%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET949+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:00:44 PM UTC 2025 % Result : Theorem 191.63s 191.87s % Output : Proof 192.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SET949+1 : TPTP v9.2.0. Released v3.2.0. % 0.13/0.15 % Command : duper %s % 0.13/0.37 % Computer : n025.cluster.edu % 0.13/0.37 % Model : x86_64 x86_64 % 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.37 % Memory : 8042.1875MB % 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.37 % CPULimit : 300 % 0.13/0.37 % WCLimit : 300 % 0.13/0.37 % DateTime : Thu Oct 2 14:24:23 EDT 2025 % 0.13/0.37 % CPUTime : % 191.63/191.87 SZS status Theorem for theBenchmark.p % 191.63/191.87 SZS output start Proof for theBenchmark.p % 191.63/191.87 Clause #2 (by assumption #[]): Eq % 191.63/191.87 (∀ (A B C : Iota), % 191.63/191.87 Iff (Eq C (cartesian_product2 A B)) % 191.63/191.87 (∀ (D : Iota), % 191.63/191.87 Iff (in D C) (Exists fun E => Exists fun F => And (And (in E A) (in F B)) (Eq D (ordered_pair E F))))) % 191.63/191.87 True % 191.63/191.87 Clause #7 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Not (And (in A (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) A)))) True % 191.63/191.87 Clause #22 (by clausification #[2]): ∀ (a : Iota), % 191.63/191.87 Eq % 191.63/191.87 (∀ (B C : Iota), % 191.63/191.87 Iff (Eq C (cartesian_product2 a B)) % 191.63/191.87 (∀ (D : Iota), % 191.63/191.87 Iff (in D C) (Exists fun E => Exists fun F => And (And (in E a) (in F B)) (Eq D (ordered_pair E F))))) % 191.63/191.87 True % 191.63/191.87 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (∀ (C : Iota), % 191.63/191.87 Iff (Eq C (cartesian_product2 a a_1)) % 191.63/191.87 (∀ (D : Iota), % 191.63/191.87 Iff (in D C) (Exists fun E => Exists fun F => And (And (in E a) (in F a_1)) (Eq D (ordered_pair E F))))) % 191.63/191.87 True % 191.63/191.87 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (Iff (Eq a (cartesian_product2 a_1 a_2)) % 191.63/191.87 (∀ (D : Iota), % 191.63/191.87 Iff (in D a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq D (ordered_pair E F))))) % 191.63/191.87 True % 191.63/191.87 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 191.63/191.87 Or (Eq (Eq a (cartesian_product2 a_1 a_2)) False) % 191.63/191.87 (Eq % 191.63/191.87 (∀ (D : Iota), % 191.63/191.87 Iff (in D a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq D (ordered_pair E F)))) % 191.63/191.87 True) % 191.63/191.87 Clause #53 (by clausification #[7]): Eq (∀ (A B C : Iota), Not (And (in A (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) A))) False % 191.63/191.87 Clause #54 (by clausification #[53]): ∀ (a : Iota), % 191.63/191.87 Eq % 191.63/191.87 (Not % 191.63/191.87 (∀ (B C : Iota), % 191.63/191.87 Not (And (in (skS.0 3 a) (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))))) % 191.63/191.87 True % 191.63/191.87 Clause #55 (by clausification #[54]): ∀ (a : Iota), % 191.63/191.87 Eq % 191.63/191.87 (∀ (B C : Iota), % 191.63/191.87 Not (And (in (skS.0 3 a) (cartesian_product2 B C)) (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))) % 191.63/191.87 False % 191.63/191.87 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (Not % 191.63/191.87 (∀ (C : Iota), % 191.63/191.87 Not % 191.63/191.87 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) C)) % 191.63/191.87 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))))) % 191.63/191.87 True % 191.63/191.87 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (∀ (C : Iota), % 191.63/191.87 Not % 191.63/191.87 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) C)) % 191.63/191.87 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))) % 191.63/191.87 False % 191.63/191.87 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (Not % 191.63/191.87 (Not % 191.63/191.87 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 191.63/191.87 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))))) % 191.63/191.87 True % 191.63/191.87 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (Not % 191.63/191.87 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 191.63/191.87 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)))) % 191.63/191.87 False % 191.63/191.87 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 191.63/191.87 Eq % 191.63/191.87 (And (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 191.63/191.87 (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a))) % 191.63/191.87 True % 191.63/191.87 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (∀ (D E : Iota), Ne (ordered_pair D E) (skS.0 3 a)) True % 191.63/191.87 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 a) (cartesian_product2 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) True % 191.63/191.87 Clause #63 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (∀ (E : Iota), Ne (ordered_pair a E) (skS.0 3 a_1)) True % 191.63/191.87 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Eq (Ne (ordered_pair a a_1) (skS.0 3 a_2)) True % 191.63/191.87 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Ne (ordered_pair a a_1) (skS.0 3 a_2) % 191.63/191.87 Clause #76 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 191.63/191.87 Or % 191.63/191.87 (Eq % 191.63/191.87 (∀ (D : Iota), % 191.63/191.87 Iff (in D a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq D (ordered_pair E F)))) % 192.04/192.29 True) % 192.04/192.29 (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 192.04/192.29 Or (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 (Eq (Iff (in a_3 a) (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq a_3 (ordered_pair E F)))) % 192.04/192.29 True) % 192.04/192.29 Clause #79 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 192.04/192.29 Or (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 (Or (Eq (in a_3 a) False) % 192.04/192.29 (Eq (Exists fun E => Exists fun F => And (And (in E a_1) (in F a_2)) (Eq a_3 (ordered_pair E F))) True)) % 192.04/192.29 Clause #319 (by clausification #[79]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 192.04/192.29 Or (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 (Or (Eq (in a_3 a) False) % 192.04/192.29 (Eq % 192.04/192.29 (Exists fun F => % 192.04/192.29 And (And (in (skS.0 8 a_1 a_2 a_3 a_4) a_1) (in F a_2)) (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) F))) % 192.04/192.29 True)) % 192.04/192.29 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 192.04/192.29 Or (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 (Or (Eq (in a_3 a) False) % 192.04/192.29 (Eq % 192.04/192.29 (And (And (in (skS.0 8 a_1 a_2 a_3 a_4) a_1) (in (skS.0 9 a_1 a_2 a_3 a_4 a_5) a_2)) % 192.04/192.29 (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) (skS.0 9 a_1 a_2 a_3 a_4 a_5)))) % 192.04/192.29 True)) % 192.04/192.29 Clause #321 (by clausification #[320]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 192.04/192.29 Or (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 (Or (Eq (in a_3 a) False) (Eq (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) (skS.0 9 a_1 a_2 a_3 a_4 a_5))) True)) % 192.04/192.29 Clause #323 (by clausification #[321]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 192.04/192.29 Or (Ne a (cartesian_product2 a_1 a_2)) % 192.04/192.29 (Or (Eq (in a_3 a) False) (Eq a_3 (ordered_pair (skS.0 8 a_1 a_2 a_3 a_4) (skS.0 9 a_1 a_2 a_3 a_4 a_5)))) % 192.04/192.29 Clause #324 (by destructive equality resolution #[323]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 192.04/192.29 Or (Eq (in a (cartesian_product2 a_1 a_2)) False) % 192.04/192.29 (Eq a (ordered_pair (skS.0 8 a_1 a_2 a a_3) (skS.0 9 a_1 a_2 a a_3 a_4))) % 192.04/192.29 Clause #325 (by superposition #[324, 62]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 192.04/192.29 Or % 192.04/192.29 (Eq (skS.0 3 a) % 192.04/192.29 (ordered_pair (skS.0 8 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3) % 192.04/192.29 (skS.0 9 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3 a_4))) % 192.04/192.29 (Eq False True) % 192.04/192.29 Clause #17777 (by clausification #[325]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 192.04/192.29 Eq (skS.0 3 a) % 192.04/192.29 (ordered_pair (skS.0 8 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3) % 192.04/192.29 (skS.0 9 (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) (skS.0 3 a) a_3 a_4)) % 192.04/192.29 Clause #17778 (by forward contextual literal cutting #[17777, 65]): False % 192.04/192.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------