0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : duper %s
0.13/0.33	% Computer : n027.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1440
0.13/0.33	% WCLimit    : 180
0.13/0.33	% DateTime   : Mon Jul  3 07:32:16 EDT 2023
0.13/0.34	% CPUTime    : 
6.16/6.31	SZS status Theorem for theBenchmark.p
6.16/6.31	SZS output start Proof for theBenchmark.p
6.16/6.31	Clause #0 (by assumption #[]): Eq (Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y) True
6.16/6.31	Clause #1 (by assumption #[]): Eq (Not (Not (∀ (F : Prop → Prop), Exists fun X => leibeq (F X) X))) True
6.16/6.31	Clause #2 (by clausification #[1]): Eq (Not (∀ (F : Prop → Prop), Exists fun X => leibeq (F X) X)) False
6.16/6.31	Clause #3 (by clausification #[2]): Eq (∀ (F : Prop → Prop), Exists fun X => leibeq (F X) X) True
6.16/6.31	Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop), Eq (Exists fun X => leibeq (a X) X) True
6.16/6.31	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
6.16/6.31	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)
6.16/6.31	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)
6.16/6.31	Clause #9 (by identity boolHoist #[6]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  Or (Eq (skS.0 0 a a_1) False) (Or (Eq (leibeq False True) True) (Eq (a (skS.0 0 a a_1)) True))
6.16/6.31	Clause #17 (by clausification #[0]): Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y
6.16/6.31	Clause #18 (by argument congruence #[17]): ∀ (a : Prop), Eq (leibeq a) ((fun X Y => ∀ (P : Prop → Prop), P X → P Y) a)
6.16/6.31	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)
6.16/6.31	Clause #20 (by betaEtaReduce #[18]): ∀ (a : Prop), Eq (leibeq a) fun Y => ∀ (P : Prop → Prop), P a → P Y
6.16/6.31	Clause #22 (by identity boolHoist #[20]): ∀ (a : Prop), Or (Eq (leibeq False) fun Y => ∀ (P : Prop → Prop), P a → P Y) (Eq a True)
6.16/6.31	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)
6.16/6.31	Clause #28 (by identity loobHoist #[7]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  Or (Eq (skS.0 0 a a_1) True) (Or (Eq (leibeq True False) True) (Eq (a (skS.0 0 a a_1)) False))
6.16/6.31	Clause #30 (by identity loobHoist #[28]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  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)))
6.16/6.31	Clause #33 (by identity boolHoist #[30]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  Or (Eq (leibeq True False) True)
6.16/6.31	    (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))))
6.16/6.31	Clause #50 (by identity loobHoist #[9]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  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)))
6.16/6.31	Clause #52 (by identity loobHoist #[50]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  Or (Eq (leibeq False True) True)
6.16/6.31	    (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))))
6.16/6.31	Clause #54 (by identity loobHoist #[52]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  Or (Eq (leibeq False True) True)
6.16/6.31	    (Or (Eq (skS.0 0 a True) False)
6.16/6.31	      (Or (Eq a_1 False) (Or (Eq (a True) True) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False)))))
6.16/6.31	Clause #56 (by eliminate duplicate literals #[54]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.31	  Or (Eq (leibeq False True) True) (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Eq (a True) True)))
6.16/6.31	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)
6.16/6.31	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))
6.16/6.31	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))
6.16/6.31	Clause #62 (by falseElim #[59]): ∀ (a : Prop), Or (Eq a True) (Eq (leibeq False True) (∀ (P : Prop → Prop), P a → P True))
6.16/6.31	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))
6.16/6.34	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))
6.16/6.34	Clause #86 (by clausification #[76]): ∀ (a : Prop),
6.16/6.34	  Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Or (Eq True False) (Eq True False)))
6.16/6.34	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))
6.16/6.34	Clause #89 (by clausification #[88]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Eq a True)
6.16/6.34	Clause #90 (by bool simp #[89]): ∀ (a : Prop), Or (Eq (leibeq False False) True) (Eq a True)
6.16/6.34	Clause #92 (by equality factoring #[90]): Or (Ne True True) (Eq (leibeq False False) True)
6.16/6.34	Clause #94 (by clausification #[92]): Or (Eq (leibeq False False) True) (Or (Eq True False) (Eq True False))
6.16/6.34	Clause #96 (by clausification #[94]): Or (Eq (leibeq False False) True) (Eq True False)
6.16/6.34	Clause #97 (by clausification #[96]): Eq (leibeq False False) True
6.16/6.34	Clause #106 (by betaEtaReduce #[19]): ∀ (a a_1 : Prop), Eq (leibeq a a_1) (∀ (P : Prop → Prop), P a → P a_1)
6.16/6.34	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)
6.16/6.34	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))
6.16/6.34	Clause #122 (by superposition #[119, 97]): ∀ (a : Prop),
6.16/6.34	  Or (Eq a True) (Or (Eq (leibeq True False) (∀ (P : Prop → Prop), P (leibeq False False) → P a)) (Eq False True))
6.16/6.34	Clause #149 (by clausification #[122]): ∀ (a : Prop), Or (Eq a True) (Eq (leibeq True False) (∀ (P : Prop → Prop), P (leibeq False False) → P a))
6.16/6.34	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))
6.16/6.34	Clause #176 (by clausification #[175]): ∀ (a : Prop) (a_1 : Prop → Prop),
6.16/6.34	  Or (Eq a True) (Or (Eq (leibeq False True) False) (Or (Eq (a_1 a) False) (Eq (a_1 True) True)))
6.16/6.34	Clause #178 (by identity boolHoist #[176]): ∀ (a : Prop) (a_1 : Prop → Prop),
6.16/6.34	  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))))
6.16/6.34	Clause #186 (by identity loobHoist #[33]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.34	  Or (Eq (leibeq True False) True)
6.16/6.34	    (Or (Eq (skS.0 0 a True) True)
6.16/6.34	      (Or (Eq a_1 False) (Or (Eq (a False) False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False)))))
6.16/6.34	Clause #188 (by eliminate duplicate literals #[186]): ∀ (a : Prop → Prop) (a_1 : Prop),
6.16/6.34	  Or (Eq (leibeq True False) True) (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Eq (a False) False)))
6.16/6.34	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))
6.16/6.34	Clause #236 (by eliminate duplicate literals #[178]): ∀ (a : Prop) (a_1 : Prop → Prop),
6.16/6.34	  Or (Eq a True) (Or (Eq (leibeq False True) False) (Or (Eq (a_1 True) True) (Eq (a_1 False) False)))
6.16/6.34	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))
6.16/6.34	Clause #283 (by betaEtaReduce #[250]): Or (Eq (leibeq True False) True) (Or (Eq (skS.0 0 (leibeq False) True) True) (Eq False True))
6.16/6.34	Clause #284 (by clausification #[283]): Or (Eq (leibeq True False) True) (Eq (skS.0 0 (leibeq False) True) True)
6.16/6.34	Clause #285 (by superposition #[284, 56]): ∀ (a : Prop),
6.16/6.34	  Or (Eq (leibeq True False) True)
6.16/6.34	    (Or (Eq (leibeq False True) True) (Or (Eq True False) (Or (Eq a False) (Eq (leibeq False True) True))))
6.16/6.34	Clause #286 (by clausification #[285]): ∀ (a : Prop),
6.16/6.34	  Or (Eq (leibeq True False) True) (Or (Eq (leibeq False True) True) (Or (Eq a False) (Eq (leibeq False True) True)))
6.16/6.34	Clause #287 (by eliminate duplicate literals #[286]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Or (Eq (leibeq False True) True) (Eq a False))
6.16/6.36	Clause #290 (by falseElim #[287]): Or (Eq (leibeq True False) True) (Eq (leibeq False True) True)
6.16/6.36	Clause #298 (by superposition #[290, 236]): ∀ (a : Prop) (a_1 : Prop → Prop),
6.16/6.36	  Or (Eq (leibeq True False) True)
6.16/6.36	    (Or (Eq a True) (Or (Eq True False) (Or (Eq (a_1 True) True) (Eq (a_1 False) False))))
6.16/6.36	Clause #300 (by clausification #[298]): ∀ (a : Prop) (a_1 : Prop → Prop),
6.16/6.36	  Or (Eq (leibeq True False) True) (Or (Eq a True) (Or (Eq (a_1 True) True) (Eq (a_1 False) False)))
6.16/6.36	Clause #305 (by neHoist #[300]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  Or (Eq (leibeq True False) True)
6.16/6.36	    (Or (Eq a True)
6.16/6.36	      (Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) True) True) (Or (Eq True False) (Eq (a_2 False) (a_3 False)))))
6.16/6.36	Clause #460 (by betaEtaReduce #[305]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  Or (Eq (leibeq True False) True)
6.16/6.36	    (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)))))
6.16/6.36	Clause #461 (by clausification #[460]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  Or (Eq (leibeq True False) True)
6.16/6.36	    (Or (Eq a True) (Or (Eq True False) (Or (Eq (a_2 False) (a_3 False)) (Ne (a_2 True) (a_3 True)))))
6.16/6.36	Clause #462 (by clausification #[461]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  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))))
6.16/6.36	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)))
6.16/6.36	Clause #490 (by betaEtaReduce #[463]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Or (Eq a True) (Eq False True))
6.16/6.36	Clause #491 (by clausification #[490]): ∀ (a : Prop), Or (Eq (leibeq True False) True) (Eq a True)
6.16/6.36	Clause #496 (by equality factoring #[491]): Or (Ne True True) (Eq (leibeq True False) True)
6.16/6.36	Clause #498 (by clausification #[496]): Or (Eq (leibeq True False) True) (Or (Eq True False) (Eq True False))
6.16/6.36	Clause #500 (by clausification #[498]): Or (Eq (leibeq True False) True) (Eq True False)
6.16/6.36	Clause #501 (by clausification #[500]): Eq (leibeq True False) True
6.16/6.36	Clause #505 (by backward demodulation #[501, 149]): ∀ (a : Prop), Or (Eq a True) (Eq True (∀ (P : Prop → Prop), P (leibeq False False) → P a))
6.16/6.36	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)
6.16/6.36	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))
6.16/6.36	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))
6.16/6.36	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)))
6.16/6.36	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))
6.16/6.36	Clause #531 (by neHoist #[526]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  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))))
6.16/6.36	Clause #643 (by betaEtaReduce #[531]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  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))))
6.16/6.36	Clause #644 (by clausification #[643]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  Or (Eq a True) (Or (Eq True False) (Or (Eq (a_2 True) (a_3 True)) (Ne (a_2 False) (a_3 False))))
6.16/6.36	Clause #645 (by clausification #[644]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x),
6.16/6.36	  Or (Eq a True) (Or (Eq (a_2 True) (a_3 True)) (Ne (a_2 False) (a_3 False)))
6.16/6.38	Clause #646 (by equality resolution #[645]): ∀ (a : Prop), Or (Eq a True) (Eq ((fun x => x) True) ((fun x => False) True))
6.16/6.38	Clause #665 (by betaEtaReduce #[646]): ∀ (a : Prop), Or (Eq a True) (Eq True False)
6.16/6.38	Clause #666 (by clausification #[665]): ∀ (a : Prop), Eq a True
6.16/6.38	Clause #667 (by falseElim #[666]): False
6.16/6.38	SZS output end Proof for theBenchmark.p
6.16/6.38	EOF