%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : TOP021+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:09:53 PM UTC 2025 % Result : Theorem 3.51s 3.74s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : TOP021+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.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 : Fri Oct 3 01:56:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.51/3.74 SZS status Theorem for theBenchmark.p % 3.51/3.74 SZS output start Proof for theBenchmark.p % 3.51/3.74 Clause #0 (by assumption #[]): Eq % 3.51/3.74 (∀ (A X A1 : Iota), % 3.51/3.74 a_continuous_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X A1) (apply X A)) % 3.51/3.74 True % 3.51/3.74 Clause #1 (by assumption #[]): Eq % 3.51/3.74 (∀ (A X A1 X1 : Iota), % 3.51/3.74 an_open_function_from_onto (the_projection_function A X A1) (the_product_top_space_over X1 A1) (apply X1 A)) % 3.51/3.74 True % 3.51/3.74 Clause #2 (by assumption #[]): Eq % 3.51/3.74 (∀ (F A B : Iota), % 3.51/3.74 And (And (an_open_function_from_onto F A B) (a_continuous_function_from_onto F A B)) % 3.51/3.74 (a_locally_compact_top_space A) → % 3.51/3.74 a_locally_compact_top_space B) % 3.51/3.74 True % 3.51/3.74 Clause #3 (by assumption #[]): Eq % 3.51/3.74 (Not % 3.51/3.74 (∀ (X1 A1 : Iota), % 3.51/3.74 a_locally_compact_top_space (the_product_top_space_over X1 A1) → % 3.51/3.74 ∀ (A : Iota), a_locally_compact_top_space (apply X1 A))) % 3.51/3.74 True % 3.51/3.74 Clause #4 (by clausification #[2]): ∀ (a : Iota), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A B : Iota), % 3.51/3.74 And (And (an_open_function_from_onto a A B) (a_continuous_function_from_onto a A B)) % 3.51/3.74 (a_locally_compact_top_space A) → % 3.51/3.74 a_locally_compact_top_space B) % 3.51/3.74 True % 3.51/3.74 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.51/3.74 Eq % 3.51/3.74 (∀ (B : Iota), % 3.51/3.74 And (And (an_open_function_from_onto a a_1 B) (a_continuous_function_from_onto a a_1 B)) % 3.51/3.74 (a_locally_compact_top_space a_1) → % 3.51/3.74 a_locally_compact_top_space B) % 3.51/3.74 True % 3.51/3.74 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.51/3.74 Eq % 3.51/3.74 (And (And (an_open_function_from_onto a a_1 a_2) (a_continuous_function_from_onto a a_1 a_2)) % 3.51/3.74 (a_locally_compact_top_space a_1) → % 3.51/3.74 a_locally_compact_top_space a_2) % 3.51/3.74 True % 3.51/3.74 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 3.51/3.74 Or % 3.51/3.74 (Eq % 3.51/3.74 (And (And (an_open_function_from_onto a a_1 a_2) (a_continuous_function_from_onto a a_1 a_2)) % 3.51/3.74 (a_locally_compact_top_space a_1)) % 3.51/3.74 False) % 3.51/3.74 (Eq (a_locally_compact_top_space a_2) True) % 3.51/3.74 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.51/3.74 Or (Eq (a_locally_compact_top_space a) True) % 3.51/3.74 (Or (Eq (And (an_open_function_from_onto a_1 a_2 a) (a_continuous_function_from_onto a_1 a_2 a)) False) % 3.51/3.74 (Eq (a_locally_compact_top_space a_2) False)) % 3.51/3.74 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.51/3.74 Or (Eq (a_locally_compact_top_space a) True) % 3.51/3.74 (Or (Eq (a_locally_compact_top_space a_1) False) % 3.51/3.74 (Or (Eq (an_open_function_from_onto a_2 a_1 a) False) (Eq (a_continuous_function_from_onto a_2 a_1 a) False))) % 3.51/3.74 Clause #10 (by clausification #[3]): Eq % 3.51/3.74 (∀ (X1 A1 : Iota), % 3.51/3.74 a_locally_compact_top_space (the_product_top_space_over X1 A1) → % 3.51/3.74 ∀ (A : Iota), a_locally_compact_top_space (apply X1 A)) % 3.51/3.74 False % 3.51/3.74 Clause #11 (by clausification #[10]): ∀ (a : Iota), % 3.51/3.74 Eq % 3.51/3.74 (Not % 3.51/3.74 (∀ (A1 : Iota), % 3.51/3.74 a_locally_compact_top_space (the_product_top_space_over (skS.0 0 a) A1) → % 3.51/3.74 ∀ (A : Iota), a_locally_compact_top_space (apply (skS.0 0 a) A))) % 3.51/3.74 True % 3.51/3.74 Clause #12 (by clausification #[11]): ∀ (a : Iota), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A1 : Iota), % 3.51/3.74 a_locally_compact_top_space (the_product_top_space_over (skS.0 0 a) A1) → % 3.51/3.74 ∀ (A : Iota), a_locally_compact_top_space (apply (skS.0 0 a) A)) % 3.51/3.74 False % 3.51/3.74 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 3.51/3.74 Eq % 3.51/3.74 (Not % 3.51/3.74 (a_locally_compact_top_space (the_product_top_space_over (skS.0 0 a) (skS.0 1 a a_1)) → % 3.51/3.74 ∀ (A : Iota), a_locally_compact_top_space (apply (skS.0 0 a) A))) % 3.51/3.74 True % 3.51/3.74 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 3.51/3.74 Eq % 3.51/3.74 (a_locally_compact_top_space (the_product_top_space_over (skS.0 0 a) (skS.0 1 a a_1)) → % 3.51/3.74 ∀ (A : Iota), a_locally_compact_top_space (apply (skS.0 0 a) A)) % 3.51/3.74 False % 3.51/3.74 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (a_locally_compact_top_space (the_product_top_space_over (skS.0 0 a) (skS.0 1 a a_1))) True % 3.51/3.74 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (A : Iota), a_locally_compact_top_space (apply (skS.0 0 a) A)) False % 3.51/3.74 Clause #17 (by superposition #[15, 9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.51/3.74 Or (Eq (a_locally_compact_top_space a) True) % 3.51/3.76 (Or (Eq True False) % 3.51/3.76 (Or (Eq (an_open_function_from_onto a_1 (the_product_top_space_over (skS.0 0 a_2) (skS.0 1 a_2 a_3)) a) False) % 3.51/3.76 (Eq (a_continuous_function_from_onto a_1 (the_product_top_space_over (skS.0 0 a_2) (skS.0 1 a_2 a_3)) a) % 3.51/3.76 False))) % 3.51/3.76 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Not (a_locally_compact_top_space (apply (skS.0 0 a) (skS.0 2 a a_1)))) True % 3.51/3.76 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (a_locally_compact_top_space (apply (skS.0 0 a) (skS.0 2 a a_1))) False % 3.51/3.76 Clause #20 (by clausification #[0]): ∀ (a : Iota), % 3.51/3.76 Eq % 3.51/3.76 (∀ (X A1 : Iota), % 3.51/3.76 a_continuous_function_from_onto (the_projection_function a X A1) (the_product_top_space_over X A1) (apply X a)) % 3.51/3.76 True % 3.51/3.76 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.51/3.76 Eq % 3.51/3.76 (∀ (A1 : Iota), % 3.51/3.76 a_continuous_function_from_onto (the_projection_function a a_1 A1) (the_product_top_space_over a_1 A1) % 3.51/3.76 (apply a_1 a)) % 3.51/3.76 True % 3.51/3.76 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 3.51/3.76 Eq % 3.51/3.76 (a_continuous_function_from_onto (the_projection_function a a_1 a_2) (the_product_top_space_over a_1 a_2) % 3.51/3.76 (apply a_1 a)) % 3.51/3.76 True % 3.51/3.76 Clause #23 (by clausification #[1]): ∀ (a : Iota), % 3.51/3.76 Eq % 3.51/3.76 (∀ (X A1 X1 : Iota), % 3.51/3.76 an_open_function_from_onto (the_projection_function a X A1) (the_product_top_space_over X1 A1) (apply X1 a)) % 3.51/3.76 True % 3.51/3.76 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 3.51/3.76 Eq % 3.51/3.76 (∀ (A1 X1 : Iota), % 3.51/3.76 an_open_function_from_onto (the_projection_function a a_1 A1) (the_product_top_space_over X1 A1) (apply X1 a)) % 3.51/3.76 True % 3.51/3.76 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.51/3.76 Eq % 3.51/3.76 (∀ (X1 : Iota), % 3.51/3.76 an_open_function_from_onto (the_projection_function a a_1 a_2) (the_product_top_space_over X1 a_2) (apply X1 a)) % 3.51/3.76 True % 3.51/3.76 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), % 3.51/3.76 Eq (an_open_function_from_onto (the_projection_function a a_1 a_2) (the_product_top_space_over a_3 a_2) (apply a_3 a)) % 3.51/3.76 True % 3.51/3.76 Clause #27 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 3.51/3.76 Or (Eq (a_locally_compact_top_space a) True) % 3.51/3.76 (Or (Eq (an_open_function_from_onto a_1 (the_product_top_space_over (skS.0 0 a_2) (skS.0 1 a_2 a_3)) a) False) % 3.51/3.76 (Eq (a_continuous_function_from_onto a_1 (the_product_top_space_over (skS.0 0 a_2) (skS.0 1 a_2 a_3)) a) False)) % 3.51/3.76 Clause #28 (by superposition #[27, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 3.51/3.76 Or (Eq (a_locally_compact_top_space (apply (skS.0 0 a) a_1)) True) % 3.51/3.76 (Or % 3.51/3.76 (Eq % 3.51/3.76 (a_continuous_function_from_onto (the_projection_function a_1 a_2 (skS.0 1 a a_3)) % 3.51/3.76 (the_product_top_space_over (skS.0 0 a) (skS.0 1 a a_3)) (apply (skS.0 0 a) a_1)) % 3.51/3.76 False) % 3.51/3.76 (Eq False True)) % 3.51/3.76 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota), % 3.51/3.76 Or (Eq (a_locally_compact_top_space (apply (skS.0 0 a) a_1)) True) % 3.51/3.76 (Eq % 3.51/3.76 (a_continuous_function_from_onto (the_projection_function a_1 a_2 (skS.0 1 a a_3)) % 3.51/3.76 (the_product_top_space_over (skS.0 0 a) (skS.0 1 a a_3)) (apply (skS.0 0 a) a_1)) % 3.51/3.76 False) % 3.51/3.76 Clause #30 (by superposition #[29, 22]): ∀ (a a_1 : Iota), Or (Eq (a_locally_compact_top_space (apply (skS.0 0 a) a_1)) True) (Eq False True) % 3.51/3.76 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (a_locally_compact_top_space (apply (skS.0 0 a) a_1)) True % 3.51/3.76 Clause #33 (by superposition #[31, 19]): Eq True False % 3.51/3.76 Clause #35 (by clausification #[33]): False % 3.51/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------