%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM414+1 : TPTP v9.2.0. Released v3.2.0. % 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 07:56:26 PM UTC 2025 % Result : Theorem 157.82s 158.05s % Output : Proof 157.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM414+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.13 % 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 08:46:38 EDT 2025 % 0.12/0.34 % CPUTime : % 157.82/158.05 SZS status Theorem for theBenchmark.p % 157.82/158.05 SZS output start Proof for theBenchmark.p % 157.82/158.05 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), And (ordinal A) (ordinal B) → Or (ordinal_subset A B) (ordinal_subset B A)) True % 157.82/158.05 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Iff (proper_subset A B) (And (subset A B) (Ne A B))) True % 157.82/158.05 Clause #30 (by assumption #[]): Eq (∀ (A B : Iota), And (ordinal A) (ordinal B) → Iff (ordinal_subset A B) (subset A B)) True % 157.82/158.05 Clause #37 (by assumption #[]): Eq % 157.82/158.05 (Not % 157.82/158.05 (∀ (A : Iota), % 157.82/158.05 ordinal A → % 157.82/158.05 ∀ (B : Iota), ordinal B → Not (And (And (Not (proper_subset A B)) (Ne A B)) (Not (proper_subset B A))))) % 157.82/158.05 True % 157.82/158.05 Clause #133 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), And (ordinal a) (ordinal B) → Or (ordinal_subset a B) (ordinal_subset B a)) True % 157.82/158.05 Clause #134 (by clausification #[133]): ∀ (a a_1 : Iota), Eq (And (ordinal a) (ordinal a_1) → Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True % 157.82/158.05 Clause #135 (by clausification #[134]): ∀ (a a_1 : Iota), % 157.82/158.05 Or (Eq (And (ordinal a) (ordinal a_1)) False) (Eq (Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True) % 157.82/158.05 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), % 157.82/158.05 Or (Eq (Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True) (Or (Eq (ordinal a) False) (Eq (ordinal a_1) False)) % 157.82/158.05 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), % 157.82/158.05 Or (Eq (ordinal a) False) % 157.82/158.05 (Or (Eq (ordinal a_1) False) (Or (Eq (ordinal_subset a a_1) True) (Eq (ordinal_subset a_1 a) True))) % 157.82/158.05 Clause #144 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (proper_subset a B) (And (subset a B) (Ne a B))) True % 157.82/158.05 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Eq (Iff (proper_subset a a_1) (And (subset a a_1) (Ne a a_1))) True % 157.82/158.05 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Eq (And (subset a a_1) (Ne a a_1)) False) % 157.82/158.05 Clause #148 (by clausification #[146]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq (Ne a a_1) False)) % 157.82/158.05 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq a a_1)) % 157.82/158.05 Clause #223 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (B : Iota), And (ordinal a) (ordinal B) → Iff (ordinal_subset a B) (subset a B)) True % 157.82/158.05 Clause #224 (by clausification #[223]): ∀ (a a_1 : Iota), Eq (And (ordinal a) (ordinal a_1) → Iff (ordinal_subset a a_1) (subset a a_1)) True % 157.82/158.05 Clause #225 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (And (ordinal a) (ordinal a_1)) False) (Eq (Iff (ordinal_subset a a_1) (subset a a_1)) True) % 157.82/158.05 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota), % 157.82/158.05 Or (Eq (Iff (ordinal_subset a a_1) (subset a a_1)) True) (Or (Eq (ordinal a) False) (Eq (ordinal a_1) False)) % 157.82/158.05 Clause #228 (by clausification #[226]): ∀ (a a_1 : Iota), % 157.82/158.05 Or (Eq (ordinal a) False) % 157.82/158.05 (Or (Eq (ordinal a_1) False) (Or (Eq (ordinal_subset a a_1) False) (Eq (subset a a_1) True))) % 157.82/158.05 Clause #263 (by clausification #[37]): Eq % 157.82/158.05 (∀ (A : Iota), % 157.82/158.05 ordinal A → ∀ (B : Iota), ordinal B → Not (And (And (Not (proper_subset A B)) (Ne A B)) (Not (proper_subset B A)))) % 157.82/158.05 False % 157.82/158.05 Clause #264 (by clausification #[263]): ∀ (a : Iota), % 157.82/158.05 Eq % 157.82/158.05 (Not % 157.82/158.05 (ordinal (skS.0 15 a) → % 157.82/158.05 ∀ (B : Iota), % 157.82/158.05 ordinal B → % 157.82/158.05 Not % 157.82/158.05 (And (And (Not (proper_subset (skS.0 15 a) B)) (Ne (skS.0 15 a) B)) % 157.82/158.05 (Not (proper_subset B (skS.0 15 a)))))) % 157.82/158.05 True % 157.82/158.05 Clause #265 (by clausification #[264]): ∀ (a : Iota), % 157.82/158.05 Eq % 157.82/158.05 (ordinal (skS.0 15 a) → % 157.82/158.05 ∀ (B : Iota), % 157.82/158.05 ordinal B → % 157.82/158.05 Not (And (And (Not (proper_subset (skS.0 15 a) B)) (Ne (skS.0 15 a) B)) (Not (proper_subset B (skS.0 15 a))))) % 157.82/158.05 False % 157.82/158.05 Clause #266 (by clausification #[265]): ∀ (a : Iota), Eq (ordinal (skS.0 15 a)) True % 157.82/158.05 Clause #267 (by clausification #[265]): ∀ (a : Iota), % 157.82/158.05 Eq % 157.82/158.05 (∀ (B : Iota), % 157.82/158.05 ordinal B → % 157.82/158.05 Not (And (And (Not (proper_subset (skS.0 15 a) B)) (Ne (skS.0 15 a) B)) (Not (proper_subset B (skS.0 15 a))))) % 157.82/158.05 False % 157.92/158.08 Clause #271 (by superposition #[266, 137]): ∀ (a a_1 : Iota), % 157.92/158.08 Or (Eq True False) % 157.92/158.08 (Or (Eq (ordinal a) False) % 157.92/158.08 (Or (Eq (ordinal_subset (skS.0 15 a_1) a) True) (Eq (ordinal_subset a (skS.0 15 a_1)) True))) % 157.92/158.08 Clause #289 (by superposition #[228, 266]): ∀ (a a_1 : Iota), % 157.92/158.08 Or (Eq True False) % 157.92/158.08 (Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 15 a_1) a) False) (Eq (subset (skS.0 15 a_1) a) True))) % 157.92/158.08 Clause #480 (by clausification #[267]): ∀ (a a_1 : Iota), % 157.92/158.08 Eq % 157.92/158.08 (Not % 157.92/158.08 (ordinal (skS.0 16 a a_1) → % 157.92/158.08 Not % 157.92/158.08 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1))) % 157.92/158.08 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a)))))) % 157.92/158.08 True % 157.92/158.08 Clause #481 (by clausification #[480]): ∀ (a a_1 : Iota), % 157.92/158.08 Eq % 157.92/158.08 (ordinal (skS.0 16 a a_1) → % 157.92/158.08 Not % 157.92/158.08 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1))) % 157.92/158.08 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a))))) % 157.92/158.08 False % 157.92/158.08 Clause #482 (by clausification #[481]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 16 a a_1)) True % 157.92/158.08 Clause #483 (by clausification #[481]): ∀ (a a_1 : Iota), % 157.92/158.08 Eq % 157.92/158.08 (Not % 157.92/158.08 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1))) % 157.92/158.08 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a))))) % 157.92/158.08 False % 157.92/158.08 Clause #491 (by superposition #[482, 228]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq True False) % 157.92/158.08 (Or (Eq (ordinal a) False) % 157.92/158.08 (Or (Eq (ordinal_subset (skS.0 16 a_1 a_2) a) False) (Eq (subset (skS.0 16 a_1 a_2) a) True))) % 157.92/158.08 Clause #507 (by clausification #[271]): ∀ (a a_1 : Iota), % 157.92/158.08 Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 15 a_1) a) True) (Eq (ordinal_subset a (skS.0 15 a_1)) True)) % 157.92/158.08 Clause #513 (by superposition #[507, 482]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.92/158.08 (Or (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) (Eq False True)) % 157.92/158.08 Clause #579 (by clausification #[289]): ∀ (a a_1 : Iota), % 157.92/158.08 Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 15 a_1) a) False) (Eq (subset (skS.0 15 a_1) a) True)) % 157.92/158.08 Clause #585 (by superposition #[579, 482]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) False) % 157.92/158.08 (Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) (Eq False True)) % 157.92/158.08 Clause #779 (by clausification #[491]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal a) False) % 157.92/158.08 (Or (Eq (ordinal_subset (skS.0 16 a_1 a_2) a) False) (Eq (subset (skS.0 16 a_1 a_2) a) True)) % 157.92/158.08 Clause #784 (by superposition #[779, 266]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal_subset (skS.0 16 a a_1) (skS.0 15 a_2)) False) % 157.92/158.08 (Or (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True) (Eq False True)) % 157.92/158.08 Clause #943 (by clausification #[483]): ∀ (a a_1 : Iota), % 157.92/158.08 Eq % 157.92/158.08 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1))) % 157.92/158.08 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a)))) % 157.92/158.08 True % 157.92/158.08 Clause #944 (by clausification #[943]): ∀ (a a_1 : Iota), Eq (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a))) True % 157.92/158.08 Clause #945 (by clausification #[943]): ∀ (a a_1 : Iota), Eq (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1))) True % 157.92/158.08 Clause #946 (by clausification #[944]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 16 a a_1) (skS.0 15 a)) False % 157.92/158.08 Clause #1018 (by clausification #[513]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.92/158.08 (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) % 157.92/158.08 Clause #1168 (by clausification #[585]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) False) (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.92/158.08 Clause #1169 (by superposition #[1168, 1018]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.92/158.08 (Or (Eq False True) (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)) % 157.92/158.08 Clause #1307 (by clausification #[784]): ∀ (a a_1 a_2 : Iota), % 157.92/158.08 Or (Eq (ordinal_subset (skS.0 16 a a_1) (skS.0 15 a_2)) False) (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True) % 157.95/158.15 Clause #1535 (by clausification #[1169]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) % 157.95/158.15 Clause #1536 (by superposition #[1535, 1307]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.95/158.15 (Or (Eq True False) (Eq (subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)) % 157.95/158.15 Clause #1537 (by clausification #[1536]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) (Eq (subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) % 157.95/158.15 Clause #1539 (by superposition #[1537, 149]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True) % 157.95/158.15 (Or (Eq (proper_subset (skS.0 15 a_2) (skS.0 16 a a_1)) True) % 157.95/158.15 (Or (Eq True False) (Eq (skS.0 15 a_2) (skS.0 16 a a_1)))) % 157.95/158.15 Clause #1559 (by clausification #[945]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 15 a) (skS.0 16 a a_1)) True % 157.95/158.15 Clause #1560 (by clausification #[945]): ∀ (a a_1 : Iota), Eq (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) True % 157.95/158.15 Clause #1561 (by clausification #[1559]): ∀ (a a_1 : Iota), Ne (skS.0 15 a) (skS.0 16 a a_1) % 157.95/158.15 Clause #1562 (by clausification #[1560]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) False % 157.95/158.15 Clause #2469 (by clausification #[1539]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True) % 157.95/158.15 (Or (Eq (proper_subset (skS.0 15 a_2) (skS.0 16 a a_1)) True) (Eq (skS.0 15 a_2) (skS.0 16 a a_1))) % 157.95/158.15 Clause #2471 (by superposition #[2469, 149]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.95/158.15 (Or (Eq (skS.0 15 a) (skS.0 16 a_1 a_2)) % 157.95/158.15 (Or (Eq (proper_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) % 157.95/158.15 (Or (Eq True False) (Eq (skS.0 16 a_1 a_2) (skS.0 15 a))))) % 157.95/158.15 Clause #7138 (by clausification #[2471]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.95/158.15 (Or (Eq (skS.0 15 a) (skS.0 16 a_1 a_2)) % 157.95/158.15 (Or (Eq (proper_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) (Eq (skS.0 16 a_1 a_2) (skS.0 15 a)))) % 157.95/158.15 Clause #7139 (by eliminate duplicate literals #[7138]): ∀ (a a_1 a_2 : Iota), % 157.95/158.15 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) % 157.95/158.15 (Or (Eq (skS.0 15 a) (skS.0 16 a_1 a_2)) (Eq (proper_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)) % 157.95/158.15 Clause #7142 (by superposition #[7139, 946]): ∀ (a a_1 : Iota), % 157.95/158.15 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) True) (Or (Eq (skS.0 15 a) (skS.0 16 a a_1)) (Eq True False)) % 157.95/158.15 Clause #7144 (by clausification #[7142]): ∀ (a a_1 : Iota), Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) True) (Eq (skS.0 15 a) (skS.0 16 a a_1)) % 157.95/158.15 Clause #7145 (by forward contextual literal cutting #[7144, 1561]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) True % 157.95/158.15 Clause #7146 (by superposition #[7145, 1562]): Eq True False % 157.95/158.15 Clause #7149 (by clausification #[7146]): False % 157.95/158.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------