%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU120+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:00:53 PM UTC 2025 % Result : Theorem 11.71s 12.03s % Output : Proof 11.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU120+1 : TPTP v9.2.0. Released v3.3.0. % 0.08/0.15 % Command : duper %s % 0.14/0.36 % Computer : n029.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 05:07:08 EDT 2025 % 0.14/0.37 % CPUTime : % 11.71/12.03 SZS status Theorem for theBenchmark.p % 11.71/12.03 SZS output start Proof for theBenchmark.p % 11.71/12.03 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 11.71/12.03 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (disjoint A B) (Eq (set_intersection2 A B) empty_set)) True % 11.71/12.03 Clause #10 (by assumption #[]): Eq % 11.71/12.03 (Not % 11.71/12.03 (∀ (A B : Iota), % 11.71/12.03 And (Not (And (Not (disjoint A B)) (∀ (C : Iota), Not (in C (set_intersection2 A B))))) % 11.71/12.03 (Not (And (Exists fun C => in C (set_intersection2 A B)) (disjoint A B))))) % 11.71/12.03 True % 11.71/12.03 Clause #28 (by clausification #[2]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 11.71/12.03 Clause #29 (by clausification #[28]): ∀ (a : Iota), Or (Eq (Eq a empty_set) True) (Eq (∀ (B : Iota), Not (in B a)) False) % 11.71/12.03 Clause #30 (by clausification #[28]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 11.71/12.03 Clause #31 (by clausification #[29]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) False) (Eq a empty_set) % 11.71/12.03 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (Not (Not (in (skS.0 2 a a_1) a))) True) % 11.71/12.03 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (Not (in (skS.0 2 a a_1) a)) False) % 11.71/12.03 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (in (skS.0 2 a a_1) a) True) % 11.71/12.03 Clause #38 (by clausification #[30]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 11.71/12.03 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 11.71/12.03 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 11.71/12.03 Clause #41 (by destructive equality resolution #[40]): ∀ (a : Iota), Eq (in a empty_set) False % 11.71/12.03 Clause #43 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (disjoint a B) (Eq (set_intersection2 a B) empty_set)) True % 11.71/12.03 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Eq (set_intersection2 a a_1) empty_set)) True % 11.71/12.03 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Eq (set_intersection2 a a_1) empty_set) False) % 11.71/12.03 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Eq (set_intersection2 a a_1) empty_set) True) % 11.71/12.03 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Ne (set_intersection2 a a_1) empty_set) % 11.71/12.03 Clause #50 (by clausification #[10]): Eq % 11.71/12.03 (∀ (A B : Iota), % 11.71/12.03 And (Not (And (Not (disjoint A B)) (∀ (C : Iota), Not (in C (set_intersection2 A B))))) % 11.71/12.03 (Not (And (Exists fun C => in C (set_intersection2 A B)) (disjoint A B)))) % 11.71/12.03 False % 11.71/12.03 Clause #51 (by clausification #[50]): ∀ (a : Iota), % 11.71/12.03 Eq % 11.71/12.03 (Not % 11.71/12.03 (∀ (B : Iota), % 11.71/12.03 And (Not (And (Not (disjoint (skS.0 3 a) B)) (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) B))))) % 11.71/12.03 (Not (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) B)) (disjoint (skS.0 3 a) B))))) % 11.71/12.03 True % 11.71/12.03 Clause #52 (by clausification #[51]): ∀ (a : Iota), % 11.71/12.03 Eq % 11.71/12.03 (∀ (B : Iota), % 11.71/12.03 And (Not (And (Not (disjoint (skS.0 3 a) B)) (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) B))))) % 11.71/12.03 (Not (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) B)) (disjoint (skS.0 3 a) B)))) % 11.71/12.03 False % 11.71/12.03 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 11.71/12.03 Eq % 11.71/12.03 (Not % 11.71/12.03 (And % 11.71/12.03 (Not % 11.71/12.03 (And (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.03 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)))))) % 11.71/12.03 (Not % 11.71/12.03 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.03 (disjoint (skS.0 3 a) (skS.0 4 a a_1)))))) % 11.71/12.03 True % 11.71/12.03 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 11.71/12.03 Eq % 11.71/12.03 (And % 11.71/12.03 (Not % 11.71/12.03 (And (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.03 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)))))) % 11.71/12.03 (Not % 11.71/12.03 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (disjoint (skS.0 3 a) (skS.0 4 a a_1))))) % 11.71/12.06 False % 11.71/12.06 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 11.71/12.06 Or % 11.71/12.06 (Eq % 11.71/12.06 (Not % 11.71/12.06 (And (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)))))) % 11.71/12.06 False) % 11.71/12.06 (Eq % 11.71/12.06 (Not % 11.71/12.06 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (disjoint (skS.0 3 a) (skS.0 4 a a_1)))) % 11.71/12.06 False) % 11.71/12.06 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 11.71/12.06 Or % 11.71/12.06 (Eq % 11.71/12.06 (Not % 11.71/12.06 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (disjoint (skS.0 3 a) (skS.0 4 a a_1)))) % 11.71/12.06 False) % 11.71/12.06 (Eq % 11.71/12.06 (And (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))))) % 11.71/12.06 True) % 11.71/12.06 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 11.71/12.06 Or % 11.71/12.06 (Eq % 11.71/12.06 (And (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))))) % 11.71/12.06 True) % 11.71/12.06 (Eq % 11.71/12.06 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 True) % 11.71/12.06 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), % 11.71/12.06 Or % 11.71/12.06 (Eq % 11.71/12.06 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 True) % 11.71/12.06 (Eq (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)))) True) % 11.71/12.06 Clause #59 (by clausification #[57]): ∀ (a a_1 : Iota), % 11.71/12.06 Or % 11.71/12.06 (Eq % 11.71/12.06 (And (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 (disjoint (skS.0 3 a) (skS.0 4 a a_1))) % 11.71/12.06 True) % 11.71/12.06 (Eq (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) True) % 11.71/12.06 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), % 11.71/12.06 Or (Eq (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)))) True) % 11.71/12.06 (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) True) % 11.71/12.06 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 11.71/12.06 Or (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) True) % 11.71/12.06 (Eq (Not (in a_2 (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)))) True) % 11.71/12.06 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 11.71/12.06 Or (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) True) % 11.71/12.06 (Eq (in a_2 (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) False) % 11.71/12.06 Clause #64 (by superposition #[63, 34]): ∀ (a a_1 : Iota), % 11.71/12.06 Or (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) True) % 11.71/12.06 (Or (Eq (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)) empty_set) (Eq False True)) % 11.71/12.06 Clause #67 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (set_intersection2 a a_1) empty_set) % 11.71/12.06 Clause #129 (by clausification #[59]): ∀ (a a_1 : Iota), % 11.71/12.06 Or (Eq (Not (disjoint (skS.0 3 a) (skS.0 4 a a_1))) True) % 11.71/12.06 (Eq (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) True) % 11.71/12.06 Clause #159 (by clausification #[64]): ∀ (a a_1 : Iota), % 11.71/12.06 Or (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) True) (Eq (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)) empty_set) % 11.71/12.06 Clause #160 (by forward contextual literal cutting #[159, 47]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) True % 11.71/12.06 Clause #163 (by superposition #[160, 67]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)) empty_set) % 11.71/12.06 Clause #168 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1)) empty_set % 11.71/12.06 Clause #1376 (by clausification #[129]): ∀ (a a_1 : Iota), % 11.71/12.06 Or (Eq (Exists fun C => in C (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) True) % 11.71/12.06 (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) False) % 11.71/12.06 Clause #1377 (by clausification #[1376]): ∀ (a a_1 a_2 : Iota), % 11.71/12.06 Or (Eq (disjoint (skS.0 3 a) (skS.0 4 a a_1)) False) % 11.71/12.06 (Eq (in (skS.0 6 a a_1 a_2) (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) True) % 11.71/12.06 Clause #1378 (by forward demodulation #[1377, 160]): ∀ (a a_1 a_2 : Iota), % 11.71/12.06 Or (Eq True False) (Eq (in (skS.0 6 a a_1 a_2) (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) True) % 11.81/12.07 Clause #1379 (by clausification #[1378]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (set_intersection2 (skS.0 3 a) (skS.0 4 a a_1))) True % 11.81/12.07 Clause #1380 (by forward demodulation #[1379, 168]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) empty_set) True % 11.81/12.07 Clause #1381 (by superposition #[1380, 41]): Eq True False % 11.81/12.07 Clause #1397 (by clausification #[1381]): False % 11.81/12.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------