%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU162+3 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:01:01 PM UTC 2025 % Result : Theorem 4.01s 4.21s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU162+3 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 03:57:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.01/4.21 SZS status Theorem for theBenchmark.p % 4.01/4.21 SZS output start Proof for theBenchmark.p % 4.01/4.21 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B))) True % 4.01/4.21 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Not (in A B) → disjoint (singleton A) B) True % 4.01/4.21 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), disjoint A B → disjoint B A) True % 4.01/4.21 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (Eq (set_difference A (singleton B)) A) (Not (in B A)))) True % 4.01/4.21 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), Iff (disjoint A B) (Eq (set_difference A B) A)) True % 4.01/4.21 Clause #10 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), disjoint a B → disjoint B a) True % 4.01/4.21 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (disjoint a a_1 → disjoint a_1 a) True % 4.01/4.21 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (disjoint a_1 a) True) % 4.01/4.21 Clause #15 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (in a B) → disjoint (singleton a) B) True % 4.01/4.21 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Not (in a a_1) → disjoint (singleton a) a_1) True % 4.01/4.21 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (disjoint (singleton a) a_1) True) % 4.01/4.21 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) True) (Eq (in a a_1) True) % 4.01/4.21 Clause #19 (by superposition #[18, 12]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Or (Eq True False) (Eq (disjoint a_1 (singleton a)) True)) % 4.01/4.21 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (disjoint (singleton a) B) (in a B))) True % 4.01/4.21 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Not (And (disjoint (singleton a) a_1) (in a a_1))) True % 4.01/4.21 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (And (disjoint (singleton a) a_1) (in a a_1)) False % 4.01/4.21 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) False) (Eq (in a a_1) False) % 4.01/4.21 Clause #30 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Eq (disjoint a_1 (singleton a)) True) % 4.01/4.21 Clause #35 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (disjoint a B) (Eq (set_difference a B) a)) True % 4.01/4.21 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Eq (set_difference a a_1) a)) True % 4.01/4.21 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Eq (set_difference a a_1) a) False) % 4.01/4.21 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Eq (set_difference a a_1) a) True) % 4.01/4.21 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Ne (set_difference a a_1) a) % 4.01/4.21 Clause #40 (by clausification #[6]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A (singleton B)) A) (Not (in B A))) False % 4.01/4.21 Clause #41 (by clausification #[40]): ∀ (a : Iota), % 4.01/4.21 Eq (Not (∀ (B : Iota), Iff (Eq (set_difference (skS.0 2 a) (singleton B)) (skS.0 2 a)) (Not (in B (skS.0 2 a))))) True % 4.01/4.21 Clause #42 (by clausification #[41]): ∀ (a : Iota), % 4.01/4.21 Eq (∀ (B : Iota), Iff (Eq (set_difference (skS.0 2 a) (singleton B)) (skS.0 2 a)) (Not (in B (skS.0 2 a)))) False % 4.01/4.21 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), % 4.01/4.21 Eq % 4.01/4.21 (Not % 4.01/4.21 (Iff (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) % 4.01/4.21 (Not (in (skS.0 3 a a_1) (skS.0 2 a))))) % 4.01/4.21 True % 4.01/4.21 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), % 4.01/4.21 Eq % 4.01/4.21 (Iff (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) % 4.01/4.21 (Not (in (skS.0 3 a a_1) (skS.0 2 a)))) % 4.01/4.21 False % 4.01/4.21 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), % 4.01/4.21 Or (Eq (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) False) % 4.01/4.21 (Eq (Not (in (skS.0 3 a a_1) (skS.0 2 a))) False) % 4.01/4.21 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), % 4.01/4.21 Or (Eq (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) True) % 4.01/4.21 (Eq (Not (in (skS.0 3 a a_1) (skS.0 2 a))) True) % 4.01/4.21 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota), % 4.07/4.23 Or (Eq (Not (in (skS.0 3 a a_1) (skS.0 2 a))) False) % 4.07/4.23 (Ne (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) % 4.07/4.23 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 4.07/4.23 Or (Ne (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) % 4.07/4.23 (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True) % 4.07/4.23 Clause #49 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (set_difference a a_1) a) % 4.07/4.23 Clause #50 (by superposition #[49, 30]): ∀ (a a_1 : Iota), Or (Eq (set_difference a (singleton a_1)) a) (Or (Eq (in a_1 a) True) (Eq False True)) % 4.07/4.23 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (set_difference a (singleton a_1)) a) (Eq (in a_1 a) True) % 4.07/4.23 Clause #53 (by backward contextual literal cutting #[52, 48]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True % 4.07/4.23 Clause #60 (by clausification #[46]): ∀ (a a_1 : Iota), % 4.07/4.23 Or (Eq (Not (in (skS.0 3 a a_1) (skS.0 2 a))) True) % 4.07/4.23 (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) % 4.07/4.23 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 4.07/4.23 Or (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) % 4.07/4.23 (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) False) % 4.07/4.23 Clause #75 (by backward demodulation #[53, 61]): ∀ (a a_1 : Iota), Or (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a)) (Eq True False) % 4.07/4.23 Clause #92 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) (skS.0 2 a) % 4.07/4.23 Clause #93 (by superposition #[92, 39]): ∀ (a a_1 : Iota), Or (Eq (disjoint (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne (skS.0 2 a) (skS.0 2 a)) % 4.07/4.23 Clause #120 (by eliminate resolved literals #[93]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 2 a) (singleton (skS.0 3 a a_1))) True % 4.07/4.23 Clause #121 (by superposition #[120, 12]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (disjoint (singleton (skS.0 3 a a_1)) (skS.0 2 a)) True) % 4.07/4.23 Clause #123 (by clausification #[121]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 3 a a_1)) (skS.0 2 a)) True % 4.07/4.23 Clause #124 (by superposition #[123, 27]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) False) % 4.07/4.23 Clause #127 (by clausification #[124]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 2 a)) False % 4.07/4.23 Clause #128 (by superposition #[127, 53]): Eq False True % 4.07/4.23 Clause #129 (by clausification #[128]): False % 4.07/4.23 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------