%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET933+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 3.37s 3.60s % Output : Proof 3.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET933+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.13/0.33 % Computer : n001.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 2 13:50:38 EDT 2025 % 0.13/0.33 % CPUTime : % 3.37/3.60 SZS status Theorem for theBenchmark.p % 3.37/3.60 SZS output start Proof for theBenchmark.p % 3.37/3.60 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True % 3.37/3.60 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) True % 3.37/3.60 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 3.37/3.60 Clause #6 (by assumption #[]): Eq (Not (∀ (A : Iota), subset (singleton A) (powerset A))) True % 3.37/3.60 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (Iota → subset a a) True % 3.37/3.60 Clause #8 (by clausification #[7]): ∀ (a : Iota), Iota → Eq (subset a a) True % 3.37/3.60 Clause #17 (by clausification #[6]): Eq (∀ (A : Iota), subset (singleton A) (powerset A)) False % 3.37/3.60 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (Not (subset (singleton (skS.0 2 a)) (powerset (skS.0 2 a)))) True % 3.37/3.60 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (subset (singleton (skS.0 2 a)) (powerset (skS.0 2 a))) False % 3.37/3.60 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True % 3.37/3.60 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True % 3.37/3.60 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) % 3.37/3.60 Clause #29 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton a) B) (in a B)) True % 3.37/3.60 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton a) a_1) (in a a_1)) True % 3.37/3.60 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False) % 3.37/3.60 Clause #39 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1)) % 3.37/3.60 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True) % 3.37/3.60 Clause #41 (by clausification #[40]): ∀ (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)) % 3.37/3.60 Clause #43 (by destructive equality resolution #[41]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (subset a a_1) False) % 3.37/3.60 Clause #44 (by superposition #[43, 8]): ∀ (a : Iota), Or (Eq (in a (powerset a)) True) (Eq False True) % 3.37/3.60 Clause #45 (by clausification #[44]): ∀ (a : Iota), Eq (in a (powerset a)) True % 3.37/3.60 Clause #47 (by superposition #[45, 31]): ∀ (a : Iota), Or (Eq (subset (singleton a) (powerset a)) True) (Eq True False) % 3.37/3.60 Clause #49 (by clausification #[47]): ∀ (a : Iota), Eq (subset (singleton a) (powerset a)) True % 3.37/3.60 Clause #50 (by superposition #[49, 19]): Eq True False % 3.37/3.60 Clause #53 (by clausification #[50]): False % 3.37/3.60 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------