%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU341+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:01:25 PM UTC 2025 % Result : Theorem 78.17s 78.38s % Output : Proof 78.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU341+1 : TPTP v9.2.0. Released v3.3.0. % 0.10/0.13 % Command : duper %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 04:05:23 EDT 2025 % 0.12/0.34 % CPUTime : % 78.17/78.38 SZS status Theorem for theBenchmark.p % 78.17/78.38 SZS output start Proof for theBenchmark.p % 78.17/78.38 Clause #16 (by assumption #[]): Eq % 78.17/78.38 (∀ (A : Iota), % 78.17/78.38 And (And (Not (empty_carrier A)) (topological_space A)) (top_str A) → % 78.17/78.38 ∀ (B : Iota), % 78.17/78.38 element B (the_carrier A) → % 78.17/78.38 ∀ (C : Iota), element C (powerset (the_carrier A)) → Iff (point_neighbourhood C A B) (in B (interior A C))) % 78.17/78.38 True % 78.17/78.38 Clause #29 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => And (element B (powerset A)) (empty B)) True % 78.17/78.38 Clause #35 (by assumption #[]): Eq % 78.17/78.38 (∀ (A : Iota), % 78.17/78.38 And (topological_space A) (top_str A) → % 78.17/78.38 ∀ (B : Iota), % 78.17/78.38 top_str B → % 78.17/78.38 ∀ (C : Iota), % 78.17/78.38 element C (powerset (the_carrier A)) → % 78.17/78.38 ∀ (D : Iota), % 78.17/78.38 element D (powerset (the_carrier B)) → % 78.17/78.38 And (open_subset D B → Eq (interior B D) D) (Eq (interior A C) C → open_subset C A)) % 78.17/78.38 True % 78.17/78.38 Clause #36 (by assumption #[]): Eq % 78.17/78.38 (Not % 78.17/78.38 (∀ (A : Iota), % 78.17/78.38 And (And (Not (empty_carrier A)) (topological_space A)) (top_str A) → % 78.17/78.39 ∀ (B : Iota), % 78.17/78.39 element B (powerset (the_carrier A)) → % 78.17/78.39 ∀ (C : Iota), element C (the_carrier A) → And (open_subset B A) (in C B) → point_neighbourhood B A C)) % 78.17/78.39 True % 78.17/78.39 Clause #38 (by assumption #[]): Eq (∀ (A : Iota), empty A → Eq A empty_set) True % 78.17/78.39 Clause #68 (by clausification #[38]): ∀ (a : Iota), Eq (empty a → Eq a empty_set) True % 78.17/78.39 Clause #69 (by clausification #[68]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (Eq a empty_set) True) % 78.17/78.39 Clause #70 (by clausification #[69]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq a empty_set) % 78.17/78.39 Clause #167 (by clausification #[29]): ∀ (a : Iota), Eq (Exists fun B => And (element B (powerset a)) (empty B)) True % 78.17/78.39 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (And (element (skS.0 4 a a_1) (powerset a)) (empty (skS.0 4 a a_1))) True % 78.17/78.39 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (empty (skS.0 4 a a_1)) True % 78.17/78.39 Clause #170 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (powerset a)) True % 78.17/78.39 Clause #171 (by superposition #[169, 70]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 4 a a_1) empty_set) % 78.17/78.39 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (skS.0 4 a a_1) empty_set % 78.17/78.39 Clause #235 (by forward demodulation #[170, 172]): ∀ (a : Iota), Eq (element empty_set (powerset a)) True % 78.17/78.39 Clause #239 (by clausification #[16]): ∀ (a : Iota), % 78.17/78.39 Eq % 78.17/78.39 (And (And (Not (empty_carrier a)) (topological_space a)) (top_str a) → % 78.17/78.39 ∀ (B : Iota), % 78.17/78.39 element B (the_carrier a) → % 78.17/78.39 ∀ (C : Iota), element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a B) (in B (interior a C))) % 78.17/78.39 True % 78.17/78.39 Clause #240 (by clausification #[239]): ∀ (a : Iota), % 78.17/78.39 Or (Eq (And (And (Not (empty_carrier a)) (topological_space a)) (top_str a)) False) % 78.17/78.39 (Eq % 78.17/78.39 (∀ (B : Iota), % 78.17/78.39 element B (the_carrier a) → % 78.17/78.39 ∀ (C : Iota), element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a B) (in B (interior a C))) % 78.17/78.39 True) % 78.17/78.39 Clause #241 (by clausification #[240]): ∀ (a : Iota), % 78.17/78.39 Or % 78.17/78.39 (Eq % 78.17/78.39 (∀ (B : Iota), % 78.17/78.39 element B (the_carrier a) → % 78.17/78.39 ∀ (C : Iota), element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a B) (in B (interior a C))) % 78.17/78.39 True) % 78.17/78.39 (Or (Eq (And (Not (empty_carrier a)) (topological_space a)) False) (Eq (top_str a) False)) % 78.17/78.39 Clause #242 (by clausification #[241]): ∀ (a a_1 : Iota), % 78.17/78.39 Or (Eq (And (Not (empty_carrier a)) (topological_space a)) False) % 78.17/78.39 (Or (Eq (top_str a) False) % 78.17/78.39 (Eq % 78.17/78.39 (element a_1 (the_carrier a) → % 78.17/78.39 ∀ (C : Iota), % 78.17/78.39 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C))) % 78.17/78.39 True)) % 78.17/78.39 Clause #243 (by clausification #[242]): ∀ (a a_1 : Iota), % 78.17/78.39 Or (Eq (top_str a) False) % 78.17/78.39 (Or % 78.17/78.39 (Eq % 78.17/78.39 (element a_1 (the_carrier a) → % 78.17/78.39 ∀ (C : Iota), % 78.17/78.39 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C))) % 78.17/78.41 True) % 78.17/78.41 (Or (Eq (Not (empty_carrier a)) False) (Eq (topological_space a) False))) % 78.17/78.41 Clause #244 (by clausification #[243]): ∀ (a a_1 : Iota), % 78.17/78.41 Or (Eq (top_str a) False) % 78.17/78.41 (Or (Eq (Not (empty_carrier a)) False) % 78.17/78.41 (Or (Eq (topological_space a) False) % 78.17/78.41 (Or (Eq (element a_1 (the_carrier a)) False) % 78.17/78.41 (Eq % 78.17/78.41 (∀ (C : Iota), % 78.17/78.41 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C))) % 78.17/78.41 True)))) % 78.17/78.41 Clause #245 (by clausification #[244]): ∀ (a a_1 : Iota), % 78.17/78.41 Or (Eq (top_str a) False) % 78.17/78.41 (Or (Eq (topological_space a) False) % 78.17/78.41 (Or (Eq (element a_1 (the_carrier a)) False) % 78.17/78.41 (Or % 78.17/78.41 (Eq % 78.17/78.41 (∀ (C : Iota), % 78.17/78.41 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C))) % 78.17/78.41 True) % 78.17/78.41 (Eq (empty_carrier a) True)))) % 78.17/78.41 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 : Iota), % 78.17/78.41 Or (Eq (top_str a) False) % 78.17/78.41 (Or (Eq (topological_space a) False) % 78.17/78.41 (Or (Eq (element a_1 (the_carrier a)) False) % 78.17/78.41 (Or (Eq (empty_carrier a) True) % 78.17/78.41 (Eq (element a_2 (powerset (the_carrier a)) → Iff (point_neighbourhood a_2 a a_1) (in a_1 (interior a a_2))) % 78.17/78.41 True)))) % 78.17/78.41 Clause #247 (by clausification #[246]): ∀ (a a_1 a_2 : Iota), % 78.17/78.41 Or (Eq (top_str a) False) % 78.17/78.41 (Or (Eq (topological_space a) False) % 78.17/78.41 (Or (Eq (element a_1 (the_carrier a)) False) % 78.17/78.41 (Or (Eq (empty_carrier a) True) % 78.17/78.41 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.17/78.41 (Eq (Iff (point_neighbourhood a_2 a a_1) (in a_1 (interior a a_2))) True))))) % 78.17/78.41 Clause #248 (by clausification #[247]): ∀ (a a_1 a_2 : Iota), % 78.17/78.41 Or (Eq (top_str a) False) % 78.17/78.41 (Or (Eq (topological_space a) False) % 78.17/78.41 (Or (Eq (element a_1 (the_carrier a)) False) % 78.17/78.41 (Or (Eq (empty_carrier a) True) % 78.17/78.41 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.17/78.41 (Or (Eq (point_neighbourhood a_2 a a_1) True) (Eq (in a_1 (interior a a_2)) False)))))) % 78.17/78.41 Clause #303 (by clausification #[36]): Eq % 78.17/78.41 (∀ (A : Iota), % 78.17/78.41 And (And (Not (empty_carrier A)) (topological_space A)) (top_str A) → % 78.17/78.41 ∀ (B : Iota), % 78.17/78.41 element B (powerset (the_carrier A)) → % 78.17/78.41 ∀ (C : Iota), element C (the_carrier A) → And (open_subset B A) (in C B) → point_neighbourhood B A C) % 78.17/78.41 False % 78.17/78.41 Clause #304 (by clausification #[303]): ∀ (a : Iota), % 78.17/78.41 Eq % 78.17/78.41 (Not % 78.17/78.41 (And (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) (top_str (skS.0 7 a)) → % 78.17/78.41 ∀ (B : Iota), % 78.17/78.41 element B (powerset (the_carrier (skS.0 7 a))) → % 78.17/78.41 ∀ (C : Iota), % 78.17/78.41 element C (the_carrier (skS.0 7 a)) → % 78.17/78.41 And (open_subset B (skS.0 7 a)) (in C B) → point_neighbourhood B (skS.0 7 a) C)) % 78.17/78.41 True % 78.17/78.41 Clause #305 (by clausification #[304]): ∀ (a : Iota), % 78.17/78.41 Eq % 78.17/78.41 (And (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) (top_str (skS.0 7 a)) → % 78.17/78.41 ∀ (B : Iota), % 78.17/78.41 element B (powerset (the_carrier (skS.0 7 a))) → % 78.17/78.41 ∀ (C : Iota), % 78.17/78.41 element C (the_carrier (skS.0 7 a)) → % 78.17/78.41 And (open_subset B (skS.0 7 a)) (in C B) → point_neighbourhood B (skS.0 7 a) C) % 78.17/78.41 False % 78.17/78.41 Clause #306 (by clausification #[305]): ∀ (a : Iota), % 78.17/78.41 Eq (And (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) (top_str (skS.0 7 a))) True % 78.17/78.41 Clause #307 (by clausification #[305]): ∀ (a : Iota), % 78.17/78.41 Eq % 78.17/78.41 (∀ (B : Iota), % 78.17/78.41 element B (powerset (the_carrier (skS.0 7 a))) → % 78.17/78.41 ∀ (C : Iota), % 78.17/78.41 element C (the_carrier (skS.0 7 a)) → % 78.17/78.41 And (open_subset B (skS.0 7 a)) (in C B) → point_neighbourhood B (skS.0 7 a) C) % 78.17/78.41 False % 78.17/78.41 Clause #308 (by clausification #[306]): ∀ (a : Iota), Eq (top_str (skS.0 7 a)) True % 78.17/78.41 Clause #309 (by clausification #[306]): ∀ (a : Iota), Eq (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) True % 78.17/78.41 Clause #312 (by superposition #[308, 248]): ∀ (a a_1 a_2 : Iota), % 78.17/78.41 Or (Eq True False) % 78.17/78.41 (Or (Eq (topological_space (skS.0 7 a)) False) % 78.26/78.43 (Or (Eq (element a_1 (the_carrier (skS.0 7 a))) False) % 78.26/78.43 (Or (Eq (empty_carrier (skS.0 7 a)) True) % 78.26/78.43 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False) % 78.26/78.43 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a) a_1) True) (Eq (in a_1 (interior (skS.0 7 a) a_2)) False)))))) % 78.26/78.43 Clause #313 (by clausification #[35]): ∀ (a : Iota), % 78.26/78.43 Eq % 78.26/78.43 (And (topological_space a) (top_str a) → % 78.26/78.43 ∀ (B : Iota), % 78.26/78.43 top_str B → % 78.26/78.43 ∀ (C : Iota), % 78.26/78.43 element C (powerset (the_carrier a)) → % 78.26/78.43 ∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier B)) → % 78.26/78.43 And (open_subset D B → Eq (interior B D) D) (Eq (interior a C) C → open_subset C a)) % 78.26/78.43 True % 78.26/78.43 Clause #314 (by clausification #[313]): ∀ (a : Iota), % 78.26/78.43 Or (Eq (And (topological_space a) (top_str a)) False) % 78.26/78.43 (Eq % 78.26/78.43 (∀ (B : Iota), % 78.26/78.43 top_str B → % 78.26/78.43 ∀ (C : Iota), % 78.26/78.43 element C (powerset (the_carrier a)) → % 78.26/78.43 ∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier B)) → % 78.26/78.43 And (open_subset D B → Eq (interior B D) D) (Eq (interior a C) C → open_subset C a)) % 78.26/78.43 True) % 78.26/78.43 Clause #315 (by clausification #[314]): ∀ (a : Iota), % 78.26/78.43 Or % 78.26/78.43 (Eq % 78.26/78.43 (∀ (B : Iota), % 78.26/78.43 top_str B → % 78.26/78.43 ∀ (C : Iota), % 78.26/78.43 element C (powerset (the_carrier a)) → % 78.26/78.43 ∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier B)) → % 78.26/78.43 And (open_subset D B → Eq (interior B D) D) (Eq (interior a C) C → open_subset C a)) % 78.26/78.43 True) % 78.26/78.43 (Or (Eq (topological_space a) False) (Eq (top_str a) False)) % 78.26/78.43 Clause #316 (by clausification #[315]): ∀ (a a_1 : Iota), % 78.26/78.43 Or (Eq (topological_space a) False) % 78.26/78.43 (Or (Eq (top_str a) False) % 78.26/78.43 (Eq % 78.26/78.43 (top_str a_1 → % 78.26/78.43 ∀ (C : Iota), % 78.26/78.43 element C (powerset (the_carrier a)) → % 78.26/78.43 ∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier a_1)) → % 78.26/78.43 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a C) C → open_subset C a)) % 78.26/78.43 True)) % 78.26/78.43 Clause #317 (by clausification #[316]): ∀ (a a_1 : Iota), % 78.26/78.43 Or (Eq (topological_space a) False) % 78.26/78.43 (Or (Eq (top_str a) False) % 78.26/78.43 (Or (Eq (top_str a_1) False) % 78.26/78.43 (Eq % 78.26/78.43 (∀ (C : Iota), % 78.26/78.43 element C (powerset (the_carrier a)) → % 78.26/78.43 ∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier a_1)) → % 78.26/78.43 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a C) C → open_subset C a)) % 78.26/78.43 True))) % 78.26/78.43 Clause #318 (by clausification #[317]): ∀ (a a_1 a_2 : Iota), % 78.26/78.43 Or (Eq (topological_space a) False) % 78.26/78.43 (Or (Eq (top_str a) False) % 78.26/78.43 (Or (Eq (top_str a_1) False) % 78.26/78.43 (Eq % 78.26/78.43 (element a_2 (powerset (the_carrier a)) → % 78.26/78.43 ∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier a_1)) → % 78.26/78.43 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a a_2) a_2 → open_subset a_2 a)) % 78.26/78.43 True))) % 78.26/78.43 Clause #319 (by clausification #[318]): ∀ (a a_1 a_2 : Iota), % 78.26/78.43 Or (Eq (topological_space a) False) % 78.26/78.43 (Or (Eq (top_str a) False) % 78.26/78.43 (Or (Eq (top_str a_1) False) % 78.26/78.43 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.26/78.43 (Eq % 78.26/78.43 (∀ (D : Iota), % 78.26/78.43 element D (powerset (the_carrier a_1)) → % 78.26/78.43 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a a_2) a_2 → open_subset a_2 a)) % 78.26/78.43 True)))) % 78.26/78.43 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.43 Or (Eq (topological_space a) False) % 78.26/78.43 (Or (Eq (top_str a) False) % 78.26/78.43 (Or (Eq (top_str a_1) False) % 78.26/78.43 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.26/78.43 (Eq % 78.26/78.43 (element a_3 (powerset (the_carrier a_1)) → % 78.26/78.43 And (open_subset a_3 a_1 → Eq (interior a_1 a_3) a_3) (Eq (interior a a_2) a_2 → open_subset a_2 a)) % 78.26/78.43 True)))) % 78.26/78.43 Clause #321 (by clausification #[320]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.43 Or (Eq (topological_space a) False) % 78.26/78.43 (Or (Eq (top_str a) False) % 78.26/78.46 (Or (Eq (top_str a_1) False) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.26/78.46 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False) % 78.26/78.46 (Eq (And (open_subset a_3 a_1 → Eq (interior a_1 a_3) a_3) (Eq (interior a a_2) a_2 → open_subset a_2 a)) % 78.26/78.46 True))))) % 78.26/78.46 Clause #323 (by clausification #[321]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.46 Or (Eq (topological_space a) False) % 78.26/78.46 (Or (Eq (top_str a) False) % 78.26/78.46 (Or (Eq (top_str a_1) False) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.26/78.46 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False) % 78.26/78.46 (Eq (open_subset a_3 a_1 → Eq (interior a_1 a_3) a_3) True))))) % 78.26/78.46 Clause #425 (by clausification #[307]): ∀ (a a_1 : Iota), % 78.26/78.46 Eq % 78.26/78.46 (Not % 78.26/78.46 (element (skS.0 8 a a_1) (powerset (the_carrier (skS.0 7 a))) → % 78.26/78.46 ∀ (C : Iota), % 78.26/78.46 element C (the_carrier (skS.0 7 a)) → % 78.26/78.46 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in C (skS.0 8 a a_1)) → % 78.26/78.46 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) C)) % 78.26/78.46 True % 78.26/78.46 Clause #426 (by clausification #[425]): ∀ (a a_1 : Iota), % 78.26/78.46 Eq % 78.26/78.46 (element (skS.0 8 a a_1) (powerset (the_carrier (skS.0 7 a))) → % 78.26/78.46 ∀ (C : Iota), % 78.26/78.46 element C (the_carrier (skS.0 7 a)) → % 78.26/78.46 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in C (skS.0 8 a a_1)) → % 78.26/78.46 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) C) % 78.26/78.46 False % 78.26/78.46 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Eq (element (skS.0 8 a a_1) (powerset (the_carrier (skS.0 7 a)))) True % 78.26/78.46 Clause #428 (by clausification #[426]): ∀ (a a_1 : Iota), % 78.26/78.46 Eq % 78.26/78.46 (∀ (C : Iota), % 78.26/78.46 element C (the_carrier (skS.0 7 a)) → % 78.26/78.46 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in C (skS.0 8 a a_1)) → % 78.26/78.46 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) C) % 78.26/78.46 False % 78.26/78.46 Clause #515 (by clausification #[309]): ∀ (a : Iota), Eq (topological_space (skS.0 7 a)) True % 78.26/78.46 Clause #516 (by clausification #[309]): ∀ (a : Iota), Eq (Not (empty_carrier (skS.0 7 a))) True % 78.26/78.46 Clause #518 (by clausification #[516]): ∀ (a : Iota), Eq (empty_carrier (skS.0 7 a)) False % 78.26/78.46 Clause #545 (by clausification #[312]): ∀ (a a_1 a_2 : Iota), % 78.26/78.46 Or (Eq (topological_space (skS.0 7 a)) False) % 78.26/78.46 (Or (Eq (element a_1 (the_carrier (skS.0 7 a))) False) % 78.26/78.46 (Or (Eq (empty_carrier (skS.0 7 a)) True) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False) % 78.26/78.46 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a) a_1) True) (Eq (in a_1 (interior (skS.0 7 a) a_2)) False))))) % 78.26/78.46 Clause #546 (by forward demodulation #[545, 515]): ∀ (a a_1 a_2 : Iota), % 78.26/78.46 Or (Eq True False) % 78.26/78.46 (Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 78.26/78.46 (Or (Eq (empty_carrier (skS.0 7 a_1)) True) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.26/78.46 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False))))) % 78.26/78.46 Clause #547 (by clausification #[546]): ∀ (a a_1 a_2 : Iota), % 78.26/78.46 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 78.26/78.46 (Or (Eq (empty_carrier (skS.0 7 a_1)) True) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.26/78.46 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False)))) % 78.26/78.46 Clause #548 (by forward demodulation #[547, 518]): ∀ (a a_1 a_2 : Iota), % 78.26/78.46 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 78.26/78.46 (Or (Eq False True) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.26/78.46 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False)))) % 78.26/78.46 Clause #549 (by clausification #[548]): ∀ (a a_1 a_2 : Iota), % 78.26/78.46 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) % 78.26/78.46 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.26/78.46 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False))) % 78.26/78.46 Clause #556 (by clausification #[323]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.46 Or (Eq (topological_space a) False) % 78.26/78.46 (Or (Eq (top_str a) False) % 78.26/78.48 (Or (Eq (top_str a_1) False) % 78.26/78.48 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.26/78.48 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False) % 78.26/78.48 (Or (Eq (open_subset a_3 a_1) False) (Eq (Eq (interior a_1 a_3) a_3) True)))))) % 78.26/78.48 Clause #557 (by clausification #[556]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq (topological_space a) False) % 78.26/78.48 (Or (Eq (top_str a) False) % 78.26/78.48 (Or (Eq (top_str a_1) False) % 78.26/78.48 (Or (Eq (element a_2 (powerset (the_carrier a))) False) % 78.26/78.48 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False) % 78.26/78.48 (Or (Eq (open_subset a_3 a_1) False) (Eq (interior a_1 a_3) a_3)))))) % 78.26/78.48 Clause #558 (by superposition #[557, 515]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq (top_str (skS.0 7 a)) False) % 78.26/78.48 (Or (Eq (top_str a_1) False) % 78.26/78.48 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False) % 78.26/78.48 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False) % 78.26/78.48 (Or (Eq (open_subset a_3 a_1) False) (Or (Eq (interior a_1 a_3) a_3) (Eq False True)))))) % 78.26/78.48 Clause #562 (by clausification #[428]): ∀ (a a_1 a_2 : Iota), % 78.26/78.48 Eq % 78.26/78.48 (Not % 78.26/78.48 (element (skS.0 9 a a_1 a_2) (the_carrier (skS.0 7 a)) → % 78.26/78.48 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) → % 78.26/78.48 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2))) % 78.26/78.48 True % 78.26/78.48 Clause #563 (by clausification #[562]): ∀ (a a_1 a_2 : Iota), % 78.26/78.48 Eq % 78.26/78.48 (element (skS.0 9 a a_1 a_2) (the_carrier (skS.0 7 a)) → % 78.26/78.48 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) → % 78.26/78.48 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) % 78.26/78.48 False % 78.26/78.48 Clause #564 (by clausification #[563]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 9 a a_1 a_2) (the_carrier (skS.0 7 a))) True % 78.26/78.48 Clause #565 (by clausification #[563]): ∀ (a a_1 a_2 : Iota), % 78.26/78.48 Eq % 78.26/78.48 (And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) → % 78.26/78.48 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) % 78.26/78.48 False % 78.26/78.48 Clause #568 (by superposition #[564, 549]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq True False) % 78.26/78.48 (Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.26/78.48 (Or (Eq (point_neighbourhood a (skS.0 7 a_1) (skS.0 9 a_1 a_2 a_3)) True) % 78.26/78.48 (Eq (in (skS.0 9 a_1 a_2 a_3) (interior (skS.0 7 a_1) a)) False))) % 78.26/78.48 Clause #825 (by clausification #[558]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq (top_str (skS.0 7 a)) False) % 78.26/78.48 (Or (Eq (top_str a_1) False) % 78.26/78.48 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False) % 78.26/78.48 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False) % 78.26/78.48 (Or (Eq (open_subset a_3 a_1) False) (Eq (interior a_1 a_3) a_3))))) % 78.26/78.48 Clause #826 (by forward demodulation #[825, 308]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq True False) % 78.26/78.48 (Or (Eq (top_str a) False) % 78.26/78.48 (Or (Eq (element a_1 (powerset (the_carrier (skS.0 7 a_2)))) False) % 78.26/78.48 (Or (Eq (element a_3 (powerset (the_carrier a))) False) % 78.26/78.48 (Or (Eq (open_subset a_3 a) False) (Eq (interior a a_3) a_3))))) % 78.26/78.48 Clause #827 (by clausification #[826]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq (top_str a) False) % 78.26/78.48 (Or (Eq (element a_1 (powerset (the_carrier (skS.0 7 a_2)))) False) % 78.26/78.48 (Or (Eq (element a_3 (powerset (the_carrier a))) False) % 78.26/78.48 (Or (Eq (open_subset a_3 a) False) (Eq (interior a a_3) a_3)))) % 78.26/78.48 Clause #829 (by superposition #[827, 308]): ∀ (a a_1 a_2 a_3 : Iota), % 78.26/78.48 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.26/78.48 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_3)))) False) % 78.26/78.48 (Or (Eq (open_subset a_2 (skS.0 7 a_3)) False) (Or (Eq (interior (skS.0 7 a_3) a_2) a_2) (Eq False True)))) % 78.26/78.48 Clause #834 (by clausification #[565]): ∀ (a a_1 a_2 : Iota), Eq (And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1))) True % 78.26/78.48 Clause #835 (by clausification #[565]): ∀ (a a_1 a_2 : Iota), Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) False % 78.26/78.48 Clause #836 (by clausification #[834]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) True % 78.34/78.52 Clause #837 (by clausification #[834]): ∀ (a a_1 : Iota), Eq (open_subset (skS.0 8 a a_1) (skS.0 7 a)) True % 78.34/78.52 Clause #883 (by clausification #[568]): ∀ (a a_1 a_2 a_3 : Iota), % 78.34/78.52 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.34/78.52 (Or (Eq (point_neighbourhood a (skS.0 7 a_1) (skS.0 9 a_1 a_2 a_3)) True) % 78.34/78.52 (Eq (in (skS.0 9 a_1 a_2 a_3) (interior (skS.0 7 a_1) a)) False)) % 78.34/78.52 Clause #885 (by superposition #[883, 427]): ∀ (a a_1 a_2 a_3 : Iota), % 78.34/78.52 Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_2 a_3)) True) % 78.34/78.52 (Or (Eq (in (skS.0 9 a a_2 a_3) (interior (skS.0 7 a) (skS.0 8 a a_1))) False) (Eq False True)) % 78.34/78.52 Clause #2004 (by clausification #[829]): ∀ (a a_1 a_2 a_3 : Iota), % 78.34/78.52 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.34/78.52 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_3)))) False) % 78.34/78.52 (Or (Eq (open_subset a_2 (skS.0 7 a_3)) False) (Eq (interior (skS.0 7 a_3) a_2) a_2))) % 78.34/78.52 Clause #2005 (by superposition #[2004, 235]): ∀ (a a_1 : Iota), % 78.34/78.52 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.34/78.52 (Or (Eq (open_subset a (skS.0 7 a_1)) False) (Or (Eq (interior (skS.0 7 a_1) a) a) (Eq False True))) % 78.34/78.52 Clause #2011 (by clausification #[2005]): ∀ (a a_1 : Iota), % 78.34/78.52 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False) % 78.34/78.52 (Or (Eq (open_subset a (skS.0 7 a_1)) False) (Eq (interior (skS.0 7 a_1) a) a)) % 78.34/78.52 Clause #2013 (by superposition #[2011, 427]): ∀ (a a_1 : Iota), % 78.34/78.52 Or (Eq (open_subset (skS.0 8 a a_1) (skS.0 7 a)) False) % 78.34/78.52 (Or (Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1)) (Eq False True)) % 78.34/78.52 Clause #2055 (by clausification #[885]): ∀ (a a_1 a_2 a_3 : Iota), % 78.34/78.52 Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_2 a_3)) True) % 78.34/78.52 (Eq (in (skS.0 9 a a_2 a_3) (interior (skS.0 7 a) (skS.0 8 a a_1))) False) % 78.34/78.52 Clause #2850 (by clausification #[2013]): ∀ (a a_1 : Iota), % 78.34/78.52 Or (Eq (open_subset (skS.0 8 a a_1) (skS.0 7 a)) False) (Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1)) % 78.34/78.52 Clause #2851 (by superposition #[2850, 837]): ∀ (a a_1 : Iota), Or (Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1)) (Eq False True) % 78.34/78.52 Clause #2852 (by clausification #[2851]): ∀ (a a_1 : Iota), Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1) % 78.34/78.52 Clause #2856 (by backward demodulation #[2852, 2055]): ∀ (a a_1 a_2 a_3 : Iota), % 78.34/78.52 Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_2 a_3)) True) % 78.34/78.52 (Eq (in (skS.0 9 a a_2 a_3) (skS.0 8 a a_1)) False) % 78.34/78.52 Clause #3592 (by superposition #[2856, 836]): ∀ (a a_1 a_2 : Iota), Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) True) (Eq False True) % 78.34/78.52 Clause #3593 (by clausification #[3592]): ∀ (a a_1 a_2 : Iota), Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) True % 78.34/78.52 Clause #3594 (by superposition #[3593, 835]): Eq True False % 78.34/78.52 Clause #3603 (by clausification #[3594]): False % 78.34/78.52 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------