%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU320+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:01:22 PM UTC 2025 % Result : Theorem 4.99s 5.21s % Output : Proof 5.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU320+1 : TPTP v9.2.0. Released v3.3.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.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 04:36:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.99/5.21 SZS status Theorem for theBenchmark.p % 4.99/5.21 SZS output start Proof for theBenchmark.p % 4.99/5.21 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), element B (powerset A) → element (subset_complement A B) (powerset A)) True % 4.99/5.21 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), element B (powerset A) → Eq (subset_complement A (subset_complement A B)) B) True % 4.99/5.21 Clause #8 (by assumption #[]): Eq % 4.99/5.21 (∀ (A : Iota), % 4.99/5.21 top_str A → % 4.99/5.21 ∀ (B : Iota), % 4.99/5.21 element B (powerset (the_carrier A)) → % 4.99/5.21 Iff (closed_subset B A) (open_subset (subset_complement (the_carrier A) B) A)) % 4.99/5.21 True % 4.99/5.21 Clause #9 (by assumption #[]): Eq % 4.99/5.21 (Not % 4.99/5.21 (∀ (A : Iota), % 4.99/5.21 top_str A → % 4.99/5.21 ∀ (B : Iota), % 4.99/5.21 element B (powerset (the_carrier A)) → % 4.99/5.21 Iff (open_subset B A) (closed_subset (subset_complement (the_carrier A) B) A))) % 4.99/5.21 True % 4.99/5.21 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset a) → element (subset_complement a B) (powerset a)) True % 4.99/5.21 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (element a (powerset a_1) → element (subset_complement a_1 a) (powerset a_1)) True % 4.99/5.21 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) False) (Eq (element (subset_complement a_1 a) (powerset a_1)) True) % 4.99/5.21 Clause #36 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset a) → Eq (subset_complement a (subset_complement a B)) B) True % 4.99/5.21 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (element a (powerset a_1) → Eq (subset_complement a_1 (subset_complement a_1 a)) a) True % 4.99/5.21 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 4.99/5.21 Or (Eq (element a (powerset a_1)) False) (Eq (Eq (subset_complement a_1 (subset_complement a_1 a)) a) True) % 4.99/5.21 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) False) (Eq (subset_complement a_1 (subset_complement a_1 a)) a) % 4.99/5.21 Clause #50 (by clausification #[8]): ∀ (a : Iota), % 4.99/5.21 Eq % 4.99/5.21 (top_str a → % 4.99/5.21 ∀ (B : Iota), % 4.99/5.21 element B (powerset (the_carrier a)) → % 4.99/5.21 Iff (closed_subset B a) (open_subset (subset_complement (the_carrier a) B) a)) % 4.99/5.21 True % 4.99/5.21 Clause #51 (by clausification #[50]): ∀ (a : Iota), % 4.99/5.21 Or (Eq (top_str a) False) % 4.99/5.21 (Eq % 4.99/5.21 (∀ (B : Iota), % 4.99/5.21 element B (powerset (the_carrier a)) → % 4.99/5.21 Iff (closed_subset B a) (open_subset (subset_complement (the_carrier a) B) a)) % 4.99/5.21 True) % 4.99/5.21 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), % 4.99/5.21 Or (Eq (top_str a) False) % 4.99/5.21 (Eq % 4.99/5.21 (element a_1 (powerset (the_carrier a)) → % 4.99/5.21 Iff (closed_subset a_1 a) (open_subset (subset_complement (the_carrier a) a_1) a)) % 4.99/5.21 True) % 4.99/5.21 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 4.99/5.21 Or (Eq (top_str a) False) % 4.99/5.21 (Or (Eq (element a_1 (powerset (the_carrier a))) False) % 4.99/5.21 (Eq (Iff (closed_subset a_1 a) (open_subset (subset_complement (the_carrier a) a_1) a)) True)) % 4.99/5.21 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 4.99/5.21 Or (Eq (top_str a) False) % 4.99/5.21 (Or (Eq (element a_1 (powerset (the_carrier a))) False) % 4.99/5.21 (Or (Eq (closed_subset a_1 a) True) (Eq (open_subset (subset_complement (the_carrier a) a_1) a) False))) % 4.99/5.21 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota), % 4.99/5.21 Or (Eq (top_str a) False) % 4.99/5.21 (Or (Eq (element a_1 (powerset (the_carrier a))) False) % 4.99/5.21 (Or (Eq (closed_subset a_1 a) False) (Eq (open_subset (subset_complement (the_carrier a) a_1) a) True))) % 4.99/5.21 Clause #63 (by clausification #[9]): Eq % 4.99/5.21 (∀ (A : Iota), % 4.99/5.21 top_str A → % 4.99/5.21 ∀ (B : Iota), % 4.99/5.21 element B (powerset (the_carrier A)) → % 4.99/5.21 Iff (open_subset B A) (closed_subset (subset_complement (the_carrier A) B) A)) % 4.99/5.21 False % 4.99/5.21 Clause #64 (by clausification #[63]): ∀ (a : Iota), % 4.99/5.21 Eq % 4.99/5.21 (Not % 4.99/5.21 (top_str (skS.0 3 a) → % 4.99/5.21 ∀ (B : Iota), % 4.99/5.21 element B (powerset (the_carrier (skS.0 3 a))) → % 4.99/5.21 Iff (open_subset B (skS.0 3 a)) % 4.99/5.21 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) B) (skS.0 3 a)))) % 4.99/5.21 True % 4.99/5.21 Clause #65 (by clausification #[64]): ∀ (a : Iota), % 4.99/5.21 Eq % 4.99/5.21 (top_str (skS.0 3 a) → % 5.07/5.24 ∀ (B : Iota), % 5.07/5.24 element B (powerset (the_carrier (skS.0 3 a))) → % 5.07/5.24 Iff (open_subset B (skS.0 3 a)) (closed_subset (subset_complement (the_carrier (skS.0 3 a)) B) (skS.0 3 a))) % 5.07/5.24 False % 5.07/5.24 Clause #66 (by clausification #[65]): ∀ (a : Iota), Eq (top_str (skS.0 3 a)) True % 5.07/5.24 Clause #67 (by clausification #[65]): ∀ (a : Iota), % 5.07/5.24 Eq % 5.07/5.24 (∀ (B : Iota), % 5.07/5.24 element B (powerset (the_carrier (skS.0 3 a))) → % 5.07/5.24 Iff (open_subset B (skS.0 3 a)) (closed_subset (subset_complement (the_carrier (skS.0 3 a)) B) (skS.0 3 a))) % 5.07/5.24 False % 5.07/5.24 Clause #69 (by superposition #[66, 54]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq True False) % 5.07/5.24 (Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False) % 5.07/5.24 (Or (Eq (closed_subset a (skS.0 3 a_1)) True) % 5.07/5.24 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) False))) % 5.07/5.24 Clause #85 (by superposition #[55, 66]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq True False) % 5.07/5.24 (Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False) % 5.07/5.24 (Or (Eq (closed_subset a (skS.0 3 a_1)) False) % 5.07/5.24 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) True))) % 5.07/5.24 Clause #87 (by clausification #[67]): ∀ (a a_1 : Iota), % 5.07/5.24 Eq % 5.07/5.24 (Not % 5.07/5.24 (element (skS.0 4 a a_1) (powerset (the_carrier (skS.0 3 a))) → % 5.07/5.24 Iff (open_subset (skS.0 4 a a_1) (skS.0 3 a)) % 5.07/5.24 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)))) % 5.07/5.24 True % 5.07/5.24 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 5.07/5.24 Eq % 5.07/5.24 (element (skS.0 4 a a_1) (powerset (the_carrier (skS.0 3 a))) → % 5.07/5.24 Iff (open_subset (skS.0 4 a a_1) (skS.0 3 a)) % 5.07/5.24 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a))) % 5.07/5.24 False % 5.07/5.24 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (powerset (the_carrier (skS.0 3 a)))) True % 5.07/5.24 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), % 5.07/5.24 Eq % 5.07/5.24 (Iff (open_subset (skS.0 4 a a_1) (skS.0 3 a)) % 5.07/5.24 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a))) % 5.07/5.24 False % 5.07/5.24 Clause #91 (by superposition #[89, 22]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq True False) % 5.07/5.24 (Eq (element (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (powerset (the_carrier (skS.0 3 a)))) % 5.07/5.24 True) % 5.07/5.24 Clause #92 (by superposition #[89, 39]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq True False) % 5.07/5.24 (Eq (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.24 (skS.0 4 a a_1)) % 5.07/5.24 Clause #101 (by clausification #[91]): ∀ (a a_1 : Iota), % 5.07/5.24 Eq (element (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (powerset (the_carrier (skS.0 3 a)))) True % 5.07/5.24 Clause #109 (by clausification #[69]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False) % 5.07/5.24 (Or (Eq (closed_subset a (skS.0 3 a_1)) True) % 5.07/5.24 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) False)) % 5.07/5.24 Clause #113 (by superposition #[109, 101]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) True) % 5.07/5.24 (Or % 5.07/5.24 (Eq % 5.07/5.24 (open_subset % 5.07/5.24 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.24 (skS.0 3 a)) % 5.07/5.24 False) % 5.07/5.24 (Eq False True)) % 5.07/5.24 Clause #118 (by clausification #[92]): ∀ (a a_1 : Iota), % 5.07/5.24 Eq (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.24 (skS.0 4 a a_1) % 5.07/5.24 Clause #120 (by clausification #[85]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False) % 5.07/5.24 (Or (Eq (closed_subset a (skS.0 3 a_1)) False) % 5.07/5.24 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) True)) % 5.07/5.24 Clause #124 (by superposition #[120, 101]): ∀ (a a_1 : Iota), % 5.07/5.24 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False) % 5.07/5.24 (Or % 5.07/5.24 (Eq % 5.07/5.24 (open_subset % 5.07/5.24 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.26 (skS.0 3 a)) % 5.07/5.26 True) % 5.07/5.26 (Eq False True)) % 5.07/5.26 Clause #132 (by clausification #[90]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) False) % 5.07/5.26 (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False) % 5.07/5.26 Clause #133 (by clausification #[90]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) % 5.07/5.26 (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) True) % 5.07/5.26 Clause #158 (by clausification #[124]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False) % 5.07/5.26 (Eq % 5.07/5.26 (open_subset % 5.07/5.26 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.26 (skS.0 3 a)) % 5.07/5.26 True) % 5.07/5.26 Clause #159 (by forward demodulation #[158, 118]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False) % 5.07/5.26 (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) % 5.07/5.26 Clause #160 (by superposition #[159, 133]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) % 5.07/5.26 (Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) (Eq False True)) % 5.07/5.26 Clause #161 (by clausification #[160]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) % 5.07/5.26 Clause #162 (by eliminate duplicate literals #[161]): ∀ (a a_1 : Iota), Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True % 5.07/5.26 Clause #163 (by backward demodulation #[162, 132]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq True False) % 5.07/5.26 (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False) % 5.07/5.26 Clause #166 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False % 5.07/5.26 Clause #167 (by clausification #[113]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) True) % 5.07/5.26 (Eq % 5.07/5.26 (open_subset % 5.07/5.26 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.26 (skS.0 3 a)) % 5.07/5.26 False) % 5.07/5.26 Clause #168 (by forward demodulation #[167, 166]): ∀ (a a_1 : Iota), % 5.07/5.26 Or (Eq False True) % 5.07/5.26 (Eq % 5.07/5.26 (open_subset % 5.07/5.26 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.26 (skS.0 3 a)) % 5.07/5.26 False) % 5.07/5.26 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), % 5.07/5.26 Eq % 5.07/5.26 (open_subset % 5.07/5.26 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1))) % 5.07/5.26 (skS.0 3 a)) % 5.07/5.26 False % 5.07/5.26 Clause #170 (by forward demodulation #[169, 118]): ∀ (a a_1 : Iota), Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) False % 5.07/5.26 Clause #171 (by superposition #[170, 162]): Eq False True % 5.07/5.26 Clause #172 (by clausification #[171]): False % 5.07/5.26 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------