%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO030^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:08:26 PM UTC 2025 % Result : Theorem 5.75s 5.93s % Output : Proof 5.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYO030^1 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % Command : duper %s % 0.15/0.34 % Computer : n008.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Fri Oct 3 13:58:53 EDT 2025 % 0.15/0.35 % CPUTime : % 5.75/5.93 SZS status Theorem for theBenchmark.p % 5.75/5.93 SZS output start Proof for theBenchmark.p % 5.75/5.93 Clause #0 (by assumption #[]): Eq (Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y) True % 5.75/5.93 Clause #1 (by assumption #[]): Eq (Not (Not (∀ (F : Prop → Prop), Exists fun X => leibeq (F X) X))) True % 5.75/5.93 Clause #2 (by clausification #[1]): Eq (Not (∀ (F : Prop → Prop), Exists fun X => leibeq (F X) X)) False % 5.75/5.93 Clause #3 (by clausification #[2]): Eq (∀ (F : Prop → Prop), Exists fun X => leibeq (F X) X) True % 5.75/5.93 Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop), Eq (Exists fun X => leibeq (a X) X) True % 5.75/5.93 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (leibeq (a (skS.0 0 a a_1)) (skS.0 0 a a_1)) True % 5.75/5.93 Clause #6 (by identity loobHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (leibeq (a (skS.0 0 a a_1)) True) True) (Eq (skS.0 0 a a_1) False) % 5.75/5.93 Clause #7 (by identity boolHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (leibeq (a (skS.0 0 a a_1)) False) True) (Eq (skS.0 0 a a_1) True) % 5.75/5.93 Clause #9 (by identity boolHoist #[6]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (skS.0 0 a a_1) False) (Or (Eq (leibeq False True) True) (Eq (a (skS.0 0 a a_1)) True)) % 5.75/5.93 Clause #17 (by clausification #[0]): Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y % 5.75/5.93 Clause #18 (by argument congruence #[17]): ∀ (a : Prop), Eq (leibeq a) ((fun X Y => ∀ (P : Prop → Prop), P X → P Y) a) % 5.75/5.93 Clause #19 (by argument congruence #[17]): ∀ (a a_1 : Prop), Eq (leibeq a a_1) ((fun X Y => ∀ (P : Prop → Prop), P X → P Y) a a_1) % 5.75/5.93 Clause #20 (by betaEtaReduce #[18]): ∀ (a : Prop), Eq (leibeq a) fun Y => ∀ (P : Prop → Prop), P a → P Y % 5.75/5.93 Clause #22 (by identity boolHoist #[20]): ∀ (a : Prop), Or (Eq (leibeq False) fun Y => ∀ (P : Prop → Prop), P a → P Y) (Eq a True) % 5.75/5.93 Clause #25 (by argument congruence #[22]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) ((fun Y => ∀ (P : Prop → Prop), P a_1 → P Y) a)) (Eq a_1 True) % 5.75/5.93 Clause #28 (by identity loobHoist #[7]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (skS.0 0 a a_1) True) (Or (Eq (leibeq True False) True) (Eq (a (skS.0 0 a a_1)) False)) % 5.75/5.93 Clause #30 (by identity loobHoist #[28]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (leibeq True False) True) (Or (Eq (a (skS.0 0 a a_1)) False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False))) % 5.75/5.93 Clause #33 (by identity boolHoist #[30]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (leibeq True False) True) % 5.75/5.93 (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq (a False) False) (Eq (skS.0 0 a a_1) True)))) % 5.75/5.93 Clause #50 (by identity loobHoist #[9]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (leibeq False True) True) (Or (Eq (a (skS.0 0 a a_1)) True) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False))) % 5.75/5.93 Clause #52 (by identity loobHoist #[50]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (leibeq False True) True) % 5.75/5.93 (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Or (Eq (a True) True) (Eq (skS.0 0 a a_1) False)))) % 5.75/5.93 Clause #54 (by identity loobHoist #[52]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (leibeq False True) True) % 5.75/5.93 (Or (Eq (skS.0 0 a True) False) % 5.75/5.93 (Or (Eq a_1 False) (Or (Eq (a True) True) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False))))) % 5.75/5.93 Clause #56 (by eliminate duplicate literals #[54]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.93 Or (Eq (leibeq False True) True) (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Eq (a True) True))) % 5.75/5.93 Clause #58 (by betaEtaReduce #[25]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) (∀ (P : Prop → Prop), P a_1 → P a)) (Eq a_1 True) % 5.75/5.93 Clause #59 (by identity loobHoist #[58]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq False True) (∀ (P : Prop → Prop), P a → P a_1)) (Eq a_1 False)) % 5.75/5.93 Clause #60 (by identity boolHoist #[58]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a_1)) (Eq a_1 True)) % 5.75/5.93 Clause #62 (by falseElim #[59]): ∀ (a : Prop), Or (Eq a True) (Eq (leibeq False True) (∀ (P : Prop → Prop), P a → P True)) % 5.75/5.93 Clause #64 (by clausify Prop equality #[62]): ∀ (a : Prop), Or (Eq a True) (Or (Eq (leibeq False True) False) (Eq (∀ (P : Prop → Prop), P a → P True) True)) % 5.75/5.95 Clause #76 (by equality factoring #[60]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Ne True True) (Eq a True)) % 5.75/5.95 Clause #86 (by clausification #[76]): ∀ (a : Prop), % 5.75/5.95 Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Or (Eq True False) (Eq True False))) % 5.75/5.95 Clause #88 (by clausification #[86]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Eq True False)) % 5.75/5.95 Clause #89 (by clausification #[88]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Eq a True) % 5.75/5.95 Clause #90 (by bool simp #[89]): ∀ (a : Prop), Or (Eq (leibeq False False) True) (Eq a True) % 5.75/5.95 Clause #92 (by equality factoring #[90]): Or (Ne True True) (Eq (leibeq False False) True) % 5.75/5.95 Clause #94 (by clausification #[92]): Or (Eq (leibeq False False) True) (Or (Eq True False) (Eq True False)) % 5.75/5.95 Clause #96 (by clausification #[94]): Or (Eq (leibeq False False) True) (Eq True False) % 5.75/5.96 Clause #97 (by clausification #[96]): Eq (leibeq False False) True % 5.75/5.96 Clause #106 (by betaEtaReduce #[19]): ∀ (a a_1 : Prop), Eq (leibeq a a_1) (∀ (P : Prop → Prop), P a → P a_1) % 5.75/5.96 Clause #108 (by identity boolHoist #[106]): ∀ (a a_1 : Prop), Or (Eq (leibeq a False) (∀ (P : Prop → Prop), P a → P a_1)) (Eq a_1 True) % 5.75/5.96 Clause #119 (by identity loobHoist #[108]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq True False) (∀ (P : Prop → Prop), P a_1 → P a)) (Eq a_1 False)) % 5.75/5.96 Clause #122 (by superposition #[119, 97]): ∀ (a : Prop), % 5.75/5.96 Or (Eq a True) (Or (Eq (leibeq True False) (∀ (P : Prop → Prop), P (leibeq False False) → P a)) (Eq False True)) % 5.75/5.96 Clause #149 (by clausification #[122]): ∀ (a : Prop), Or (Eq a True) (Eq (leibeq True False) (∀ (P : Prop → Prop), P (leibeq False False) → P a)) % 5.75/5.96 Clause #175 (by clausification #[64]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a True) (Or (Eq (leibeq False True) False) (Eq (a_1 a → a_1 True) True)) % 5.75/5.96 Clause #176 (by clausification #[175]): ∀ (a : Prop) (a_1 : Prop → Prop), % 5.75/5.96 Or (Eq a True) (Or (Eq (leibeq False True) False) (Or (Eq (a_1 a) False) (Eq (a_1 True) True))) % 5.75/5.96 Clause #178 (by identity boolHoist #[176]): ∀ (a : Prop) (a_1 : Prop → Prop), % 5.75/5.96 Or (Eq a True) (Or (Eq (leibeq False True) False) (Or (Eq (a_1 True) True) (Or (Eq (a_1 False) False) (Eq a True)))) % 5.75/5.96 Clause #186 (by identity loobHoist #[33]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.96 Or (Eq (leibeq True False) True) % 5.75/5.96 (Or (Eq (skS.0 0 a True) True) % 5.75/5.96 (Or (Eq a_1 False) (Or (Eq (a False) False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False))))) % 5.75/5.96 Clause #188 (by eliminate duplicate literals #[186]): ∀ (a : Prop → Prop) (a_1 : Prop), % 5.75/5.96 Or (Eq (leibeq True False) True) (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Eq (a False) False))) % 5.75/5.96 Clause #190 (by falseElim #[188]): ∀ (a : Prop → Prop), Or (Eq (leibeq True False) True) (Or (Eq (skS.0 0 a True) True) (Eq (a False) False)) % 5.75/5.96 Clause #236 (by eliminate duplicate literals #[178]): ∀ (a : Prop) (a_1 : Prop → Prop), % 5.75/5.96 Or (Eq a True) (Or (Eq (leibeq False True) False) (Or (Eq (a_1 True) True) (Eq (a_1 False) False))) % 5.75/5.96 Clause #250 (by superposition #[190, 97]): Or (Eq (leibeq True False) True) (Or (Eq (skS.0 0 (fun x => leibeq False x) True) True) (Eq False True)) % 5.75/5.96 Clause #283 (by betaEtaReduce #[250]): Or (Eq (leibeq True False) True) (Or (Eq (skS.0 0 (leibeq False) True) True) (Eq False True)) % 5.75/5.96 Clause #284 (by clausification #[283]): Or (Eq (leibeq True False) True) (Eq (skS.0 0 (leibeq False) True) True) % 5.75/5.96 Clause #285 (by superposition #[284, 56]): ∀ (a : Prop), % 5.75/5.96 Or (Eq (leibeq True False) True) % 5.75/5.96 (Or (Eq (leibeq False True) True) (Or (Eq True False) (Or (Eq a False) (Eq (leibeq False True) True)))) % 5.75/5.96 Clause #286 (by clausification #[285]): ∀ (a : Prop), % 5.75/5.96 Or (Eq (leibeq True False) True) (Or (Eq (leibeq False True) True) (Or (Eq a False) (Eq (leibeq False True) True))) % 5.75/5.96 Clause #287 (by eliminate duplicate literals #[286]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Or (Eq (leibeq False True) True) (Eq a False)) % 5.75/5.98 Clause #290 (by falseElim #[287]): Or (Eq (leibeq True False) True) (Eq (leibeq False True) True) % 5.75/5.98 Clause #298 (by superposition #[290, 236]): ∀ (a : Prop) (a_1 : Prop → Prop), % 5.75/5.98 Or (Eq (leibeq True False) True) % 5.75/5.98 (Or (Eq a True) (Or (Eq True False) (Or (Eq (a_1 True) True) (Eq (a_1 False) False)))) % 5.75/5.98 Clause #300 (by clausification #[298]): ∀ (a : Prop) (a_1 : Prop → Prop), % 5.75/5.98 Or (Eq (leibeq True False) True) (Or (Eq a True) (Or (Eq (a_1 True) True) (Eq (a_1 False) False))) % 5.75/5.98 Clause #305 (by neHoist #[300]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq (leibeq True False) True) % 5.75/5.98 (Or (Eq a True) % 5.75/5.98 (Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) True) True) (Or (Eq True False) (Eq (a_2 False) (a_3 False))))) % 5.75/5.98 Clause #460 (by betaEtaReduce #[305]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq (leibeq True False) True) % 5.75/5.98 (Or (Eq a True) (Or (Eq (Ne (a_2 True) (a_3 True)) True) (Or (Eq True False) (Eq (a_2 False) (a_3 False))))) % 5.75/5.98 Clause #461 (by clausification #[460]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq (leibeq True False) True) % 5.75/5.98 (Or (Eq a True) (Or (Eq True False) (Or (Eq (a_2 False) (a_3 False)) (Ne (a_2 True) (a_3 True))))) % 5.75/5.98 Clause #462 (by clausification #[461]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq (leibeq True False) True) (Or (Eq a True) (Or (Eq (a_2 False) (a_3 False)) (Ne (a_2 True) (a_3 True)))) % 5.75/5.98 Clause #463 (by equality resolution #[462]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Or (Eq a True) (Eq ((fun x => x) False) ((fun x => True) False))) % 5.75/5.98 Clause #490 (by betaEtaReduce #[463]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Or (Eq a True) (Eq False True)) % 5.75/5.98 Clause #491 (by clausification #[490]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Eq a True) % 5.75/5.98 Clause #496 (by equality factoring #[491]): Or (Ne True True) (Eq (leibeq True False) True) % 5.75/5.98 Clause #498 (by clausification #[496]): Or (Eq (leibeq True False) True) (Or (Eq True False) (Eq True False)) % 5.75/5.98 Clause #500 (by clausification #[498]): Or (Eq (leibeq True False) True) (Eq True False) % 5.75/5.98 Clause #501 (by clausification #[500]): Eq (leibeq True False) True % 5.75/5.98 Clause #505 (by backward demodulation #[501, 149]): ∀ (a : Prop), Or (Eq a True) (Eq True (∀ (P : Prop → Prop), P (leibeq False False) → P a)) % 5.75/5.98 Clause #507 (by clausification #[505]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a True) (Eq (a_1 (leibeq False False) → a_1 a) True) % 5.75/5.98 Clause #508 (by clausification #[507]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a True) (Or (Eq (a_1 (leibeq False False)) False) (Eq (a_1 a) True)) % 5.75/5.98 Clause #509 (by forward demodulation #[508, 97]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a True) (Or (Eq (a_1 True) False) (Eq (a_1 a) True)) % 5.75/5.98 Clause #511 (by identity boolHoist #[509]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a True) (Or (Eq (a_1 True) False) (Or (Eq (a_1 False) True) (Eq a True))) % 5.75/5.98 Clause #526 (by eliminate duplicate literals #[511]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a True) (Or (Eq (a_1 True) False) (Eq (a_1 False) True)) % 5.75/5.98 Clause #531 (by neHoist #[526]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq a True) (Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) False) True) (Or (Eq True False) (Eq (a_2 True) (a_3 True)))) % 5.75/5.98 Clause #643 (by betaEtaReduce #[531]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq a True) (Or (Eq (Ne (a_2 False) (a_3 False)) True) (Or (Eq True False) (Eq (a_2 True) (a_3 True)))) % 5.75/5.98 Clause #644 (by clausification #[643]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq a True) (Or (Eq True False) (Or (Eq (a_2 True) (a_3 True)) (Ne (a_2 False) (a_3 False)))) % 5.75/5.98 Clause #645 (by clausification #[644]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 5.75/5.98 Or (Eq a True) (Or (Eq (a_2 True) (a_3 True)) (Ne (a_2 False) (a_3 False))) % 5.83/5.99 Clause #646 (by equality resolution #[645]): ∀ (a : Prop), Or (Eq a True) (Eq ((fun x => x) True) ((fun x => False) True)) % 5.83/5.99 Clause #665 (by betaEtaReduce #[646]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 5.83/5.99 Clause #666 (by clausification #[665]): ∀ (a : Prop), Eq a True % 5.83/5.99 Clause #667 (by falseElim #[666]): False % 5.83/5.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------