TSTP Solution File: NUM637^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM637^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n065.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:14 EST 2018
% Result : Timeout 288.24s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM637^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.24 % Computer : n065.star.cs.uiowa.edu
% 0.03/0.24 % Model : x86_64 x86_64
% 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.24 % Memory : 32218.625MB
% 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.24 % CPULimit : 300
% 0.03/0.24 % DateTime : Fri Jan 5 11:17:15 CST 2018
% 0.03/0.24 % CPUTime :
% 0.06/0.27 Python 2.7.13
% 29.35/29.80 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de5ca170>, <kernel.Type object at 0x2b99de271878>) of role type named nat_type
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring nat:Type
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de5ca518>, <kernel.Constant object at 0x2b99de271b48>) of role type named x
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring x:nat
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de5cac20>, <kernel.Constant object at 0x2b99de271b90>) of role type named n_1
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring n_1:nat
% 29.35/29.80 FOF formula (not (((eq nat) x) n_1)) of role axiom named n
% 29.35/29.80 A new axiom: (not (((eq nat) x) n_1))
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de5ca170>, <kernel.DependentProduct object at 0x2b99de271c68>) of role type named suc
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring suc:(nat->nat)
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de271cb0>, <kernel.Type object at 0x2b99de271908>) of role type named set_type
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring set:Type
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de271998>, <kernel.DependentProduct object at 0x2b99de271b90>) of role type named esti
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring esti:(nat->(set->Prop))
% 29.35/29.80 FOF formula (<kernel.Constant object at 0x2b99de271878>, <kernel.DependentProduct object at 0x2b99de271710>) of role type named setof
% 29.35/29.80 Using role type
% 29.35/29.80 Declaring setof:((nat->Prop)->set)
% 29.35/29.80 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))) of role axiom named estie
% 29.35/29.80 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs)))
% 29.35/29.80 FOF formula (forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs))))) of role axiom named ax5
% 29.35/29.80 A new axiom: (forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs)))))
% 29.35/29.80 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))) of role axiom named estii
% 29.35/29.80 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp))))
% 29.35/29.80 FOF formula (forall (Xa:Prop), (((Xa->False)->False)->Xa)) of role axiom named et
% 29.35/29.80 A new axiom: (forall (Xa:Prop), (((Xa->False)->False)->Xa))
% 29.35/29.80 FOF formula ((forall (Xx_0:nat), (not (((eq nat) x) (suc Xx_0))))->False) of role conjecture named satz3
% 29.35/29.80 Conjecture to prove = ((forall (Xx_0:nat), (not (((eq nat) x) (suc Xx_0))))->False):Prop
% 29.35/29.80 Parameter set_DUMMY:set.
% 29.35/29.80 We need to prove ['((forall (Xx_0:nat), (not (((eq nat) x) (suc Xx_0))))->False)']
% 29.35/29.80 Parameter nat:Type.
% 29.35/29.80 Parameter x:nat.
% 29.35/29.80 Parameter n_1:nat.
% 29.35/29.80 Axiom n:(not (((eq nat) x) n_1)).
% 29.35/29.80 Parameter suc:(nat->nat).
% 29.35/29.80 Parameter set:Type.
% 29.35/29.80 Parameter esti:(nat->(set->Prop)).
% 29.35/29.80 Parameter setof:((nat->Prop)->set).
% 29.35/29.80 Axiom estie:(forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))).
% 29.35/29.80 Axiom ax5:(forall (Xs:set), (((esti n_1) Xs)->((forall (Xx:nat), (((esti Xx) Xs)->((esti (suc Xx)) Xs)))->(forall (Xx:nat), ((esti Xx) Xs))))).
% 29.35/29.80 Axiom estii:(forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))).
% 29.35/29.80 Axiom et:(forall (Xa:Prop), (((Xa->False)->False)->Xa)).
% 29.35/29.80 Trying to prove ((forall (Xx_0:nat), (not (((eq nat) x) (suc Xx_0))))->False)
% 29.35/29.80 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 29.35/29.80 Found (eq_ref00 P) as proof of (P0 x)
% 29.35/29.80 Found ((eq_ref0 x) P) as proof of (P0 x)
% 29.35/29.80 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 29.35/29.80 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 29.35/29.80 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 29.35/29.80 Found (eq_ref00 P) as proof of (P0 x)
% 29.35/29.80 Found ((eq_ref0 x) P) as proof of (P0 x)
% 29.35/29.80 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 29.35/29.80 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 29.35/29.80 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 29.35/29.80 Found (eq_ref00 P) as proof of (P0 x)
% 29.35/29.80 Found ((eq_ref0 x) P) as proof of (P0 x)
% 29.35/29.80 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 29.35/29.80 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 29.35/29.80 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 29.35/29.80 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 29.35/29.80 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 29.35/29.80 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 29.35/29.80 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 29.35/29.80 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 66.10/66.49 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 66.10/66.49 Found (eq_ref00 P) as proof of (P0 x)
% 66.10/66.49 Found ((eq_ref0 x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 66.10/66.49 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 66.10/66.49 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 66.10/66.49 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 66.10/66.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 66.10/66.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 66.10/66.49 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 66.10/66.49 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 66.10/66.49 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 66.10/66.49 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 66.10/66.49 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 66.10/66.49 Found (eq_ref00 P) as proof of (P0 x)
% 66.10/66.49 Found ((eq_ref0 x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 66.10/66.49 Found (eq_ref00 P) as proof of (P0 x)
% 66.10/66.49 Found ((eq_ref0 x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 66.10/66.49 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 66.10/66.49 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 66.10/66.49 Found (eq_ref00 P) as proof of (P0 x)
% 66.10/66.49 Found ((eq_ref0 x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 66.10/66.49 Found (eq_ref00 P) as proof of (P0 x)
% 66.10/66.49 Found ((eq_ref0 x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 66.10/66.49 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 66.10/66.49 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 66.10/66.49 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 66.10/66.49 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 66.10/66.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 66.10/66.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 66.10/66.49 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 66.10/66.49 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 66.10/66.49 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 79.44/79.89 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 79.44/79.89 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 79.44/79.89 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 79.44/79.89 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 79.44/79.89 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 79.44/79.89 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 79.44/79.89 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 79.44/79.89 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 79.44/79.89 Found (eq_ref00 P) as proof of (P0 x)
% 79.44/79.89 Found ((eq_ref0 x) P) as proof of (P0 x)
% 79.44/79.89 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 79.44/79.89 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 79.44/79.89 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 79.44/79.89 Found (eq_ref00 P) as proof of (P0 x)
% 79.44/79.89 Found ((eq_ref0 x) P) as proof of (P0 x)
% 79.44/79.89 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 79.44/79.89 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 79.44/79.89 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 79.44/79.89 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 79.44/79.89 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 79.44/79.89 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 79.44/79.89 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 79.44/79.89 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 79.44/79.89 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 79.44/79.89 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 79.44/79.89 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 79.44/79.89 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 79.44/79.89 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 79.44/79.89 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 79.44/79.89 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 116.87/117.29 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 116.87/117.29 Found (eq_ref00 P) as proof of (P0 x)
% 116.87/117.29 Found ((eq_ref0 x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 116.87/117.29 Found (eq_ref00 P) as proof of (P0 x)
% 116.87/117.29 Found ((eq_ref0 x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 116.87/117.29 Found (eq_ref00 P) as proof of (P0 x)
% 116.87/117.29 Found ((eq_ref0 x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 116.87/117.29 Found (eq_ref00 P) as proof of (P0 x)
% 116.87/117.29 Found ((eq_ref0 x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 116.87/117.29 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 116.87/117.29 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 116.87/117.29 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 116.87/117.29 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 116.87/117.29 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 116.87/117.29 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 116.87/117.29 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 116.87/117.29 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 116.87/117.29 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 116.87/117.29 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 116.87/117.29 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 116.87/117.29 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 116.87/117.29 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 131.91/132.30 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 131.91/132.30 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 131.91/132.30 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 131.91/132.30 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 131.91/132.30 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 131.91/132.30 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 131.91/132.30 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 131.91/132.30 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 131.91/132.30 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 131.91/132.30 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 131.91/132.30 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 131.91/132.30 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 131.91/132.30 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 131.91/132.30 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 131.91/132.30 Found estie100:=(estie10 x1):False
% 131.91/132.30 Found (estie10 x1) as proof of False
% 131.91/132.30 Found ((estie1 (fun (x4:nat)=> False)) x1) as proof of False
% 131.91/132.30 Found (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1) as proof of False
% 131.91/132.30 Found (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)) as proof of False
% 131.91/132.30 Found (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)) as proof of ((((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False)->False)
% 131.91/132.30 Found (et0 (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))
% 131.91/132.30 Found ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))
% 131.91/132.30 Found (fun (x1:((esti Xx) (setof (fun (x10:nat)=> False))))=> ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))
% 131.91/132.30 Found (fun (Xx:nat) (x1:((esti Xx) (setof (fun (x10:nat)=> False))))=> ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)))) as proof of (((esti Xx) (setof (fun (x10:nat)=> False)))->((esti (suc Xx)) (setof (fun (x1:nat)=> False))))
% 131.91/132.30 Found (fun (Xx:nat) (x1:((esti Xx) (setof (fun (x10:nat)=> False))))=> ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)))) as proof of (forall (Xx:nat), (((esti Xx) (setof (fun (x10:nat)=> False)))->((esti (suc Xx)) (setof (fun (x1:nat)=> False)))))
% 131.91/132.30 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 131.91/132.30 Found (eq_ref00 P) as proof of (P0 x)
% 131.91/132.30 Found ((eq_ref0 x) P) as proof of (P0 x)
% 131.91/132.30 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 131.91/132.30 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 131.91/132.30 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 131.91/132.30 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 149.53/149.98 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 149.53/149.98 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 149.53/149.98 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 149.53/149.98 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 149.53/149.98 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 149.53/149.98 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 149.53/149.98 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 149.53/149.98 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 149.53/149.98 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 149.53/149.98 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 149.53/149.98 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 149.53/149.98 Found (eq_ref00 P) as proof of (P0 x)
% 149.53/149.98 Found ((eq_ref0 x) P) as proof of (P0 x)
% 149.53/149.98 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 149.53/149.98 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 149.53/149.98 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 149.53/149.98 Found (eq_ref00 P) as proof of (P0 x)
% 149.53/149.98 Found ((eq_ref0 x) P) as proof of (P0 x)
% 149.53/149.98 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 149.53/149.98 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 149.53/149.98 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 149.53/149.98 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 149.53/149.98 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 149.53/149.98 Found estii000:=(estii00 x00):((esti n_1) (setof P))
% 149.53/149.98 Found (estii00 x00) as proof of ((esti n_1) (setof P))
% 149.53/149.98 Found ((estii0 n_1) x00) as proof of ((esti n_1) (setof P))
% 149.53/149.98 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 149.53/149.98 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 149.53/149.98 Found eq_ref00:=(eq_ref0 (suc Xx)):(((eq nat) (suc Xx)) (suc Xx))
% 149.53/149.98 Found (eq_ref0 (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 149.53/149.98 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 149.53/149.98 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 149.53/149.98 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 149.53/149.98 Found (estii00 ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 176.46/176.90 Found ((estii0 (suc Xx)) ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 176.46/176.90 Found (((estii (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))) (suc Xx)) ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 176.46/176.90 Found (fun (x1:((esti Xx) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0))))))=> (((estii (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))) (suc Xx)) ((eq_ref nat) (suc Xx)))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 176.46/176.90 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 176.46/176.90 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 176.46/176.90 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 176.46/176.90 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 176.46/176.90 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 176.46/176.90 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 176.46/176.90 Found eq_ref000:=(eq_ref00 P):((P (suc Xx))->(P (suc Xx)))
% 176.46/176.90 Found (eq_ref00 P) as proof of (P0 (suc Xx))
% 176.46/176.90 Found ((eq_ref0 (suc Xx)) P) as proof of (P0 (suc Xx))
% 176.46/176.90 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 176.46/176.90 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 176.46/176.90 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 176.46/176.90 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 176.46/176.90 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 176.46/176.90 Found (eq_ref00 P) as proof of (P0 x)
% 176.46/176.90 Found ((eq_ref0 x) P) as proof of (P0 x)
% 176.46/176.90 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 176.46/176.90 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 176.46/176.90 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 176.46/176.90 Found (eq_ref00 P) as proof of (P0 x)
% 176.46/176.90 Found ((eq_ref0 x) P) as proof of (P0 x)
% 176.46/176.90 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 176.46/176.90 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 176.46/176.90 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 176.46/176.90 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 176.46/176.90 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 176.46/176.90 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 176.46/176.90 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 176.46/176.90 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 176.46/176.90 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 176.46/176.90 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 176.46/176.90 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 205.78/206.24 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 205.78/206.24 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 205.78/206.24 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 205.78/206.24 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 205.78/206.24 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 205.78/206.24 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 205.78/206.24 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 205.78/206.24 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 205.78/206.24 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 205.78/206.24 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 205.78/206.24 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 205.78/206.24 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 205.78/206.24 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 205.78/206.24 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 205.78/206.24 Found estie100:=(estie10 x1):False
% 205.78/206.24 Found (estie10 x1) as proof of False
% 205.78/206.24 Found ((estie1 (fun (x4:nat)=> False)) x1) as proof of False
% 205.78/206.24 Found (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1) as proof of False
% 205.78/206.24 Found (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)) as proof of False
% 205.78/206.24 Found (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)) as proof of ((((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False)->False)
% 220.01/220.49 Found (et0 (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))
% 220.01/220.49 Found ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))
% 220.01/220.49 Found (fun (x1:((esti Xx) (setof (fun (x10:nat)=> False))))=> ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))
% 220.01/220.49 Found (fun (Xx:nat) (x1:((esti Xx) (setof (fun (x10:nat)=> False))))=> ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)))) as proof of (((esti Xx) (setof (fun (x10:nat)=> False)))->((esti (suc Xx)) (setof (fun (x1:nat)=> False))))
% 220.01/220.49 Found (fun (Xx:nat) (x1:((esti Xx) (setof (fun (x10:nat)=> False))))=> ((et ((esti (suc Xx)) (setof (fun (x10:nat)=> False)))) (fun (x2:(((esti (suc Xx)) (setof (fun (x10:nat)=> False)))->False))=> (((fun (Xp:(nat->Prop))=> ((estie Xp) Xx)) (fun (x4:nat)=> False)) x1)))) as proof of (forall (Xx:nat), (((esti Xx) (setof (fun (x10:nat)=> False)))->((esti (suc Xx)) (setof (fun (x1:nat)=> False)))))
% 220.01/220.49 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 220.01/220.49 Found (eq_ref00 P) as proof of (P0 x)
% 220.01/220.49 Found ((eq_ref0 x) P) as proof of (P0 x)
% 220.01/220.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 220.01/220.49 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 220.01/220.49 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 220.01/220.49 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 220.01/220.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 220.01/220.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 220.01/220.49 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found estii000:=(estii00 x00):((esti n_1) (setof P))
% 220.01/220.49 Found (estii00 x00) as proof of ((esti n_1) (setof P))
% 220.01/220.49 Found ((estii0 n_1) x00) as proof of ((esti n_1) (setof P))
% 220.01/220.49 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 220.01/220.49 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 220.01/220.49 Found eq_ref00:=(eq_ref0 (suc Xx)):(((eq nat) (suc Xx)) (suc Xx))
% 220.01/220.49 Found (eq_ref0 (suc Xx)) as proof of (((eq nat) (suc Xx)) b)
% 220.01/220.49 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) b)
% 220.01/220.49 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) b)
% 220.01/220.49 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) b)
% 220.01/220.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 220.01/220.49 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 220.01/220.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 220.01/220.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 220.01/220.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 220.01/220.49 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 220.01/220.49 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 220.01/220.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 220.01/220.49 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 220.01/220.49 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 220.01/220.49 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 233.58/234.11 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 233.58/234.11 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 233.58/234.11 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 233.58/234.11 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 233.58/234.11 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 233.58/234.11 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 233.58/234.11 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 233.58/234.11 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 233.58/234.11 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 233.58/234.11 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 233.58/234.11 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 233.58/234.11 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 233.58/234.11 Found (eq_ref00 P) as proof of (P0 x)
% 233.58/234.11 Found ((eq_ref0 x) P) as proof of (P0 x)
% 233.58/234.11 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 233.58/234.11 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 233.58/234.11 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 233.58/234.11 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 233.58/234.11 Found eq_ref00:=(eq_ref0 (suc Xx)):(((eq nat) (suc Xx)) (suc Xx))
% 233.58/234.11 Found (eq_ref0 (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 233.58/234.11 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 233.58/234.11 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 233.58/234.11 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 233.58/234.11 Found (estii00 ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 233.58/234.11 Found ((estii0 (suc Xx)) ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 233.58/234.11 Found (((estii (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))) (suc Xx)) ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 233.58/234.11 Found (fun (x1:((esti Xx) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0))))))=> (((estii (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))) (suc Xx)) ((eq_ref nat) (suc Xx)))) as proof of ((esti (suc Xx)) (setof (fun (x10:nat)=> (((eq nat) x10) (suc Xx_0)))))
% 233.58/234.11 Found estii000:=(estii00 x00):((esti n_1) (setof P))
% 262.94/263.42 Found (estii00 x00) as proof of ((esti n_1) (setof P))
% 262.94/263.42 Found ((estii0 n_1) x00) as proof of ((esti n_1) (setof P))
% 262.94/263.42 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 262.94/263.42 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 262.94/263.42 Found eq_ref000:=(eq_ref00 P):((P (suc Xx))->(P (suc Xx)))
% 262.94/263.42 Found (eq_ref00 P) as proof of (P0 (suc Xx))
% 262.94/263.42 Found ((eq_ref0 (suc Xx)) P) as proof of (P0 (suc Xx))
% 262.94/263.42 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 262.94/263.42 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 262.94/263.42 Found eq_ref00:=(eq_ref0 (suc Xx)):(((eq nat) (suc Xx)) (suc Xx))
% 262.94/263.42 Found (eq_ref0 (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 262.94/263.42 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 262.94/263.42 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 262.94/263.42 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 262.94/263.42 Found (estii00 ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0)))))
% 262.94/263.42 Found ((estii0 (suc Xx)) ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0)))))
% 262.94/263.43 Found (((estii (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0)))) (suc Xx)) ((eq_ref nat) (suc Xx))) as proof of ((esti (suc Xx)) (setof (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0)))))
% 262.94/263.43 Found (fun (x2:((esti Xx) (setof (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0))))))=> (((estii (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0)))) (suc Xx)) ((eq_ref nat) (suc Xx)))) as proof of ((esti (suc Xx)) (setof (fun (x20:nat)=> (((eq nat) x20) (suc Xx_0)))))
% 262.94/263.43 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 262.94/263.43 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 262.94/263.43 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 262.94/263.43 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 262.94/263.43 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 262.94/263.43 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 262.94/263.43 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 262.94/263.43 Found (((estii (fun (x2:nat)=> (((eq nat) x2) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x2:nat)=> (((eq nat) x2) n_1))))
% 262.94/263.43 Found estii000:=(estii00 x00):((esti n_1) (setof P))
% 262.94/263.43 Found (estii00 x00) as proof of ((esti n_1) (setof P))
% 262.94/263.43 Found ((estii0 n_1) x00) as proof of ((esti n_1) (setof P))
% 262.94/263.43 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 262.94/263.43 Found (((estii P) n_1) x00) as proof of ((esti n_1) (setof P))
% 262.94/263.43 Found eq_ref00:=(eq_ref0 x):(((eq nat) x) x)
% 262.94/263.43 Found (eq_ref0 x) as proof of (((eq nat) x) b)
% 262.94/263.43 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 262.94/263.43 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 262.94/263.43 Found ((eq_ref nat) x) as proof of (((eq nat) x) b)
% 262.94/263.43 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 262.94/263.43 Found (eq_ref0 b) as proof of (((eq nat) b) n_1)
% 262.94/263.43 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 262.94/263.43 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 262.94/263.43 Found ((eq_ref nat) b) as proof of (((eq nat) b) n_1)
% 262.94/263.43 Found x00:(P x)
% 262.94/263.43 Instantiate: b:=x:nat
% 262.94/263.43 Found x00 as proof of (P0 b)
% 262.94/263.43 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 262.94/263.43 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 262.94/263.43 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 262.94/263.43 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 262.94/263.43 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 262.94/263.43 Found eq_ref000:=(eq_ref00 P):((P (suc Xx))->(P (suc Xx)))
% 262.94/263.43 Found (eq_ref00 P) as proof of (P0 (suc Xx))
% 262.94/263.43 Found ((eq_ref0 (suc Xx)) P) as proof of (P0 (suc Xx))
% 262.94/263.43 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 262.94/263.43 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 262.94/263.43 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 262.94/263.43 Found (eq_ref00 P) as proof of (P0 x)
% 262.94/263.43 Found ((eq_ref0 x) P) as proof of (P0 x)
% 262.94/263.43 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 262.94/263.43 Found (((eq_ref nat) x) P) as proof of (P0 x)
% 262.94/263.43 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 262.94/263.43 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 262.94/263.43 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 262.94/263.43 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found (((estii ((eq nat) n_1)) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof ((eq nat) n_1)))
% 288.24/288.79 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 288.24/288.79 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found eq_ref000:=(eq_ref00 P):((P (suc Xx))->(P (suc Xx)))
% 288.24/288.79 Found (eq_ref00 P) as proof of (P0 (suc Xx))
% 288.24/288.79 Found ((eq_ref0 (suc Xx)) P) as proof of (P0 (suc Xx))
% 288.24/288.79 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 288.24/288.79 Found (((eq_ref nat) (suc Xx)) P) as proof of (P0 (suc Xx))
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 288.24/288.79 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 288.24/288.79 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 288.24/288.79 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 288.24/288.79 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 288.24/288.79 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 288.24/288.79 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 288.24/288.79 Found (eq_ref0 b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found ((eq_ref nat) b) as proof of (((eq nat) b) x)
% 288.24/288.79 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 288.24/288.79 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 288.24/288.79 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 292.20/292.71 Found x00:(P x)
% 292.20/292.71 Instantiate: b:=x:nat
% 292.20/292.71 Found x00 as proof of (P0 b)
% 292.20/292.71 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 292.20/292.71 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) b)
% 292.20/292.71 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 292.20/292.71 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 292.20/292.71 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) b)
% 292.20/292.71 Found eq_ref00:=(eq_ref0 n_1):(((eq nat) n_1) n_1)
% 292.20/292.71 Found (eq_ref0 n_1) as proof of (((eq nat) n_1) n_1)
% 292.20/292.71 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 292.20/292.71 Found ((eq_ref nat) n_1) as proof of (((eq nat) n_1) n_1)
% 292.20/292.71 Found (estii00 ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 292.20/292.71 Found ((estii0 n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 292.20/292.71 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 292.20/292.71 Found (((estii (fun (x1:nat)=> (((eq nat) x1) n_1))) n_1) ((eq_ref nat) n_1)) as proof of ((esti n_1) (setof (fun (x1:nat)=> (((eq nat) x1) n_1))))
% 292.20/292.71 Found eq_ref00:=(eq_ref0 (suc Xx)):(((eq nat) (suc Xx)) (suc Xx))
% 292.20/292.71 Found (eq_ref0 (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 292.20/292.71 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 292.20/292.71 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 292.20/292.71 Found ((eq_ref nat) (suc Xx)) as proof of (((eq nat) (suc Xx)) (suc Xx_0))
% 292.20/292.71 Found (x10 ((eq_ref nat) (suc Xx))) as proof of False
% 292.20/292.71 Found ((x1 Xx) ((eq_ref nat) (suc Xx))) as proof of False
% 292.20/292.71 Found (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx)))) as proof of False
% 292.20/292.71 Found (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx)))) as proof of (not (forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))
% 292.20/292.71 Found (estii00 (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx))))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))))
% 292.20/292.71 Found ((estii0 (suc Xx)) (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx))))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))))
% 292.20/292.71 Found (((estii (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))) (suc Xx)) (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx))))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))))
% 292.20/292.71 Found (fun (x0:((esti Xx) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0)))))))))=> (((estii (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))) (suc Xx)) (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx)))))) as proof of ((esti (suc Xx)) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))))
% 292.20/292.71 Found (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0)))))))))=> (((estii (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))) (suc Xx)) (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx)))))) as proof of (((esti Xx) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))))->((esti (suc Xx)) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0)))))))))
% 292.20/292.71 Found (fun (Xx:nat) (x0:((esti Xx) (setof (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0)))))))))=> (((estii (fun (x1:nat)=> (not (forall (Xx_0:nat), (not (((eq nat) x1) (suc Xx_0))))))) (suc Xx)) (fun (x1:(forall (Xx_0:nat), (not (((eq nat) (suc Xx)) (suc Xx_0)))))=> ((x1 Xx) ((eq_ref nat) (suc Xx)))))) as proof of (forall (Xx:nat), (((esti Xx) (setof (fun (x1:nat)=> (not (for
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