TSTP Solution File: NUM711^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM711^1 : TPTP v7.0.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n151.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 13:11:32 EST 2018
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM711^1 : TPTP v7.0.0. Released v3.7.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n151.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 13:25:06 CST 2018
% 0.02/0.23 % CPUTime :
% 0.07/0.24 Python 2.7.13
% 0.07/0.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f5771200>, <kernel.Type object at 0x2b42f505f638>) of role type named nat_type
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring nat:Type
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f5771128>, <kernel.Constant object at 0x2b42f505ffc8>) of role type named x
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring x:nat
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f5771200>, <kernel.Constant object at 0x2b42f505f5f0>) of role type named y
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring y:nat
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f5771128>, <kernel.Constant object at 0x2b42f505f170>) of role type named z
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring z:nat
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f5771200>, <kernel.DependentProduct object at 0x2b42f505f5f0>) of role type named ts
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring ts:(nat->(nat->nat))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f5771200>, <kernel.DependentProduct object at 0x2b42f505f9e0>) of role type named pl
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring pl:(nat->(nat->nat))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f505f170>, <kernel.Type object at 0x2b42f505fe18>) of role type named set_type
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring set:Type
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f505f5f0>, <kernel.DependentProduct object at 0x2b42f505fd88>) of role type named esti
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring esti:(nat->(set->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f505f638>, <kernel.DependentProduct object at 0x2b42f505f1b8>) of role type named setof
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring setof:((nat->Prop)->set)
% 0.07/0.52 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))) of role axiom named estie
% 0.07/0.52 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs)))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f505f3f8>, <kernel.Constant object at 0x2b42f505fea8>) of role type named n_1
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring n_1:nat
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b42f505f638>, <kernel.DependentProduct object at 0x2b42f505f170>) of role type named suc
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring suc:(nat->nat)
% 0.07/0.52 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
% 0.07/0.52 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)))))
% 0.07/0.52 FOF formula (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))) of role axiom named estii
% 0.07/0.52 A new axiom: (forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp))))
% 0.07/0.52 FOF formula (forall (Xx:nat), (((eq nat) Xx) ((ts Xx) n_1))) of role axiom named satz28e
% 0.07/0.52 A new axiom: (forall (Xx:nat), (((eq nat) Xx) ((ts Xx) n_1)))
% 0.07/0.52 FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) (suc Xy))) ((pl ((ts Xx) Xy)) Xx))) of role axiom named satz28b
% 0.07/0.52 A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) (suc Xy))) ((pl ((ts Xx) Xy)) Xx)))
% 0.07/0.52 FOF formula (forall (Xx:nat), (((eq nat) ((pl Xx) n_1)) (suc Xx))) of role axiom named satz4a
% 0.07/0.52 A new axiom: (forall (Xx:nat), (((eq nat) ((pl Xx) n_1)) (suc Xx)))
% 0.07/0.52 FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) ((pl ((ts Xx) Xy)) Xx)) ((ts Xx) (suc Xy)))) of role axiom named satz28f
% 0.07/0.52 A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) ((pl ((ts Xx) Xy)) Xx)) ((ts Xx) (suc Xy))))
% 0.07/0.52 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((eq nat) ((pl ((pl Xx) Xy)) Xz)) ((pl Xx) ((pl Xy) Xz)))) of role axiom named satz5
% 0.07/0.52 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((eq nat) ((pl ((pl Xx) Xy)) Xz)) ((pl Xx) ((pl Xy) Xz))))
% 0.07/0.52 FOF formula (forall (Xx:nat) (Xy:nat), (((eq nat) ((pl Xx) (suc Xy))) (suc ((pl Xx) Xy)))) of role axiom named satz4b
% 0.07/0.52 A new axiom: (forall (Xx:nat) (Xy:nat), (((eq nat) ((pl Xx) (suc Xy))) (suc ((pl Xx) Xy))))
% 0.07/0.52 FOF formula (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z))) of role conjecture named satz30
% 0.07/0.52 Conjecture to prove = (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z))):Prop
% 0.07/0.52 Parameter set_DUMMY:set.
% 0.07/0.52 We need to prove ['(((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))']
% 73.28/73.48 Parameter nat:Type.
% 73.28/73.48 Parameter x:nat.
% 73.28/73.48 Parameter y:nat.
% 73.28/73.48 Parameter z:nat.
% 73.28/73.48 Parameter ts:(nat->(nat->nat)).
% 73.28/73.48 Parameter pl:(nat->(nat->nat)).
% 73.28/73.48 Parameter set:Type.
% 73.28/73.48 Parameter esti:(nat->(set->Prop)).
% 73.28/73.48 Parameter setof:((nat->Prop)->set).
% 73.28/73.48 Axiom estie:(forall (Xp:(nat->Prop)) (Xs:nat), (((esti Xs) (setof Xp))->(Xp Xs))).
% 73.28/73.48 Parameter n_1:nat.
% 73.28/73.48 Parameter suc:(nat->nat).
% 73.28/73.48 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))))).
% 73.28/73.48 Axiom estii:(forall (Xp:(nat->Prop)) (Xs:nat), ((Xp Xs)->((esti Xs) (setof Xp)))).
% 73.28/73.48 Axiom satz28e:(forall (Xx:nat), (((eq nat) Xx) ((ts Xx) n_1))).
% 73.28/73.48 Axiom satz28b:(forall (Xx:nat) (Xy:nat), (((eq nat) ((ts Xx) (suc Xy))) ((pl ((ts Xx) Xy)) Xx))).
% 73.28/73.48 Axiom satz4a:(forall (Xx:nat), (((eq nat) ((pl Xx) n_1)) (suc Xx))).
% 73.28/73.48 Axiom satz28f:(forall (Xx:nat) (Xy:nat), (((eq nat) ((pl ((ts Xx) Xy)) Xx)) ((ts Xx) (suc Xy)))).
% 73.28/73.48 Axiom satz5:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((eq nat) ((pl ((pl Xx) Xy)) Xz)) ((pl Xx) ((pl Xy) Xz)))).
% 73.28/73.49 Axiom satz4b:(forall (Xx:nat) (Xy:nat), (((eq nat) ((pl Xx) (suc Xy))) (suc ((pl Xx) Xy)))).
% 73.28/73.49 Trying to prove (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found x01:(P ((ts x) ((pl y) z)))
% 73.28/73.49 Found (fun (x01:(P ((ts x) ((pl y) z))))=> x01) as proof of (P ((ts x) ((pl y) z)))
% 73.28/73.49 Found (fun (x01:(P ((ts x) ((pl y) z))))=> x01) as proof of (P0 ((ts x) ((pl y) z)))
% 73.28/73.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 73.28/73.49 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found eq_ref00:=(eq_ref0 ((ts x) ((pl y) z))):(((eq nat) ((ts x) ((pl y) z))) ((ts x) ((pl y) z)))
% 73.28/73.49 Found (eq_ref0 ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 73.28/73.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 73.28/73.49 Found (eq_ref0 b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 73.28/73.49 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found x0:(P ((ts x) ((pl y) z)))
% 73.28/73.49 Instantiate: b:=((ts x) ((pl y) z)):nat
% 73.28/73.49 Found x0 as proof of (P0 b)
% 73.28/73.49 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 73.28/73.49 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 73.28/73.49 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 73.28/73.49 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 82.36/82.58 Found eq_ref00:=(eq_ref0 ((ts x) ((pl y) z))):(((eq nat) ((ts x) ((pl y) z))) ((ts x) ((pl y) z)))
% 82.36/82.58 Found (eq_ref0 ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found x0:(P ((pl ((ts x) y)) ((ts x) z)))
% 82.36/82.58 Instantiate: b:=((pl ((ts x) y)) ((ts x) z)):nat
% 82.36/82.58 Found x0 as proof of (P0 b)
% 82.36/82.58 Found eq_ref00:=(eq_ref0 ((ts x) ((pl y) z))):(((eq nat) ((ts x) ((pl y) z))) ((ts x) ((pl y) z)))
% 82.36/82.58 Found (eq_ref0 ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 82.36/82.58 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z))))))
% 82.36/82.58 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) b)
% 82.36/82.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) b)
% 82.36/82.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) b)
% 82.36/82.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))) b)
% 82.36/82.58 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 82.36/82.58 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 82.36/82.58 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 82.36/82.58 Found x0:(P0 b)
% 82.36/82.58 Instantiate: b:=((ts x) ((pl y) z)):nat
% 82.36/82.58 Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((ts x) ((pl y) z)))
% 82.36/82.58 Found (fun (P0:(nat->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((ts x) ((pl y) z))))
% 82.36/82.58 Found (fun (P0:(nat->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 82.36/82.58 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))
% 82.36/82.58 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) b)
% 82.36/82.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) b)
% 82.36/82.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) b)
% 82.36/82.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))) b)
% 100.87/101.10 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))
% 100.87/101.10 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) b)
% 100.87/101.10 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) b)
% 100.87/101.10 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) b)
% 100.87/101.10 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))) b)
% 100.87/101.10 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))
% 100.87/101.10 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) b)
% 100.87/101.10 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) b)
% 100.87/101.10 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) b)
% 100.87/101.10 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))) b)
% 100.87/101.10 Found x02:(P ((ts x) ((pl y) z)))
% 100.87/101.10 Found (fun (x02:(P ((ts x) ((pl y) z))))=> x02) as proof of (P ((ts x) ((pl y) z)))
% 100.87/101.10 Found (fun (x02:(P ((ts x) ((pl y) z))))=> x02) as proof of (P0 ((ts x) ((pl y) z)))
% 100.87/101.10 Found eq_ref00:=(eq_ref0 ((ts x) ((pl y) z))):(((eq nat) ((ts x) ((pl y) z))) ((ts x) ((pl y) z)))
% 100.87/101.10 Found (eq_ref0 ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 100.87/101.10 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 100.87/101.10 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 100.87/101.10 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b)
% 100.87/101.10 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 100.87/101.10 Found (eq_ref0 b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 100.87/101.10 Found (eq_ref0 b0) as proof of (((eq nat) b0) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) ((pl ((ts x) y)) ((ts x) z)))
% 100.87/101.10 Found eq_ref00:=(eq_ref0 ((ts x) ((pl y) z))):(((eq nat) ((ts x) ((pl y) z))) ((ts x) ((pl y) z)))
% 100.87/101.10 Found (eq_ref0 ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b0)
% 149.46/149.72 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b0)
% 149.46/149.72 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b0)
% 149.46/149.72 Found ((eq_ref nat) ((ts x) ((pl y) z))) as proof of (((eq nat) ((ts x) ((pl y) z))) b0)
% 149.46/149.72 Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 149.46/149.72 Found (eq_ref0 a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 149.46/149.72 Found (eq_ref0 a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((ts x) z))
% 149.46/149.72 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 149.46/149.72 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) z))) ((pl ((ts x) y)) ((ts x) z)))))
% 149.46/149.72 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 149.46/149.72 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))
% 149.46/149.72 Found eta_expansion000:=(eta_expansion00 a):(((eq (nat->Prop)) a) (fun (x:nat)=> (a x)))
% 149.46/149.72 Found (eta_expansion00 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))
% 149.46/149.72 Found ((eta_expansion0 Prop) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))
% 149.46/149.72 Found (((eta_expansion nat) Prop) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))
% 149.46/149.72 Found (((eta_expansion nat) Prop) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))
% 149.46/149.72 Found (((eta_expansion nat) Prop) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))
% 149.46/149.72 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 149.46/149.72 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))
% 149.46/149.72 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))
% 149.46/149.72 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 149.46/149.72 Found (eq_ref0 b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 149.46/149.72 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 149.46/149.72 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 149.46/149.72 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 149.46/149.72 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 149.46/149.72 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 152.41/152.67 Found (eq_ref0 b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 152.41/152.67 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 152.41/152.67 Found (eq_ref0 b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 152.41/152.67 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 152.41/152.67 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 152.41/152.67 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1)))))))))
% 152.41/152.67 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) b)
% 152.41/152.67 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) b)
% 152.41/152.67 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) b)
% 152.41/152.67 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))) b)
% 152.41/152.67 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10)))))))))
% 152.53/152.79 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))) b)
% 152.53/152.79 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z)))))))))
% 152.53/152.79 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) z))) ((pl ((ts x) x10)) ((ts x) z))))))))) b)
% 152.53/152.79 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z)))))))))
% 152.53/152.79 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) b)
% 152.53/152.79 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))) b)
% 153.01/153.27 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z)))))))))
% 153.01/153.27 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))) b)
% 153.01/153.27 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z)))))))))
% 153.01/153.27 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) b)
% 153.01/153.27 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))) b)
% 153.01/153.27 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z)))))))))
% 153.23/153.53 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))) b)
% 153.23/153.53 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1)))))))))
% 153.23/153.53 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))) b)
% 153.23/153.53 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z)))))))))
% 153.23/153.53 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) b)
% 153.23/153.53 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))) b)
% 153.52/153.75 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10)))))))))
% 153.52/153.75 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))) b)
% 153.52/153.75 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1)))))))))
% 153.52/153.75 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) b)
% 153.52/153.75 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))) b)
% 153.52/153.75 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))):(((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10)))))))))
% 190.11/190.36 Found (eq_ref0 (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) as proof of (((eq set) (setof (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))) b)
% 190.11/190.36 Found satz28e0:=(satz28e ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts ((pl ((ts x) y)) ((ts x) z))) n_1))
% 190.11/190.36 Found (satz28e ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 190.11/190.36 Found (satz28e ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 190.11/190.36 Found (satz28e ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 190.11/190.36 Found x01:(P ((ts x) ((pl y) z)))
% 190.11/190.36 Found (fun (x01:(P ((ts x) ((pl y) z))))=> x01) as proof of (P ((ts x) ((pl y) z)))
% 190.11/190.36 Found (fun (x01:(P ((ts x) ((pl y) z))))=> x01) as proof of (P0 ((ts x) ((pl y) z)))
% 190.11/190.36 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1))))))
% 190.11/190.36 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) x1))) ((ts x) ((pl y) x1)))))) b)
% 190.11/190.36 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z))))))
% 190.11/190.36 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) b)
% 190.11/190.36 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x1) y)) ((ts x1) z))) ((ts x1) ((pl y) z)))))) b)
% 205.32/205.58 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z))))))
% 205.32/205.58 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts x) ((pl y) z)))))) b)
% 205.32/205.58 Found eq_ref00:=(eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))):(((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z))))))
% 205.32/205.58 Found (eq_ref0 (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) b)
% 205.32/205.58 Found ((eq_ref set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) as proof of (((eq set) (setof (fun (x1:nat)=> (((eq nat) ((pl ((ts x) x1)) ((ts x) z))) ((ts x) ((pl x1) z)))))) b)
% 205.32/205.58 Found x02:(P ((pl ((ts x) y)) ((ts x) z)))
% 205.32/205.58 Found (fun (x02:(P ((pl ((ts x) y)) ((ts x) z))))=> x02) as proof of (P ((pl ((ts x) y)) ((ts x) z)))
% 205.32/205.58 Found (fun (x02:(P ((pl ((ts x) y)) ((ts x) z))))=> x02) as proof of (P0 ((pl ((ts x) y)) ((ts x) z)))
% 205.32/205.58 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 205.32/205.58 Found (eq_ref0 b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 205.32/205.58 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 205.32/205.58 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 205.32/205.58 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 205.32/205.58 Found eq_ref00:=(eq_ref0 ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((pl ((ts x) y)) ((ts x) z)))
% 205.32/205.58 Found (eq_ref0 ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 205.32/205.58 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 205.32/205.58 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 205.32/205.58 Found ((eq_ref nat) ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b)
% 205.32/205.58 Found eq_ref00:=(eq_ref0 b):(((eq nat) b) b)
% 205.32/205.58 Found (eq_ref0 b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 205.32/205.58 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 246.44/246.71 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 246.44/246.71 Found ((eq_ref nat) b) as proof of (((eq nat) b) ((ts x) ((pl y) z)))
% 246.44/246.71 Found (estii00 ((eq_ref nat) b)) as proof of (P b)
% 246.44/246.71 Found ((estii0 n_1) ((eq_ref nat) b)) as proof of (P b)
% 246.44/246.71 Found (((estii (fun (x10:nat)=> (((eq nat) b) ((ts x) ((pl y) z))))) n_1) ((eq_ref nat) b)) as proof of (P b)
% 246.44/246.71 Found (((estii (fun (x10:nat)=> (((eq nat) b) ((ts x) ((pl y) z))))) n_1) ((eq_ref nat) b)) as proof of (P b)
% 246.44/246.71 Found eq_ref00:=(eq_ref0 b0):(((eq nat) b0) b0)
% 246.44/246.71 Found (eq_ref0 b0) as proof of (((eq nat) b0) ((ts x) ((pl y) z)))
% 246.44/246.71 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) ((ts x) ((pl y) z)))
% 246.44/246.71 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) ((ts x) ((pl y) z)))
% 246.44/246.71 Found ((eq_ref nat) b0) as proof of (((eq nat) b0) ((ts x) ((pl y) z)))
% 246.44/246.71 Found satz28e0:=(satz28e ((pl ((ts x) y)) ((ts x) z))):(((eq nat) ((pl ((ts x) y)) ((ts x) z))) ((ts ((pl ((ts x) y)) ((ts x) z))) n_1))
% 246.44/246.71 Found (satz28e ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b0)
% 246.44/246.71 Found (satz28e ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b0)
% 246.44/246.71 Found (satz28e ((pl ((ts x) y)) ((ts x) z))) as proof of (((eq nat) ((pl ((ts x) y)) ((ts x) z))) b0)
% 246.44/246.71 Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 246.44/246.71 Found (eq_ref0 a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found eq_ref00:=(eq_ref0 a):(((eq nat) a) a)
% 246.44/246.71 Found (eq_ref0 a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found ((eq_ref nat) a) as proof of (((eq nat) a) ((pl y) z))
% 246.44/246.71 Found x01:(P ((ts x) ((pl y) z)))
% 246.44/246.71 Found (fun (x01:(P ((ts x) ((pl y) z))))=> x01) as proof of (P ((ts x) ((pl y) z)))
% 246.44/246.71 Found (fun (x01:(P ((ts x) ((pl y) z))))=> x01) as proof of (P0 ((ts x) ((pl y) z)))
% 246.44/246.71 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 246.44/246.71 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) z))) ((pl ((ts x1) y)) ((ts x1) z))))))))
% 246.44/246.71 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 246.44/246.71 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x1))) ((pl ((ts x) y)) ((ts x) x1))))))))
% 246.44/246.71 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 246.44/246.71 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))
% 246.44/246.71 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti n_1) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) z))) ((pl ((ts x) x1)) ((ts x) z))))))))
% 247.21/247.49 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (nat->Prop)) a) (fun (x:nat)=> (a x)))
% 247.21/247.49 Found (eta_expansion_dep00 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))
% 247.21/247.49 Found ((eta_expansion_dep0 (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))
% 247.21/247.49 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))
% 247.21/247.49 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))
% 247.21/247.49 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl x1) z))) ((pl ((ts x10) x1)) ((ts x10) z))))))))
% 247.21/247.49 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 247.21/247.49 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x1) x10))) ((pl ((ts x) x1)) ((ts x) x10))))))))
% 247.21/247.49 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 247.21/247.49 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))
% 247.21/247.49 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl y) x10))) ((pl ((ts x1) y)) ((ts x1) x10))))))))
% 247.21/247.49 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (nat->Prop)) a) (fun (x:nat)=> (a x)))
% 247.21/247.49 Found (eta_expansion_dep00 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))
% 247.21/247.49 Found ((eta_expansion_dep0 (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))
% 247.21/247.49 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))
% 247.21/247.49 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))
% 247.21/247.49 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) x1))) ((pl ((ts x10) y)) ((ts x10) x1))))))))
% 260.73/261.02 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 260.73/261.02 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl x10) x1))) ((pl ((ts x) x10)) ((ts x) x1))))))))
% 260.73/261.02 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 260.73/261.02 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti y) (setof (fun (x10:nat)=> (((eq nat) ((ts x1) ((pl x10) z))) ((pl ((ts x1) x10)) ((ts x1) z))))))))
% 260.73/261.02 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (nat->Prop)) a) (fun (x:nat)=> (a x)))
% 260.73/261.02 Found (eta_expansion_dep00 a) as proof of (((eq (nat->Prop)) a) (fun (x100:nat)=> (((eq nat) ((ts x100) ((pl y) z))) ((pl ((ts x100) y)) ((ts x100) z)))))
% 260.73/261.02 Found ((eta_expansion_dep0 (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x100:nat)=> (((eq nat) ((ts x100) ((pl y) z))) ((pl ((ts x100) y)) ((ts x100) z)))))
% 260.73/261.02 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x100:nat)=> (((eq nat) ((ts x100) ((pl y) z))) ((pl ((ts x100) y)) ((ts x100) z)))))
% 260.73/261.02 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x100:nat)=> (((eq nat) ((ts x100) ((pl y) z))) ((pl ((ts x100) y)) ((ts x100) z)))))
% 260.73/261.02 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x100:nat)=> (((eq nat) ((ts x100) ((pl y) z))) ((pl ((ts x100) y)) ((ts x100) z)))))
% 260.73/261.02 Found eq_ref00:=(eq_ref0 a):(((eq (nat->Prop)) a) a)
% 260.73/261.02 Found (eq_ref0 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))
% 260.73/261.02 Found ((eq_ref (nat->Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti x) (setof (fun (x10:nat)=> (((eq nat) ((ts x10) ((pl y) z))) ((pl ((ts x10) y)) ((ts x10) z))))))))
% 260.73/261.02 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (nat->Prop)) a) (fun (x:nat)=> (a x)))
% 260.73/261.02 Found (eta_expansion_dep00 a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))
% 260.73/261.02 Found ((eta_expansion_dep0 (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10))) ((pl ((ts x) y)) ((ts x) x10))))))))
% 260.73/261.02 Found (((eta_expansion_dep nat) (fun (x1:nat)=> Prop)) a) as proof of (((eq (nat->Prop)) a) (fun (x1:nat)=> ((esti z) (setof (fun (x10:nat)=> (((eq nat) ((ts x) ((pl y) x10)))
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