%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET917+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:00:41 PM UTC 2025 % Result : Theorem 3.63s 3.80s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET917+1 : TPTP v9.2.0. Released v3.2.0. % 0.13/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 13:52:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.63/3.80 SZS status Theorem for theBenchmark.p % 3.63/3.80 SZS output start Proof for theBenchmark.p % 3.63/3.80 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True % 3.63/3.80 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Not (in A B) → disjoint (singleton A) B) True % 3.63/3.80 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), in A B → Eq (set_intersection2 B (singleton A)) (singleton A)) True % 3.63/3.80 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), Or (disjoint (singleton A) B) (Eq (set_intersection2 (singleton A) B) (singleton A)))) True % 3.63/3.80 Clause #16 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (in a B) → disjoint (singleton a) B) True % 3.63/3.80 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Not (in a a_1) → disjoint (singleton a) a_1) True % 3.63/3.80 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (disjoint (singleton a) a_1) True) % 3.63/3.80 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) True) (Eq (in a a_1) True) % 3.63/3.80 Clause #25 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True % 3.63/3.80 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True % 3.63/3.80 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a) % 3.63/3.80 Clause #34 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Eq (set_intersection2 B (singleton a)) (singleton a)) True % 3.63/3.80 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (in a a_1 → Eq (set_intersection2 a_1 (singleton a)) (singleton a)) True % 3.63/3.80 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Eq (set_intersection2 a_1 (singleton a)) (singleton a)) True) % 3.63/3.80 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_intersection2 a_1 (singleton a)) (singleton a)) % 3.63/3.80 Clause #38 (by clausification #[8]): Eq (∀ (A B : Iota), Or (disjoint (singleton A) B) (Eq (set_intersection2 (singleton A) B) (singleton A))) False % 3.63/3.80 Clause #39 (by clausification #[38]): ∀ (a : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (∀ (B : Iota), % 3.63/3.80 Or (disjoint (singleton (skS.0 2 a)) B) % 3.63/3.80 (Eq (set_intersection2 (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a))))) % 3.63/3.80 True % 3.63/3.80 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 3.63/3.80 Eq % 3.63/3.80 (∀ (B : Iota), % 3.63/3.80 Or (disjoint (singleton (skS.0 2 a)) B) % 3.63/3.80 (Eq (set_intersection2 (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a)))) % 3.63/3.80 False % 3.63/3.80 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (Or (disjoint (singleton (skS.0 2 a)) (skS.0 3 a a_1)) % 3.63/3.80 (Eq (set_intersection2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))))) % 3.63/3.80 True % 3.63/3.80 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Or (disjoint (singleton (skS.0 2 a)) (skS.0 3 a a_1)) % 3.63/3.80 (Eq (set_intersection2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)))) % 3.63/3.80 False % 3.63/3.80 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) False % 3.63/3.80 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 2 a)) (skS.0 3 a a_1)) False % 3.63/3.80 Clause #45 (by clausification #[43]): ∀ (a a_1 : Iota), Ne (set_intersection2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)) % 3.63/3.80 Clause #46 (by superposition #[44, 19]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) % 3.63/3.80 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True % 3.63/3.80 Clause #49 (by superposition #[47, 37]): ∀ (a a_1 : Iota), % 3.63/3.80 Or (Eq True False) (Eq (set_intersection2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) % 3.63/3.80 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (set_intersection2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a)) % 3.63/3.80 Clause #53 (by superposition #[51, 27]): ∀ (a a_1 : Iota), Eq (set_intersection2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)) % 3.63/3.80 Clause #54 (by forward contextual literal cutting #[53, 45]): False % 3.63/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------