%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET876+1 : TPTP v9.2.0. Released v3.2.0. % 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 08:00:37 PM UTC 2025 % Result : Theorem 3.65s 3.84s % Output : Proof 3.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET876+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.13 % Command : duper %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 14:55:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.65/3.84 SZS status Theorem for theBenchmark.p % 3.65/3.84 SZS output start Proof for theBenchmark.p % 3.65/3.84 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.65/3.84 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Not (in A B) → disjoint (singleton A) B) True % 3.65/3.84 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), disjoint A B → disjoint B A) True % 3.65/3.84 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Ne A B → disjoint (singleton A) (singleton B))) True % 3.65/3.84 Clause #9 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), disjoint a B → disjoint B a) True % 3.65/3.84 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (disjoint a a_1 → disjoint a_1 a) True % 3.65/3.84 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (disjoint a_1 a) True) % 3.65/3.84 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (in a B) → disjoint (singleton a) B) True % 3.65/3.84 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Not (in a a_1) → disjoint (singleton a) a_1) True % 3.65/3.84 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (disjoint (singleton a) a_1) True) % 3.65/3.84 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) True) (Eq (in a a_1) True) % 3.65/3.84 Clause #22 (by superposition #[21, 11]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Or (Eq True False) (Eq (disjoint a_1 (singleton a)) True)) % 3.65/3.84 Clause #23 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.65/3.84 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.65/3.84 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.65/3.84 Clause #33 (by clausification #[6]): Eq (∀ (A B : Iota), Ne A B → disjoint (singleton A) (singleton B)) False % 3.65/3.84 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Ne (skS.0 3 a) B → disjoint (singleton (skS.0 3 a)) (singleton B))) True % 3.65/3.84 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (B : Iota), Ne (skS.0 3 a) B → disjoint (singleton (skS.0 3 a)) (singleton B)) False % 3.65/3.84 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.65/3.84 Eq (Not (Ne (skS.0 3 a) (skS.0 4 a a_1) → disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1)))) True % 3.65/3.84 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.65/3.84 Eq (Ne (skS.0 3 a) (skS.0 4 a a_1) → disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) False % 3.65/3.84 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) True % 3.65/3.84 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) False % 3.65/3.84 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Ne (skS.0 3 a) (skS.0 4 a a_1) % 3.65/3.84 Clause #41 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Eq (disjoint a_1 (singleton a)) True) % 3.65/3.84 Clause #44 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.65/3.84 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.65/3.84 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 3.65/3.84 Clause #62 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.65/3.84 Clause #63 (by destructive equality resolution #[62]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.65/3.84 Clause #69 (by superposition #[39, 41]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 4 a a_1) (singleton (skS.0 3 a))) True) (Eq True False) % 3.65/3.84 Clause #72 (by clausification #[69]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (singleton (skS.0 3 a))) True % 3.65/3.84 Clause #73 (by superposition #[72, 63]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 4 a a_1) (skS.0 3 a)) % 3.65/3.84 Clause #76 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (skS.0 4 a a_1) (skS.0 3 a) % 3.65/3.84 Clause #77 (by forward contextual literal cutting #[76, 40]): False % 3.65/3.84 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------