%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET908+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:00:40 PM UTC 2025 % Result : Theorem 3.84s 4.01s % Output : Proof 3.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET908+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.14 % Command : duper %s % 0.14/0.35 % Computer : n006.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 13:59:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.84/4.01 SZS status Theorem for theBenchmark.p % 3.84/4.01 SZS output start Proof for theBenchmark.p % 3.84/4.01 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 3.84/4.01 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.84/4.01 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 3.84/4.01 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_union2 A B)) (∀ (D : Iota), Iff (in D C) (Or (in D A) (in D B)))) True % 3.84/4.01 Clause #11 (by assumption #[]): Eq (Not (∀ (A B : Iota), Ne (set_union2 (singleton A) B) empty_set)) True % 3.84/4.01 Clause #25 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 3.84/4.01 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 3.84/4.01 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 3.84/4.01 Clause #37 (by clausification #[11]): Eq (∀ (A B : Iota), Ne (set_union2 (singleton A) B) empty_set) False % 3.84/4.01 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Ne (set_union2 (singleton (skS.0 2 a)) B) empty_set)) True % 3.84/4.01 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (B : Iota), Ne (set_union2 (singleton (skS.0 2 a)) B) empty_set) False % 3.84/4.01 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (Ne (set_union2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set)) True % 3.84/4.01 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Ne (set_union2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) False % 3.84/4.01 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set % 3.84/4.01 Clause #45 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.84/4.01 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.84/4.01 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.84/4.01 Clause #55 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 3.84/4.01 Clause #57 (by clausification #[55]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 3.84/4.01 Clause #65 (by clausification #[57]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 3.84/4.01 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 3.84/4.01 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 3.84/4.01 Clause #68 (by destructive equality resolution #[67]): ∀ (a : Iota), Eq (in a empty_set) False % 3.84/4.01 Clause #76 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (Eq C (set_union2 a B)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D B)))) True % 3.84/4.01 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 3.84/4.01 Eq (∀ (C : Iota), Iff (Eq C (set_union2 a a_1)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D a_1)))) True % 3.84/4.01 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Eq a (set_union2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2)))) True % 3.84/4.01 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 3.84/4.01 Or (Eq (Eq a (set_union2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) % 3.84/4.01 Clause #92 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.84/4.01 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.84/4.01 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 3.84/4.01 Clause #96 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 3.84/4.01 Clause #97 (by destructive equality resolution #[96]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 3.84/4.01 Clause #98 (by destructive equality resolution #[97]): ∀ (a : Iota), Eq (in a (singleton a)) True % 3.84/4.01 Clause #210 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) (Ne a (set_union2 a_1 a_2)) % 3.84/4.01 Clause #211 (by clausification #[210]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Eq (Iff (in a_3 a) (Or (in a_3 a_1) (in a_3 a_2))) True) % 3.84/4.01 Clause #212 (by clausification #[211]): ∀ (a a_1 a_2 a_3 : Iota), % 3.84/4.01 Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (in a_3 a_1) (in a_3 a_2)) False)) % 3.84/4.01 Clause #214 (by clausification #[212]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (in a_3 a_2) False)) % 3.84/4.01 Clause #216 (by destructive equality resolution #[214]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_2) False) % 3.84/4.01 Clause #217 (by superposition #[216, 98]): ∀ (a a_1 : Iota), Or (Eq (in a (set_union2 a_1 (singleton a))) True) (Eq False True) % 3.84/4.01 Clause #223 (by clausification #[217]): ∀ (a a_1 : Iota), Eq (in a (set_union2 a_1 (singleton a))) True % 3.84/4.01 Clause #227 (by superposition #[223, 27]): ∀ (a a_1 : Iota), Eq (in a (set_union2 (singleton a) a_1)) True % 3.84/4.01 Clause #236 (by superposition #[227, 42]): ∀ (a : Iota), Eq (in (skS.0 2 a) empty_set) True % 3.84/4.01 Clause #242 (by superposition #[236, 68]): Eq True False % 3.84/4.01 Clause #251 (by clausification #[242]): False % 3.84/4.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------