS.0 2 a) (powerset (union (skS.0 2 a)))) False % 6.62/6.82 Clause #17 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → subset a (union B)) True % 6.62/6.82 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (in a a_1 → subset a (union a_1)) True % 6.62/6.82 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (subset a (union a_1)) True) % 6.62/6.82 Clause #24 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 6.62/6.82 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 6.62/6.82 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 6.62/6.82 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 6.62/6.82 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 6.62/6.82 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1) False) % 6.62/6.82 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a) True) % 6.62/6.82 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a_1) False) % 6.62/6.82 Clause #32 (by superposition #[30, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq True False) (Eq (subset (skS.0 3 a a_1 a_2) (union a)) True)) % 6.62/6.82 Clause #38 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True % 6.62/6.82 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True % 6.62/6.82 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) % 6.62/6.82 Clause #47 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1)) % 6.62/6.82 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True) % 6.62/6.82 Clause #49 (by clausification #[48]): ∀ (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)) % 6.62/6.82 Clause #51 (by destructive equality resolution #[49]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (subset a a_1) False) % 6.62/6.82 Clause #65 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (subset (skS.0 3 a a_1 a_2) (union a)) True) % 6.62/6.82 Clause #67 (by superposition #[65, 51]): ∀ (a a_1 a_2 : Iota), % 6.62/6.82 Or (Eq (subset a a_1) True) (Or (Eq (in (skS.0 3 a a_1 a_2) (powerset (union a))) True) (Eq True False)) % 6.62/6.82 Clause #175 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) (powerset (union a))) True) % 6.62/6.82 Clause #176 (by superposition #[175, 31]): ∀ (a : Iota), % 6.62/6.82 Or (Eq (subset a (powerset (union a))) True) (Or (Eq (subset a (powerset (union a))) True) (Eq True False)) % 6.62/6.82 Clause #555 (by clausification #[176]): ∀ (a : Iota), Or (Eq (subset a (powerset (union a))) True) (Eq (subset a (powerset (union a))) True) % 6.62/6.82 Clause #556 (by eliminate duplicate literals #[555]): ∀ (a : Iota), Eq (subset a (powerset (union a))) True % 6.62/6.82 Clause #557 (by superposition #[556, 16]): Eq True False % 6.62/6.82 Clause #562 (by clausification #[557]): False % 6.62/6.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------