%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET979+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:00:46 PM UTC 2025 % Result : Theorem 3.71s 3.89s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET979+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n027.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 14:20:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.71/3.89 SZS status Theorem for theBenchmark.p % 3.71/3.89 SZS output start Proof for theBenchmark.p % 3.71/3.89 Clause #7 (by assumption #[]): Eq % 3.71/3.89 (∀ (A B C : Iota), % 3.71/3.89 And (Eq (cartesian_product2 (set_union2 A B) C) (set_union2 (cartesian_product2 A C) (cartesian_product2 B C))) % 3.71/3.89 (Eq (cartesian_product2 C (set_union2 A B)) (set_union2 (cartesian_product2 C A) (cartesian_product2 C B)))) % 3.71/3.89 True % 3.71/3.89 Clause #8 (by assumption #[]): Eq % 3.71/3.89 (Not % 3.71/3.89 (∀ (A B C : Iota), % 3.71/3.89 And % 3.71/3.89 (Eq (cartesian_product2 (unordered_pair A B) C) % 3.71/3.89 (set_union2 (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) C))) % 3.71/3.89 (Eq (cartesian_product2 C (unordered_pair A B)) % 3.71/3.89 (set_union2 (cartesian_product2 C (singleton A)) (cartesian_product2 C (singleton B)))))) % 3.71/3.89 True % 3.71/3.89 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (set_union2 (singleton A) (singleton B))) True % 3.71/3.89 Clause #34 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (set_union2 (singleton a) (singleton B))) True % 3.71/3.89 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (set_union2 (singleton a) (singleton a_1))) True % 3.71/3.89 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (set_union2 (singleton a) (singleton a_1)) % 3.71/3.89 Clause #39 (by clausification #[7]): ∀ (a : Iota), % 3.71/3.89 Eq % 3.71/3.89 (∀ (B C : Iota), % 3.71/3.89 And (Eq (cartesian_product2 (set_union2 a B) C) (set_union2 (cartesian_product2 a C) (cartesian_product2 B C))) % 3.71/3.89 (Eq (cartesian_product2 C (set_union2 a B)) (set_union2 (cartesian_product2 C a) (cartesian_product2 C B)))) % 3.71/3.89 True % 3.71/3.89 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 3.71/3.89 Eq % 3.71/3.89 (∀ (C : Iota), % 3.71/3.89 And % 3.71/3.89 (Eq (cartesian_product2 (set_union2 a a_1) C) (set_union2 (cartesian_product2 a C) (cartesian_product2 a_1 C))) % 3.71/3.89 (Eq (cartesian_product2 C (set_union2 a a_1)) (set_union2 (cartesian_product2 C a) (cartesian_product2 C a_1)))) % 3.71/3.89 True % 3.71/3.89 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Eq % 3.71/3.89 (And % 3.71/3.89 (Eq (cartesian_product2 (set_union2 a a_1) a_2) % 3.71/3.89 (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))) % 3.71/3.89 (Eq (cartesian_product2 a_2 (set_union2 a a_1)) % 3.71/3.89 (set_union2 (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)))) % 3.71/3.89 True % 3.71/3.89 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Eq (Eq (cartesian_product2 a (set_union2 a_1 a_2)) (set_union2 (cartesian_product2 a a_1) (cartesian_product2 a a_2))) % 3.71/3.89 True % 3.71/3.89 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Eq % 3.71/3.89 (Eq (cartesian_product2 (set_union2 a a_1) a_2) % 3.71/3.89 (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))) % 3.71/3.89 True % 3.71/3.89 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Eq (cartesian_product2 a (set_union2 a_1 a_2)) (set_union2 (cartesian_product2 a a_1) (cartesian_product2 a a_2)) % 3.71/3.89 Clause #56 (by clausification #[8]): Eq % 3.71/3.89 (∀ (A B C : Iota), % 3.71/3.89 And % 3.71/3.89 (Eq (cartesian_product2 (unordered_pair A B) C) % 3.71/3.89 (set_union2 (cartesian_product2 (singleton A) C) (cartesian_product2 (singleton B) C))) % 3.71/3.89 (Eq (cartesian_product2 C (unordered_pair A B)) % 3.71/3.89 (set_union2 (cartesian_product2 C (singleton A)) (cartesian_product2 C (singleton B))))) % 3.71/3.89 False % 3.71/3.89 Clause #57 (by clausification #[56]): ∀ (a : Iota), % 3.71/3.89 Eq % 3.71/3.89 (Not % 3.71/3.89 (∀ (B C : Iota), % 3.71/3.89 And % 3.71/3.89 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) B) C) % 3.71/3.89 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C) (cartesian_product2 (singleton B) C))) % 3.71/3.89 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) B)) % 3.71/3.89 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a))) (cartesian_product2 C (singleton B)))))) % 3.71/3.89 True % 3.71/3.89 Clause #58 (by clausification #[57]): ∀ (a : Iota), % 3.71/3.89 Eq % 3.71/3.89 (∀ (B C : Iota), % 3.71/3.89 And % 3.71/3.89 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) B) C) % 3.71/3.89 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C) (cartesian_product2 (singleton B) C))) % 3.71/3.89 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) B)) % 3.71/3.89 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a))) (cartesian_product2 C (singleton B))))) % 3.76/3.91 False % 3.76/3.91 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 3.76/3.91 Eq % 3.76/3.91 (Not % 3.76/3.91 (∀ (C : Iota), % 3.76/3.91 And % 3.76/3.91 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) C))) % 3.76/3.91 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a))) % 3.76/3.91 (cartesian_product2 C (singleton (skS.0 3 a a_1))))))) % 3.76/3.91 True % 3.76/3.91 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), % 3.76/3.91 Eq % 3.76/3.91 (∀ (C : Iota), % 3.76/3.91 And % 3.76/3.91 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) C) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) C))) % 3.76/3.91 (Eq (cartesian_product2 C (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 C (singleton (skS.0 2 a))) % 3.76/3.91 (cartesian_product2 C (singleton (skS.0 3 a a_1)))))) % 3.76/3.91 False % 3.76/3.91 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 3.76/3.91 Eq % 3.76/3.91 (Not % 3.76/3.91 (And % 3.76/3.91 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.91 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.91 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))))) % 3.76/3.91 True % 3.76/3.91 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 3.76/3.91 Eq % 3.76/3.91 (And % 3.76/3.91 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.91 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.91 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1)))))) % 3.76/3.91 False % 3.76/3.91 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 3.76/3.91 Or % 3.76/3.91 (Eq % 3.76/3.91 (Eq (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.91 False) % 3.76/3.91 (Eq % 3.76/3.91 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.91 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))) % 3.76/3.91 False) % 3.76/3.91 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 3.76/3.91 Or % 3.76/3.91 (Eq % 3.76/3.91 (Eq (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.91 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))) % 3.76/3.91 False) % 3.76/3.91 (Ne (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.91 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 3.76/3.91 Or % 3.76/3.91 (Ne (cartesian_product2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.91 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.91 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.91 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.92 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))) % 3.76/3.92 Clause #66 (by forward demodulation #[65, 36]): ∀ (a a_1 a_2 : Iota), % 3.76/3.92 Or % 3.76/3.92 (Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.92 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.76/3.92 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.92 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))) % 3.76/3.92 Clause #67 (by forward demodulation #[66, 36]): ∀ (a a_1 a_2 : Iota), % 3.76/3.92 Or % 3.76/3.92 (Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.92 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)))) % 3.76/3.92 (set_union2 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a))) % 3.76/3.92 (cartesian_product2 (skS.0 4 a a_1 a_2) (singleton (skS.0 3 a a_1))))) % 3.76/3.92 Clause #68 (by forward demodulation #[67, 44]): ∀ (a a_1 a_2 : Iota), % 3.76/3.92 Or % 3.76/3.92 (Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 3.76/3.92 (Ne (cartesian_product2 (skS.0 4 a a_1 a_2) (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)))) % 3.76/3.92 (cartesian_product2 (skS.0 4 a a_1 a_2) (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))))) % 3.76/3.92 Clause #69 (by eliminate resolved literals #[68]): ∀ (a a_1 a_2 : Iota), % 3.76/3.92 Ne (cartesian_product2 (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (set_union2 (cartesian_product2 (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2)) % 3.76/3.92 (cartesian_product2 (singleton (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))) % 3.76/3.92 Clause #70 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 3.76/3.92 Eq (cartesian_product2 (set_union2 a a_1) a_2) (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)) % 3.76/3.92 Clause #72 (by backward contextual literal cutting #[70, 69]): False % 3.76/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------