TSTP Solution File: SYO217^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO217^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:56 EDT 2022
% Result : Timeout 288.23s 288.67s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO217^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.11 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Fri Mar 11 19:33:18 EST 2022
% 0.11/0.32 % CPUTime :
% 0.18/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.18/0.33 Python 2.7.5
% 9.02/9.28 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 9.02/9.28 FOF formula (<kernel.Constant object at 0x2b10c6076e60>, <kernel.Type object at 0x2b10c6076a28>) of role type named b_type
% 9.02/9.28 Using role type
% 9.02/9.28 Declaring b:Type
% 9.02/9.28 FOF formula (<kernel.Constant object at 0x2280fc8>, <kernel.Type object at 0x2b10c6076bd8>) of role type named a_type
% 9.02/9.28 Using role type
% 9.02/9.28 Declaring a:Type
% 9.02/9.28 FOF formula (forall (Xr:(b->(a->Prop))) (Xs:(b->(a->Prop))), ((forall (Xx:b) (Xy:a), ((iff ((Xr Xx) Xy)) ((Xs Xx) Xy)))->(((eq (b->(a->Prop))) Xr) Xs))) of role conjecture named cTHM174
% 9.02/9.28 Conjecture to prove = (forall (Xr:(b->(a->Prop))) (Xs:(b->(a->Prop))), ((forall (Xx:b) (Xy:a), ((iff ((Xr Xx) Xy)) ((Xs Xx) Xy)))->(((eq (b->(a->Prop))) Xr) Xs))):Prop
% 9.02/9.28 Parameter b_DUMMY:b.
% 9.02/9.28 Parameter a_DUMMY:a.
% 9.02/9.28 We need to prove ['(forall (Xr:(b->(a->Prop))) (Xs:(b->(a->Prop))), ((forall (Xx:b) (Xy:a), ((iff ((Xr Xx) Xy)) ((Xs Xx) Xy)))->(((eq (b->(a->Prop))) Xr) Xs)))']
% 9.02/9.28 Parameter b:Type.
% 9.02/9.28 Parameter a:Type.
% 9.02/9.28 Trying to prove (forall (Xr:(b->(a->Prop))) (Xs:(b->(a->Prop))), ((forall (Xx:b) (Xy:a), ((iff ((Xr Xx) Xy)) ((Xs Xx) Xy)))->(((eq (b->(a->Prop))) Xr) Xs)))
% 9.02/9.28 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 9.02/9.28 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 9.02/9.28 Found eq_ref00:=(eq_ref0 Xr):(((eq (b->(a->Prop))) Xr) Xr)
% 9.02/9.28 Found (eq_ref0 Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 9.02/9.28 Found x00:(P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 9.02/9.28 Found x00:(P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 9.02/9.28 Found x00:(P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 9.02/9.28 Found x00:(P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 9.02/9.28 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 9.02/9.28 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 9.02/9.28 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 9.02/9.28 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 9.02/9.28 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 9.02/9.28 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 9.02/9.28 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 9.02/9.28 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 9.02/9.28 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 9.02/9.28 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 9.02/9.28 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 9.02/9.28 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 9.02/9.28 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 9.02/9.28 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 9.02/9.28 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 9.02/9.28 Found eta_expansion000:=(eta_expansion00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 9.02/9.28 Found (eta_expansion00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 9.02/9.28 Found ((eta_expansion0 Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 9.02/9.28 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 9.02/9.28 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 9.02/9.28 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 9.02/9.28 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 9.02/9.28 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 24.84/25.09 Found eta_expansion000:=(eta_expansion00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 24.84/25.09 Found (eta_expansion00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 24.84/25.09 Found ((eta_expansion0 Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 24.84/25.09 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 24.84/25.09 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 24.84/25.09 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 24.84/25.09 Found x00:(P Xs)
% 24.84/25.09 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 24.84/25.09 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 24.84/25.09 Found x00:(P Xs)
% 24.84/25.09 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 24.84/25.09 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 24.84/25.09 Found x10:(P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 24.84/25.09 Found x10:(P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 24.84/25.09 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 24.84/25.09 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 24.84/25.09 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 24.84/25.09 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 24.84/25.09 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 24.84/25.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 24.84/25.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 24.84/25.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 24.84/25.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 24.84/25.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 24.84/25.09 Found x00:(P Xs)
% 24.84/25.09 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 24.84/25.09 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 24.84/25.09 Found x10:(P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 24.84/25.09 Found x10:(P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 24.84/25.09 Found x10:(P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 24.84/25.09 Found x10:(P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 24.84/25.09 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 24.84/25.09 Found x10:(P ((Xr x0) y))
% 24.84/25.09 Found (fun (x10:(P ((Xr x0) y)))=> x10) as proof of (P ((Xr x0) y))
% 24.84/25.09 Found (fun (x10:(P ((Xr x0) y)))=> x10) as proof of (P0 ((Xr x0) y))
% 24.84/25.09 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 24.84/25.09 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 24.84/25.09 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 24.84/25.09 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 24.84/25.09 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 24.84/25.09 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 24.84/25.09 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 24.84/25.09 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 24.84/25.09 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 24.84/25.09 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 31.13/31.37 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 31.13/31.37 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 31.13/31.37 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 31.13/31.37 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 31.13/31.37 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 31.13/31.37 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 31.13/31.37 Found x10:(P (Xs x0))
% 31.13/31.37 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 31.13/31.37 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 31.13/31.37 Found x10:(P (Xs x0))
% 31.13/31.37 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 31.13/31.37 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 31.13/31.37 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 31.13/31.37 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 31.13/31.37 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 31.13/31.37 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 31.13/31.37 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 31.13/31.37 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 31.13/31.37 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 31.13/31.37 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 36.66/36.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 36.66/36.91 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 36.66/36.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 36.66/36.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 36.66/36.91 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 36.66/36.91 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 36.66/36.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 36.66/36.91 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 36.66/36.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 36.66/36.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x10:(P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 36.66/36.91 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 36.66/36.91 Found x20:(P ((Xr x0) x1))
% 36.66/36.91 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 36.66/36.91 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 36.66/36.91 Found x20:(P ((Xr x0) x1))
% 36.66/36.91 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 36.66/36.91 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 36.66/36.91 Found x20:(P ((Xr x0) x1))
% 36.66/36.91 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 53.73/53.93 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 53.73/53.93 Found x20:(P ((Xr x0) x1))
% 53.73/53.93 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 53.73/53.93 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 53.73/53.93 Found x10:(P ((Xs x0) y))
% 53.73/53.93 Found (fun (x10:(P ((Xs x0) y)))=> x10) as proof of (P ((Xs x0) y))
% 53.73/53.93 Found (fun (x10:(P ((Xs x0) y)))=> x10) as proof of (P0 ((Xs x0) y))
% 53.73/53.93 Found x0:(P Xr)
% 53.73/53.93 Instantiate: b0:=Xr:(b->(a->Prop))
% 53.73/53.93 Found x0 as proof of (P0 b0)
% 53.73/53.93 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 53.73/53.93 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 53.73/53.93 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 53.73/53.93 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 53.73/53.93 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 53.73/53.93 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 53.73/53.93 Found x0:(P Xr)
% 53.73/53.93 Instantiate: f:=Xr:(b->(a->Prop))
% 53.73/53.93 Found x0 as proof of (P0 f)
% 53.73/53.93 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (a->Prop)) (f x1)) (f x1))
% 53.73/53.93 Found (eq_ref0 (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (forall (x:b), (((eq (a->Prop)) (f x)) (Xs x)))
% 53.73/53.93 Found x0:(P Xr)
% 53.73/53.93 Instantiate: f:=Xr:(b->(a->Prop))
% 53.73/53.93 Found x0 as proof of (P0 f)
% 53.73/53.93 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (a->Prop)) (f x1)) (f x1))
% 53.73/53.93 Found (eq_ref0 (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (((eq (a->Prop)) (f x1)) (Xs x1))
% 53.73/53.93 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (forall (x:b), (((eq (a->Prop)) (f x)) (Xs x)))
% 53.73/53.93 Found x0:(P Xr)
% 53.73/53.93 Instantiate: f:=Xr:(b->(a->Prop))
% 53.73/53.93 Found x0 as proof of (P0 f)
% 53.73/53.93 Found eq_ref00:=(eq_ref0 ((f x1) y)):(((eq Prop) ((f x1) y)) ((f x1) y))
% 53.73/53.93 Found (eq_ref0 ((f x1) y)) as proof of (((eq Prop) ((f x1) y)) ((Xs x1) y))
% 53.73/53.93 Found ((eq_ref Prop) ((f x1) y)) as proof of (((eq Prop) ((f x1) y)) ((Xs x1) y))
% 53.73/53.93 Found ((eq_ref Prop) ((f x1) y)) as proof of (((eq Prop) ((f x1) y)) ((Xs x1) y))
% 53.73/53.93 Found (fun (y:a)=> ((eq_ref Prop) ((f x1) y))) as proof of (((eq Prop) ((f x1) y)) ((Xs x1) y))
% 53.73/53.93 Found (fun (x1:b) (y:a)=> ((eq_ref Prop) ((f x1) y))) as proof of (forall (y:a), (((eq Prop) ((f x1) y)) ((Xs x1) y)))
% 53.73/53.93 Found (fun (x1:b) (y:a)=> ((eq_ref Prop) ((f x1) y))) as proof of (forall (x:b) (y:a), (((eq Prop) ((f x) y)) ((Xs x) y)))
% 53.73/53.93 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 53.73/53.93 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 53.73/53.93 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 53.73/53.93 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 53.73/53.93 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 53.73/53.93 Found eq_ref00:=(eq_ref0 Xr):(((eq (b->(a->Prop))) Xr) Xr)
% 53.73/53.93 Found (eq_ref0 Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 53.73/53.93 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 53.73/53.93 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 53.73/53.93 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 53.73/53.93 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 53.73/53.93 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 53.73/53.93 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 53.73/53.93 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 53.73/53.93 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 53.73/53.93 Found eta_expansion000:=(eta_expansion00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 53.73/53.93 Found (eta_expansion00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 53.73/53.93 Found ((eta_expansion0 Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 62.50/62.70 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 62.50/62.70 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 62.50/62.70 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 62.50/62.70 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 62.50/62.70 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 62.50/62.70 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 62.50/62.70 Found eta_expansion_dep000:=(eta_expansion_dep00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 62.50/62.70 Found (eta_expansion_dep00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 62.50/62.70 Found ((eta_expansion_dep0 (fun (x1:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 62.50/62.70 Found (((eta_expansion_dep b) (fun (x1:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 62.50/62.70 Found (((eta_expansion_dep b) (fun (x1:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 62.50/62.70 Found (((eta_expansion_dep b) (fun (x1:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 62.50/62.70 Found x0:(P0 b0)
% 62.50/62.70 Instantiate: b0:=Xr:(b->(a->Prop))
% 62.50/62.70 Found (fun (x0:(P0 b0))=> x0) as proof of (P0 Xr)
% 62.50/62.70 Found (fun (P0:((b->(a->Prop))->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 Xr))
% 62.50/62.70 Found (fun (P0:((b->(a->Prop))->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% 62.50/62.70 Found x00:(P Xr)
% 62.50/62.70 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 62.50/62.70 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 62.50/62.70 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 62.50/62.70 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 62.50/62.70 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 62.50/62.70 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 62.50/62.70 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 62.50/62.70 Found eq_ref00:=(eq_ref0 Xr):(((eq (b->(a->Prop))) Xr) Xr)
% 62.50/62.70 Found (eq_ref0 Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found x0:(P Xs)
% 62.50/62.70 Instantiate: b0:=Xs:(b->(a->Prop))
% 62.50/62.70 Found x0 as proof of (P0 b0)
% 62.50/62.70 Found eta_expansion000:=(eta_expansion00 Xr):(((eq (b->(a->Prop))) Xr) (fun (x:b)=> (Xr x)))
% 62.50/62.70 Found (eta_expansion00 Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found ((eta_expansion0 (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found (((eta_expansion b) (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found (((eta_expansion b) (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found (((eta_expansion b) (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 62.50/62.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 62.50/62.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 62.50/62.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 62.50/62.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 62.50/62.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 62.50/62.70 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 62.50/62.70 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 62.50/62.70 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 62.50/62.70 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 62.50/62.70 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 62.50/62.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 62.50/62.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 62.50/62.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.50/63.76 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.50/63.76 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.50/63.76 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.50/63.76 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 63.50/63.76 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.50/63.76 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 63.50/63.76 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 63.50/63.76 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.81/68.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 67.81/68.04 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.81/68.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 67.81/68.04 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.81/68.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 67.81/68.04 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.81/68.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 67.81/68.04 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.81/68.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) x1))
% 67.81/68.04 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 67.81/68.04 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 67.81/68.04 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.81/68.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 67.81/68.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 67.81/68.04 Found eq_ref00:=(eq_ref0 b00):(((eq (b->(a->Prop))) b00) b00)
% 67.81/68.04 Found (eq_ref0 b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 75.30/75.57 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 75.30/75.57 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 75.30/75.57 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 75.30/75.57 Found eta_expansion000:=(eta_expansion00 Xr):(((eq (b->(a->Prop))) Xr) (fun (x:b)=> (Xr x)))
% 75.30/75.57 Found (eta_expansion00 Xr) as proof of (((eq (b->(a->Prop))) Xr) b00)
% 75.30/75.57 Found ((eta_expansion0 (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b00)
% 75.30/75.57 Found (((eta_expansion b) (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b00)
% 75.30/75.57 Found (((eta_expansion b) (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b00)
% 75.30/75.57 Found (((eta_expansion b) (a->Prop)) Xr) as proof of (((eq (b->(a->Prop))) Xr) b00)
% 75.30/75.57 Found x10:(P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 75.30/75.57 Found x10:(P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 75.30/75.57 Found x10:(P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 75.30/75.57 Found x10:(P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 75.30/75.57 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 75.30/75.57 Found x0:(P Xs)
% 75.30/75.57 Instantiate: f:=Xs:(b->(a->Prop))
% 75.30/75.57 Found x0 as proof of (P0 f)
% 75.30/75.57 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (a->Prop)) (f x1)) (f x1))
% 75.30/75.57 Found (eq_ref0 (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (forall (x:b), (((eq (a->Prop)) (f x)) (Xr x)))
% 75.30/75.57 Found x0:(P Xs)
% 75.30/75.57 Instantiate: f:=Xs:(b->(a->Prop))
% 75.30/75.57 Found x0 as proof of (P0 f)
% 75.30/75.57 Found eq_ref00:=(eq_ref0 (f x1)):(((eq (a->Prop)) (f x1)) (f x1))
% 75.30/75.57 Found (eq_ref0 (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found ((eq_ref (a->Prop)) (f x1)) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (((eq (a->Prop)) (f x1)) (Xr x1))
% 75.30/75.57 Found (fun (x1:b)=> ((eq_ref (a->Prop)) (f x1))) as proof of (forall (x:b), (((eq (a->Prop)) (f x)) (Xr x)))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x20:(P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P ((Xs x0) x1))
% 75.30/75.57 Found (fun (x20:(P ((Xs x0) x1)))=> x20) as proof of (P0 ((Xs x0) x1))
% 75.30/75.57 Found x1:(P (Xr x0))
% 75.30/75.57 Instantiate: b0:=(Xr x0):(a->Prop)
% 75.30/75.57 Found x1 as proof of (P0 b0)
% 75.30/75.57 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 75.30/75.57 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found x1:(P (Xr x0))
% 81.99/82.25 Instantiate: b0:=(Xr x0):(a->Prop)
% 81.99/82.25 Found x1 as proof of (P0 b0)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 81.99/82.25 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 81.99/82.25 Found x0:(P Xs)
% 81.99/82.25 Instantiate: f:=Xs:(b->(a->Prop))
% 81.99/82.25 Found x0 as proof of (P0 f)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 81.99/82.25 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 Xs):(((eq (b->(a->Prop))) Xs) Xs)
% 81.99/82.25 Found (eq_ref0 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 81.99/82.25 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 Xs):(((eq (b->(a->Prop))) Xs) Xs)
% 81.99/82.25 Found (eq_ref0 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 81.99/82.25 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 Xs):(((eq (b->(a->Prop))) Xs) Xs)
% 81.99/82.25 Found (eq_ref0 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 ((f x1) y)):(((eq Prop) ((f x1) y)) ((f x1) y))
% 81.99/82.25 Found (eq_ref0 ((f x1) y)) as proof of (((eq Prop) ((f x1) y)) ((Xr x1) y))
% 81.99/82.25 Found ((eq_ref Prop) ((f x1) y)) as proof of (((eq Prop) ((f x1) y)) ((Xr x1) y))
% 81.99/82.25 Found ((eq_ref Prop) ((f x1) y)) as proof of (((eq Prop) ((f x1) y)) ((Xr x1) y))
% 81.99/82.25 Found (fun (y:a)=> ((eq_ref Prop) ((f x1) y))) as proof of (((eq Prop) ((f x1) y)) ((Xr x1) y))
% 81.99/82.25 Found (fun (x1:b) (y:a)=> ((eq_ref Prop) ((f x1) y))) as proof of (forall (y:a), (((eq Prop) ((f x1) y)) ((Xr x1) y)))
% 81.99/82.25 Found (fun (x1:b) (y:a)=> ((eq_ref Prop) ((f x1) y))) as proof of (forall (x:b) (y:a), (((eq Prop) ((f x) y)) ((Xr x) y)))
% 81.99/82.25 Found x1:(P (Xr x0))
% 81.99/82.25 Instantiate: f:=(Xr x0):(a->Prop)
% 81.99/82.25 Found x1 as proof of (P0 f)
% 81.99/82.25 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 81.99/82.25 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 81.99/82.25 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 81.99/82.25 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 81.99/82.25 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xs x0) x)))
% 90.60/90.80 Found x1:(P (Xr x0))
% 90.60/90.80 Instantiate: f:=(Xr x0):(a->Prop)
% 90.60/90.80 Found x1 as proof of (P0 f)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 90.60/90.80 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xs x0) x)))
% 90.60/90.80 Found x1:(P (Xr x0))
% 90.60/90.80 Instantiate: f:=(Xr x0):(a->Prop)
% 90.60/90.80 Found x1 as proof of (P0 f)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 90.60/90.80 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xs x0) x)))
% 90.60/90.80 Found x1:(P (Xr x0))
% 90.60/90.80 Instantiate: f:=(Xr x0):(a->Prop)
% 90.60/90.80 Found x1 as proof of (P0 f)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 90.60/90.80 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xs x0) x2))
% 90.60/90.80 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xs x0) x)))
% 90.60/90.80 Found x00:(P Xr)
% 90.60/90.80 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 90.60/90.80 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 90.60/90.80 Found x1:(P ((Xr x0) y))
% 90.60/90.80 Instantiate: b0:=((Xr x0) y):Prop
% 90.60/90.80 Found x1 as proof of (P0 b0)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 90.60/90.80 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 90.60/90.80 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 90.60/90.80 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 90.60/90.80 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 90.60/90.80 Found x00:(P Xr)
% 90.60/90.80 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 90.60/90.80 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 90.60/90.80 Found x00:(P Xr)
% 90.60/90.80 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 90.60/90.80 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 90.60/90.80 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 90.60/90.80 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 90.60/90.80 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 90.60/90.80 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 90.60/90.80 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 90.60/90.80 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 96.59/96.81 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 96.59/96.81 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 96.59/96.81 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 96.59/96.81 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 96.59/96.81 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 96.59/96.81 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 96.59/96.81 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 96.59/96.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 96.59/96.81 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 96.59/96.81 Found x00:(P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P2 Xs)
% 96.59/96.81 Found x00:(P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P2 Xs)
% 96.59/96.81 Found x00:(P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P2 Xs)
% 96.59/96.81 Found x00:(P1 Xs)
% 96.59/96.81 Found (fun (x00:(P1 Xs))=> x00) as proof of (P1 Xs)
% 110.17/110.42 Found (fun (x00:(P1 Xs))=> x00) as proof of (P2 Xs)
% 110.17/110.42 Found x00:(P Xr)
% 110.17/110.42 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 110.17/110.42 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 110.17/110.42 Found x00:(P Xs)
% 110.17/110.42 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 110.17/110.42 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 110.17/110.42 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 110.17/110.42 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 110.17/110.42 Found eq_ref00:=(eq_ref0 Xs):(((eq (b->(a->Prop))) Xs) Xs)
% 110.17/110.42 Found (eq_ref0 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 110.17/110.42 Found x10:(P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 110.17/110.42 Found x10:(P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 110.17/110.42 Found x10:(P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 110.17/110.42 Found x10:(P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 110.17/110.42 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 110.17/110.42 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 110.17/110.42 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 110.17/110.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 110.17/110.42 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 110.17/110.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 110.17/110.42 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 110.17/110.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 110.17/110.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 110.17/110.42 Found x00:(P1 Xs)
% 110.17/110.42 Found (fun (x00:(P1 Xs))=> x00) as proof of (P1 Xs)
% 110.17/110.42 Found (fun (x00:(P1 Xs))=> x00) as proof of (P2 Xs)
% 110.17/110.42 Found x00:(P1 Xs)
% 110.17/110.42 Found (fun (x00:(P1 Xs))=> x00) as proof of (P1 Xs)
% 110.17/110.42 Found (fun (x00:(P1 Xs))=> x00) as proof of (P2 Xs)
% 110.17/110.42 Found eq_ref00:=(eq_ref0 b00):(((eq (b->(a->Prop))) b00) b00)
% 110.17/110.42 Found (eq_ref0 b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 110.17/110.42 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 114.36/114.68 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) b0)
% 114.36/114.68 Found eq_ref00:=(eq_ref0 Xs):(((eq (b->(a->Prop))) Xs) Xs)
% 114.36/114.68 Found (eq_ref0 Xs) as proof of (((eq (b->(a->Prop))) Xs) b00)
% 114.36/114.68 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b00)
% 114.36/114.68 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b00)
% 114.36/114.68 Found ((eq_ref (b->(a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b00)
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P1 (Xr x0))
% 114.36/114.68 Found (fun (x10:(P1 (Xr x0)))=> x10) as proof of (P2 (Xr x0))
% 114.36/114.68 Found x10:(P (Xr x0))
% 114.36/114.68 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 114.36/114.68 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 114.36/114.68 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 114.36/114.68 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 114.36/114.68 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found x10:(P (Xr x0))
% 114.36/114.68 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 114.36/114.68 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 114.36/114.68 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 114.36/114.68 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 114.36/114.68 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 114.36/114.68 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 114.36/114.68 Found eta_expansion000:=(eta_expansion00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 114.36/114.68 Found (eta_expansion00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 114.36/114.68 Found ((eta_expansion0 Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 114.36/114.68 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 114.36/114.68 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 114.36/114.68 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 114.36/114.68 Found x1:(P0 b0)
% 114.36/114.68 Instantiate: b0:=(Xr x0):(a->Prop)
% 114.36/114.68 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (Xr x0))
% 114.36/114.68 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (Xr x0)))
% 114.36/114.68 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 119.68/119.97 Found eta_expansion000:=(eta_expansion00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 119.68/119.97 Found (eta_expansion00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 119.68/119.97 Found ((eta_expansion0 Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 119.68/119.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 119.68/119.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 119.68/119.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 119.68/119.97 Found x1:(P0 b0)
% 119.68/119.97 Instantiate: b0:=(Xr x0):(a->Prop)
% 119.68/119.97 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (Xr x0))
% 119.68/119.97 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (Xr x0)))
% 119.68/119.97 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 119.68/119.97 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 119.68/119.97 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found x1:(P0 (b0 x0))
% 119.68/119.97 Instantiate: b0:=Xr:(b->(a->Prop))
% 119.68/119.97 Found (fun (x1:(P0 (b0 x0)))=> x1) as proof of (P0 (Xr x0))
% 119.68/119.97 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of ((P0 (b0 x0))->(P0 (Xr x0)))
% 119.68/119.97 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of (P b0)
% 119.68/119.97 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 119.68/119.97 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 119.68/119.97 Found x1:(P0 (b0 x0))
% 119.68/119.97 Instantiate: b0:=Xr:(b->(a->Prop))
% 119.68/119.97 Found (fun (x1:(P0 (b0 x0)))=> x1) as proof of (P0 (Xr x0))
% 119.68/119.97 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of ((P0 (b0 x0))->(P0 (Xr x0)))
% 119.68/119.97 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of (P b0)
% 119.68/119.97 Found x10:(P1 ((Xr x0) y))
% 119.68/119.97 Found (fun (x10:(P1 ((Xr x0) y)))=> x10) as proof of (P1 ((Xr x0) y))
% 119.68/119.97 Found (fun (x10:(P1 ((Xr x0) y)))=> x10) as proof of (P2 ((Xr x0) y))
% 119.68/119.97 Found x10:(P1 ((Xr x0) y))
% 119.68/119.97 Found (fun (x10:(P1 ((Xr x0) y)))=> x10) as proof of (P1 ((Xr x0) y))
% 119.68/119.97 Found (fun (x10:(P1 ((Xr x0) y)))=> x10) as proof of (P2 ((Xr x0) y))
% 119.68/119.97 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 119.68/119.97 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 119.68/119.97 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 119.68/119.97 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 119.68/119.97 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 119.68/119.97 Found eq_ref00:=(eq_ref0 b00):(((eq (b->(a->Prop))) b00) b00)
% 119.68/119.97 Found (eq_ref0 b00) as proof of (((eq (b->(a->Prop))) b00) Xr)
% 119.68/119.97 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) Xr)
% 119.68/119.97 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) Xr)
% 119.68/119.97 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) Xr)
% 119.68/119.97 Found x1:(P (Xs x0))
% 119.68/119.97 Instantiate: b0:=(Xs x0):(a->Prop)
% 119.68/119.97 Found x1 as proof of (P0 b0)
% 119.68/119.97 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 119.68/119.97 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 119.68/119.97 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 119.68/119.97 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 119.68/119.97 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 119.68/119.97 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 119.68/119.97 Found x1:(P (Xs x0))
% 126.17/126.44 Instantiate: b0:=(Xs x0):(a->Prop)
% 126.17/126.44 Found x1 as proof of (P0 b0)
% 126.17/126.44 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 126.17/126.44 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 126.17/126.44 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 126.17/126.44 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 126.17/126.44 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 126.17/126.44 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 126.17/126.44 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 126.17/126.44 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 126.17/126.44 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 126.17/126.44 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 126.17/126.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 126.17/126.44 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 126.17/126.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 126.17/126.44 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 126.17/126.44 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 126.17/126.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 126.17/126.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 126.17/126.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 127.97/128.26 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.97/128.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.97/128.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 127.97/128.26 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 127.97/128.26 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.97/128.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.97/128.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 127.97/128.26 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.97/128.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 127.97/128.26 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 127.97/128.26 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 127.97/128.26 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 127.97/128.26 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 127.97/128.26 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 127.97/128.26 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 127.97/128.26 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xs)
% 127.97/128.26 Found eq_ref00:=(eq_ref0 Xr):(((eq (b->(a->Prop))) Xr) Xr)
% 127.97/128.26 Found (eq_ref0 Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 127.97/128.26 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 127.97/128.26 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 127.97/128.26 Found ((eq_ref (b->(a->Prop))) Xr) as proof of (((eq (b->(a->Prop))) Xr) b0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 130.76/131.05 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 130.76/131.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 130.76/131.05 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 130.76/131.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 130.76/131.05 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 130.76/131.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 130.76/131.05 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 130.76/131.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 130.76/131.05 Found x10:(P ((Xr x0) y))
% 130.76/131.05 Found (fun (x10:(P ((Xr x0) y)))=> x10) as proof of (P ((Xr x0) y))
% 130.76/131.05 Found (fun (x10:(P ((Xr x0) y)))=> x10) as proof of (P0 ((Xr x0) y))
% 130.76/131.05 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 130.76/131.05 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 130.76/131.05 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 130.76/131.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 130.76/131.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) y))
% 130.76/131.05 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 130.76/131.05 Found (eq_ref0 a0) as proof of (((eq b) a0) x0)
% 130.76/131.05 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 130.76/131.05 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 130.76/131.05 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 130.76/131.05 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 130.76/131.05 Found (eq_ref0 a0) as proof of (((eq b) a0) x0)
% 130.76/131.05 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 130.76/131.05 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 151.64/151.93 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 151.64/151.93 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 151.64/151.93 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 151.64/151.93 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 151.64/151.93 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 151.64/151.93 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 151.64/151.93 Found x1:(P0 b0)
% 151.64/151.93 Instantiate: b0:=((Xr x0) y):Prop
% 151.64/151.93 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 ((Xr x0) y))
% 151.64/151.93 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 ((Xr x0) y)))
% 151.64/151.93 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 151.64/151.93 Found x00:(P Xs)
% 151.64/151.93 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 151.64/151.93 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 151.64/151.93 Found x1:(P (Xs x0))
% 151.64/151.93 Instantiate: b0:=(Xs x0):(a->Prop)
% 151.64/151.93 Found x1 as proof of (P0 b0)
% 151.64/151.93 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 151.64/151.93 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found x1:(P (Xs x0))
% 151.64/151.93 Instantiate: b0:=(Xs x0):(a->Prop)
% 151.64/151.93 Found x1 as proof of (P0 b0)
% 151.64/151.93 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 151.64/151.93 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 151.64/151.93 Found eta_expansion_dep000:=(eta_expansion_dep00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 151.64/151.93 Found (eta_expansion_dep00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 151.64/151.93 Found ((eta_expansion_dep0 (fun (x2:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 151.64/151.93 Found (((eta_expansion_dep b) (fun (x2:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 151.64/151.93 Found (((eta_expansion_dep b) (fun (x2:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 151.64/151.93 Found (((eta_expansion_dep b) (fun (x2:b)=> (a->Prop))) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 151.64/151.93 Found x1:(P0 ((b0 x0) y))
% 151.64/151.93 Instantiate: b0:=Xr:(b->(a->Prop))
% 151.64/151.93 Found (fun (x1:(P0 ((b0 x0) y)))=> x1) as proof of (P0 ((Xr x0) y))
% 151.64/151.93 Found (fun (P0:(Prop->Prop)) (x1:(P0 ((b0 x0) y)))=> x1) as proof of ((P0 ((b0 x0) y))->(P0 ((Xr x0) y)))
% 151.64/151.93 Found (fun (P0:(Prop->Prop)) (x1:(P0 ((b0 x0) y)))=> x1) as proof of (P b0)
% 151.64/151.93 Found x00:(P Xr)
% 151.64/151.93 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 151.64/151.93 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 151.64/151.93 Found x1:(P ((Xs x0) y))
% 151.64/151.93 Instantiate: b0:=((Xs x0) y):Prop
% 151.64/151.93 Found x1 as proof of (P0 b0)
% 151.64/151.93 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 151.64/151.93 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 151.64/151.93 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 151.64/151.93 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 151.64/151.93 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 151.64/151.93 Found x00:(P Xr)
% 151.64/151.93 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 151.64/151.93 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 151.64/151.93 Found x00:(P Xr)
% 151.64/151.93 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 151.64/151.93 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 151.64/151.93 Found x1:(P (Xs x0))
% 151.64/151.93 Instantiate: f:=(Xs x0):(a->Prop)
% 151.64/151.93 Found x1 as proof of (P0 f)
% 151.64/151.93 Found x1:(P (Xs x0))
% 151.64/151.93 Instantiate: f:=(Xs x0):(a->Prop)
% 151.64/151.93 Found x1 as proof of (P0 f)
% 151.64/151.93 Found x1:(P (Xs x0))
% 151.64/151.93 Instantiate: f:=(Xs x0):(a->Prop)
% 154.79/155.07 Found x1 as proof of (P0 f)
% 154.79/155.07 Found x1:(P (Xs x0))
% 154.79/155.07 Instantiate: f:=(Xs x0):(a->Prop)
% 154.79/155.07 Found x1 as proof of (P0 f)
% 154.79/155.07 Found x1:(P (Xs x0))
% 154.79/155.07 Instantiate: f:=(Xs x0):(a->Prop)
% 154.79/155.07 Found x1 as proof of (P0 f)
% 154.79/155.07 Found x1:(P (Xs x0))
% 154.79/155.07 Instantiate: f:=(Xs x0):(a->Prop)
% 154.79/155.07 Found x1 as proof of (P0 f)
% 154.79/155.07 Found x1:(P (Xs x0))
% 154.79/155.07 Instantiate: f:=(Xs x0):(a->Prop)
% 154.79/155.07 Found x1 as proof of (P0 f)
% 154.79/155.07 Found x1:(P (Xs x0))
% 154.79/155.07 Instantiate: f:=(Xs x0):(a->Prop)
% 154.79/155.07 Found x1 as proof of (P0 f)
% 154.79/155.07 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 154.79/155.07 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 154.79/155.07 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 154.79/155.07 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) (b0 x0))
% 154.79/155.07 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 154.79/155.07 Found (eta_expansion_dep00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b1)
% 154.79/155.07 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 154.79/155.07 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 154.79/155.07 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 154.79/155.07 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 154.79/155.07 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 154.79/155.07 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 154.79/155.07 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 154.79/155.07 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 154.79/155.07 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 160.14/160.43 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 160.14/160.43 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 160.14/160.43 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 160.14/160.43 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 160.14/160.43 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 160.14/160.43 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 160.14/160.43 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 160.14/160.43 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((Xr x0) x2))
% 160.14/160.43 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((Xr x0) x)))
% 160.14/160.43 Found x20:(P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 160.14/160.43 Found x20:(P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 160.14/160.43 Found x20:(P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 160.14/160.43 Found x20:(P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 160.14/160.43 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 160.14/160.43 Found x2:(P ((Xr x0) x1))
% 160.14/160.43 Instantiate: b0:=((Xr x0) x1):Prop
% 160.14/160.43 Found x2 as proof of (P0 b0)
% 160.14/160.43 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 160.14/160.43 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 160.14/160.43 Found (eq_ref0 a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found ((eq_ref a) a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found ((eq_ref a) a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found ((eq_ref a) a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found x2:(P ((Xr x0) x1))
% 160.14/160.43 Instantiate: b0:=((Xr x0) x1):Prop
% 160.14/160.43 Found x2 as proof of (P0 b0)
% 160.14/160.43 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 160.14/160.43 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 160.14/160.43 Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% 160.14/160.43 Found (eq_ref0 a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found ((eq_ref a) a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found ((eq_ref a) a0) as proof of (((eq a) a0) y)
% 160.14/160.43 Found ((eq_ref a) a0) as proof of (((eq a) a0) y)
% 178.31/178.61 Found x2:(P ((Xr x0) x1))
% 178.31/178.61 Instantiate: b0:=((Xr x0) x1):Prop
% 178.31/178.61 Found x2 as proof of (P0 b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 178.31/178.61 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found x2:(P ((Xr x0) x1))
% 178.31/178.61 Instantiate: b0:=((Xr x0) x1):Prop
% 178.31/178.61 Found x2 as proof of (P0 b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 178.31/178.61 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 178.31/178.61 Found x1:(P ((Xs x0) y))
% 178.31/178.61 Instantiate: b0:=((Xs x0) y):Prop
% 178.31/178.61 Found x1 as proof of (P0 b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 178.31/178.61 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 178.31/178.61 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 178.31/178.61 Found x00:(P Xr)
% 178.31/178.61 Found (fun (x00:(P Xr))=> x00) as proof of (P Xr)
% 178.31/178.61 Found (fun (x00:(P Xr))=> x00) as proof of (P0 Xr)
% 178.31/178.61 Found x00:(P Xs)
% 178.31/178.61 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 178.31/178.61 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 178.31/178.61 Found x00:(P Xs)
% 178.31/178.61 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 178.31/178.61 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 178.31/178.61 Found x00:(P b0)
% 178.31/178.61 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 178.31/178.61 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 178.31/178.61 Found x00:(P b0)
% 178.31/178.61 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 178.31/178.61 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 178.31/178.61 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 178.31/178.61 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 178.31/178.61 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 178.31/178.61 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 178.31/178.61 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 178.31/178.61 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 178.31/178.61 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 178.31/178.61 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 180.40/180.75 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 180.40/180.75 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 180.40/180.75 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 180.40/180.75 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 180.40/180.75 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 180.40/180.75 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 180.40/180.75 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 180.40/180.75 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 180.40/180.75 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 180.40/180.75 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 180.40/180.75 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 180.40/180.75 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 180.40/180.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 182.31/182.69 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 182.31/182.69 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 182.31/182.69 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 182.31/182.69 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 182.31/182.69 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 182.31/182.69 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 182.31/182.69 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 182.31/182.69 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 182.31/182.69 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 182.31/182.69 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 182.31/182.69 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 182.31/182.69 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found eta_expansion000:=(eta_expansion00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 183.63/183.97 Found (eta_expansion00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found ((eta_expansion0 Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 183.63/183.97 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 183.63/183.97 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 183.63/183.97 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 183.63/183.97 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 183.63/183.97 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found eta_expansion000:=(eta_expansion00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 183.63/183.97 Found (eta_expansion00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found ((eta_expansion0 Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 183.63/183.97 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 183.63/183.97 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 183.63/183.97 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 183.63/183.97 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 208.93/209.30 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 208.93/209.30 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 208.93/209.30 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 208.93/209.30 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 208.93/209.30 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 208.93/209.30 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 208.93/209.30 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 208.93/209.30 Found (eq_ref0 b1) as proof of (((eq Prop) b1) ((Xs x0) y))
% 208.93/209.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xs x0) y))
% 208.93/209.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xs x0) y))
% 208.93/209.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xs x0) y))
% 208.93/209.30 Found x10:(P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 208.93/209.30 Found x10:(P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 208.93/209.30 Found x10:(P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 208.93/209.30 Found x10:(P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 208.93/209.30 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 208.93/209.30 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b1)
% 208.93/209.30 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 208.93/209.30 Found (eq_ref0 b1) as proof of (((eq Prop) b1) ((b0 x0) y))
% 208.93/209.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((b0 x0) y))
% 208.93/209.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((b0 x0) y))
% 208.93/209.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((b0 x0) y))
% 208.93/209.30 Found x00:(P b0)
% 208.93/209.30 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 208.93/209.30 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 208.93/209.30 Found x00:(P Xs)
% 208.93/209.30 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 208.93/209.30 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 208.93/209.30 Found x10:(P (Xr x0))
% 208.93/209.30 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P (Xr x0))
% 213.51/213.83 Found (fun (x10:(P (Xr x0)))=> x10) as proof of (P0 (Xr x0))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 213.51/213.83 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 213.51/213.83 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 213.51/213.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 213.51/213.83 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 213.51/213.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 213.51/213.83 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 213.51/213.83 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 213.51/213.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 213.51/213.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 213.51/213.83 Found x10:(P1 (Xs x0))
% 213.51/213.83 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 215.20/215.56 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.20/215.56 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.20/215.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.20/215.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 215.20/215.56 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found x10:(P1 (Xs x0))
% 215.20/215.56 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 215.20/215.56 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 215.20/215.56 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.20/215.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.20/215.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 215.20/215.56 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 215.20/215.56 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.20/215.56 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.20/215.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.20/215.56 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.20/215.56 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.20/215.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.99/216.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.99/216.31 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.99/216.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.99/216.31 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.99/216.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.99/216.31 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.99/216.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.99/216.31 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.99/216.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.99/216.31 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 215.99/216.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 215.99/216.31 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 215.99/216.31 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 215.99/216.31 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 217.20/217.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 217.20/217.57 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 217.20/217.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 217.20/217.57 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 217.20/217.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 217.20/217.57 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 217.20/217.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 217.20/217.57 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 217.20/217.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 217.20/217.57 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 217.20/217.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 217.20/217.57 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 217.20/217.57 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 217.20/217.57 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 220.17/220.54 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 220.17/220.54 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 220.17/220.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 220.17/220.54 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 220.17/220.54 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 220.17/220.54 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.17/220.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 220.17/220.54 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 220.17/220.54 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 220.17/220.54 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 220.17/220.54 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 236.26/236.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 236.26/236.67 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 236.26/236.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 236.26/236.67 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 236.26/236.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 236.26/236.67 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 236.26/236.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 236.26/236.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 236.26/236.67 Found eq_ref00:=(eq_ref0 b00):(((eq (b->(a->Prop))) b00) b00)
% 236.26/236.67 Found (eq_ref0 b00) as proof of (((eq (b->(a->Prop))) b00) Xs)
% 236.26/236.67 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) Xs)
% 236.26/236.67 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) Xs)
% 236.26/236.67 Found ((eq_ref (b->(a->Prop))) b00) as proof of (((eq (b->(a->Prop))) b00) Xs)
% 236.26/236.67 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->(a->Prop))) b0) (fun (x:b)=> (b0 x)))
% 236.26/236.67 Found (eta_expansion_dep00 b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 236.26/236.67 Found ((eta_expansion_dep0 (fun (x1:b)=> (a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 236.26/236.67 Found (((eta_expansion_dep b) (fun (x1:b)=> (a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 236.26/236.67 Found (((eta_expansion_dep b) (fun (x1:b)=> (a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 236.26/236.67 Found (((eta_expansion_dep b) (fun (x1:b)=> (a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) b00)
% 236.26/236.67 Found x10:(P b0)
% 236.26/236.67 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 236.26/236.67 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 236.26/236.67 Found x10:(P ((Xr x0) y))
% 236.26/236.67 Found (fun (x10:(P ((Xr x0) y)))=> x10) as proof of (P ((Xr x0) y))
% 236.26/236.67 Found (fun (x10:(P ((Xr x0) y)))=> x10) as proof of (P0 ((Xr x0) y))
% 236.26/236.67 Found x10:(P (Xs x0))
% 236.26/236.67 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 236.26/236.67 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 236.26/236.67 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 236.26/236.67 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 236.26/236.67 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 236.26/236.67 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 236.26/236.67 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 240.18/240.50 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found x10:(P (Xs x0))
% 240.18/240.50 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 240.18/240.50 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 240.18/240.50 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 240.18/240.50 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 240.18/240.50 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 240.18/240.50 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 240.18/240.50 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found eq_ref00:=(eq_ref0 b0):(((eq (b->(a->Prop))) b0) b0)
% 240.18/240.50 Found (eq_ref0 b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found ((eq_ref (b->(a->Prop))) b0) as proof of (((eq (b->(a->Prop))) b0) Xr)
% 240.18/240.50 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 240.18/240.50 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 240.18/240.50 Found x10:(P (Xs x0))
% 240.18/240.50 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 240.18/240.50 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 240.18/240.50 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 240.18/240.50 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 240.18/240.50 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 240.18/240.50 Found x10:(P (Xs x0))
% 240.18/240.50 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P (Xs x0))
% 240.18/240.50 Found (fun (x10:(P (Xs x0)))=> x10) as proof of (P0 (Xs x0))
% 240.18/240.50 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 240.18/240.50 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 240.18/240.50 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 246.15/246.52 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xr x0))
% 246.15/246.52 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 246.15/246.52 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 246.15/246.52 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 246.15/246.52 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 246.15/246.52 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 246.15/246.52 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 246.15/246.52 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 246.15/246.52 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found x10:(P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P1 (Xs x0))
% 261.04/261.38 Found (fun (x10:(P1 (Xs x0)))=> x10) as proof of (P2 (Xs x0))
% 261.04/261.38 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 261.04/261.38 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found x1:(P0 b0)
% 261.04/261.38 Instantiate: b0:=(Xs x0):(a->Prop)
% 261.04/261.38 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (Xs x0))
% 261.04/261.38 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (Xs x0)))
% 261.04/261.38 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 261.04/261.38 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 261.04/261.38 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 261.04/261.38 Found x1:(P0 b0)
% 261.04/261.38 Instantiate: b0:=(Xs x0):(a->Prop)
% 261.04/261.38 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (Xs x0))
% 261.04/261.38 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (Xs x0)))
% 261.04/261.38 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 261.04/261.38 Found x20:(P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 261.04/261.38 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x20:(P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P1 ((Xr x0) x1))
% 265.95/266.32 Found (fun (x20:(P1 ((Xr x0) x1)))=> x20) as proof of (P2 ((Xr x0) x1))
% 265.95/266.32 Found x10:(P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P2 ((Xs x0) y))
% 265.95/266.32 Found x10:(P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P2 ((Xs x0) y))
% 265.95/266.32 Found x10:(P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P2 ((Xs x0) y))
% 265.95/266.32 Found x10:(P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P1 ((Xs x0) y))
% 265.95/266.32 Found (fun (x10:(P1 ((Xs x0) y)))=> x10) as proof of (P2 ((Xs x0) y))
% 265.95/266.32 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 265.95/266.32 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 265.95/266.32 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 265.95/266.32 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 265.95/266.32 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 265.95/266.32 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 265.95/266.32 Found x1:(P (Xr x0))
% 265.95/266.32 Instantiate: b0:=(Xr x0):(a->Prop)
% 265.95/266.32 Found x1 as proof of (P0 b0)
% 265.95/266.32 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 265.95/266.32 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 265.95/266.32 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 265.95/266.32 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 265.95/266.32 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 265.95/266.32 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 265.95/266.32 Found x1:(P (Xr x0))
% 265.95/266.32 Instantiate: b0:=(Xr x0):(a->Prop)
% 265.95/266.32 Found x1 as proof of (P0 b0)
% 265.95/266.32 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 268.46/268.84 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 268.46/268.84 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 268.46/268.84 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 268.46/268.84 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 268.46/268.84 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 268.46/268.84 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 268.46/268.84 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 268.46/268.84 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 268.46/268.84 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found eq_ref00:=(eq_ref0 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (Xr x0))
% 268.46/268.84 Found (eq_ref0 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 268.46/268.84 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 268.46/268.84 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found eq_ref00:=(eq_ref0 b1):(((eq (a->Prop)) b1) b1)
% 268.46/268.84 Found (eq_ref0 b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found ((eq_ref (a->Prop)) b1) as proof of (((eq (a->Prop)) b1) b0)
% 268.46/268.84 Found eta_expansion000:=(eta_expansion00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 268.46/268.84 Found (eta_expansion00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found ((eta_expansion0 Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b1)
% 268.46/268.84 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 268.46/268.84 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 268.46/268.84 Found eta_expansion000:=(eta_expansion00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 268.46/268.84 Found (eta_expansion00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found ((eta_expansion0 Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 268.46/268.84 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 284.34/284.74 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 284.34/284.74 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 284.34/284.74 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 284.34/284.74 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (Xs x0))
% 284.34/284.74 Found eta_expansion000:=(eta_expansion00 (Xr x0)):(((eq (a->Prop)) (Xr x0)) (fun (x:a)=> ((Xr x0) x)))
% 284.34/284.74 Found (eta_expansion00 (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found ((eta_expansion0 Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found (((eta_expansion a) Prop) (Xr x0)) as proof of (((eq (a->Prop)) (Xr x0)) b0)
% 284.34/284.74 Found x10:(P ((Xs x0) y))
% 284.34/284.74 Found (fun (x10:(P ((Xs x0) y)))=> x10) as proof of (P ((Xs x0) y))
% 284.34/284.74 Found (fun (x10:(P ((Xs x0) y)))=> x10) as proof of (P0 ((Xs x0) y))
% 284.34/284.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 284.34/284.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 284.34/284.74 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 284.34/284.74 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 284.34/284.74 Found x20:(P ((Xr x0) x1))
% 284.34/284.74 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 284.34/284.74 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 284.34/284.74 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 284.34/284.74 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 284.34/284.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found x20:(P ((Xr x0) x1))
% 284.34/284.74 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 284.34/284.74 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 284.34/284.74 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 284.34/284.74 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 284.34/284.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 284.34/284.74 Found x20:(P ((Xr x0) x1))
% 284.34/284.74 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 284.34/284.74 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 284.34/284.74 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 284.34/284.74 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 284.34/284.74 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 288.23/288.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.23/288.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found x20:(P ((Xr x0) x1))
% 288.23/288.67 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P ((Xr x0) x1))
% 288.23/288.67 Found (fun (x20:(P ((Xr x0) x1)))=> x20) as proof of (P0 ((Xr x0) x1))
% 288.23/288.67 Found eq_ref00:=(eq_ref0 ((Xr x0) x1)):(((eq Prop) ((Xr x0) x1)) ((Xr x0) x1))
% 288.23/288.67 Found (eq_ref0 ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 288.23/288.67 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 288.23/288.67 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 288.23/288.67 Found ((eq_ref Prop) ((Xr x0) x1)) as proof of (((eq Prop) ((Xr x0) x1)) b0)
% 288.23/288.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.23/288.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xs x0) x1))
% 288.23/288.67 Found x1:(P (Xr x0))
% 288.23/288.67 Instantiate: b0:=Xr:(b->(a->Prop))
% 288.23/288.67 Found x1 as proof of (P0 b0)
% 288.23/288.67 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 288.23/288.67 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 288.23/288.67 Found (eq_ref0 a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 288.23/288.67 Found (eq_ref0 a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 288.23/288.67 Found x1:(P (Xr x0))
% 288.23/288.67 Instantiate: b0:=Xr:(b->(a->Prop))
% 288.23/288.67 Found x1 as proof of (P0 b0)
% 288.23/288.67 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 288.23/288.67 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 288.23/288.67 Found x10:(P ((Xs x0) y))
% 288.23/288.67 Found (fun (x10:(P ((Xs x0) y)))=> x10) as proof of (P ((Xs x0) y))
% 288.23/288.67 Found (fun (x10:(P ((Xs x0) y)))=> x10) as proof of (P0 ((Xs x0) y))
% 288.23/288.67 Found eq_ref00:=(eq_ref0 ((Xs x0) y)):(((eq Prop) ((Xs x0) y)) ((Xs x0) y))
% 288.23/288.67 Found (eq_ref0 ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 288.23/288.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 288.23/288.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 288.23/288.67 Found ((eq_ref Prop) ((Xs x0) y)) as proof of (((eq Prop) ((Xs x0) y)) b0)
% 288.23/288.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.23/288.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 288.23/288.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xr x0) y))
% 288.23/288.67 Found x00:(P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 288.23/288.67 Found x00:(P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 288.23/288.67 Found x00:(P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 288.23/288.67 Found x00:(P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P Xs)
% 288.23/288.67 Found (fun (x00:(P Xs))=> x00) as proof of (P0 Xs)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 297.45/297.86 Found (eq_ref0 a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 297.45/297.86 Found (eq_ref0 a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found ((eq_ref b) a0) as proof of (((eq b) a0) x0)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 297.45/297.86 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found x2:(P0 b0)
% 297.45/297.86 Instantiate: b0:=((Xr x0) x1):Prop
% 297.45/297.86 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((Xr x0) x1)))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 297.45/297.86 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found x2:(P0 b0)
% 297.45/297.86 Instantiate: b0:=((Xr x0) x1):Prop
% 297.45/297.86 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((Xr x0) x1)))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 297.45/297.86 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found x2:(P0 b0)
% 297.45/297.86 Instantiate: b0:=((Xr x0) x1):Prop
% 297.45/297.86 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((Xr x0) x1)))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 ((Xs x0) x1)):(((eq Prop) ((Xs x0) x1)) ((Xs x0) x1))
% 297.45/297.86 Found (eq_ref0 ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xs x0) x1)) as proof of (((eq Prop) ((Xs x0) x1)) b0)
% 297.45/297.86 Found x2:(P0 b0)
% 297.45/297.86 Instantiate: b0:=((Xr x0) x1):Prop
% 297.45/297.86 Found (fun (x2:(P0 b0))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of ((P0 b0)->(P0 ((Xr x0) x1)))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x2:(P0 b0))=> x2) as proof of (P b0)
% 297.45/297.86 Found eq_ref00:=(eq_ref0 ((Xr x0) y)):(((eq Prop) ((Xr x0) y)) ((Xr x0) y))
% 297.45/297.86 Found (eq_ref0 ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 297.45/297.86 Found ((eq_ref Prop) ((Xr x0) y)) as proof of (((eq Prop) ((Xr x0) y)) b0)
% 297.45/297.86 Found x1:(P0 b0)
% 297.45/297.86 Instantiate: b0:=((Xs x0) y):Prop
% 297.45/297.86 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 ((Xs x0) y))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 ((Xs x0) y)))
% 297.45/297.86 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 297.45/297.86 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 297.45/297.86 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.45/297.86 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.45/297.86 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found x2:(P0 (b0 x1))
% 297.93/298.34 Instantiate: b0:=(Xr x0):(a->Prop)
% 297.93/298.34 Found (fun (x2:(P0 (b0 x1)))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.93/298.34 Found (fun (P0:(Prop->Prop)) (x2:(P0 (b0 x1)))=> x2) as proof of ((P0 (b0 x1))->(P0 ((Xr x0) x1)))
% 297.93/298.34 Found (fun (P0:(Prop->Prop)) (x2:(P0 (b0 x1)))=> x2) as proof of (P b0)
% 297.93/298.34 Found eta_expansion000:=(eta_expansion00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 297.93/298.34 Found (eta_expansion00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found ((eta_expansion0 Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion a) Prop) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found x2:(P0 (b0 x1))
% 297.93/298.34 Instantiate: b0:=(Xr x0):(a->Prop)
% 297.93/298.34 Found (fun (x2:(P0 (b0 x1)))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.93/298.34 Found (fun (P0:(Prop->Prop)) (x2:(P0 (b0 x1)))=> x2) as proof of ((P0 (b0 x1))->(P0 ((Xr x0) x1)))
% 297.93/298.34 Found (fun (P0:(Prop->Prop)) (x2:(P0 (b0 x1)))=> x2) as proof of (P b0)
% 297.93/298.34 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 297.93/298.34 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found x1:(P0 (Xr x0))
% 297.93/298.34 Instantiate: b0:=Xr:(b->(a->Prop))
% 297.93/298.34 Found (fun (x1:(P0 (Xr x0)))=> x1) as proof of (P0 (b0 x0))
% 297.93/298.34 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (Xr x0)))=> x1) as proof of ((P0 (Xr x0))->(P0 (b0 x0)))
% 297.93/298.34 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (Xr x0)))=> x1) as proof of (P b0)
% 297.93/298.34 Found eta_expansion000:=(eta_expansion00 Xs):(((eq (b->(a->Prop))) Xs) (fun (x:b)=> (Xs x)))
% 297.93/298.34 Found (eta_expansion00 Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found ((eta_expansion0 (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found (((eta_expansion b) (a->Prop)) Xs) as proof of (((eq (b->(a->Prop))) Xs) b0)
% 297.93/298.34 Found x1:(P0 (Xr x0))
% 297.93/298.34 Instantiate: b0:=Xr:(b->(a->Prop))
% 297.93/298.34 Found (fun (x1:(P0 (Xr x0)))=> x1) as proof of (P0 (b0 x0))
% 297.93/298.34 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (Xr x0)))=> x1) as proof of ((P0 (Xr x0))->(P0 (b0 x0)))
% 297.93/298.34 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 (Xr x0)))=> x1) as proof of (P b0)
% 297.93/298.34 Found eta_expansion_dep000:=(eta_expansion_dep00 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (fun (x:a)=> ((Xs x0) x)))
% 297.93/298.34 Found (eta_expansion_dep00 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found x2:(P0 (b0 x1))
% 297.93/298.34 Instantiate: b0:=(Xr x0):(a->Prop)
% 297.93/298.34 Found (fun (x2:(P0 (b0 x1)))=> x2) as proof of (P0 ((Xr x0) x1))
% 297.93/298.34 Found (fun (P0:(Prop->Prop)) (x2:(P0 (b0 x1)))=> x2) as proof of ((P0 (b0 x1))->(P0 ((Xr x0) x1)))
% 297.93/298.34 Found (fun (P0:(Prop->Prop)) (x2:(P0 (b0 x1)))=> x2) as proof of (P b0)
% 297.93/298.34 Found eq_ref00:=(eq_ref0 (Xs x0)):(((eq (a->Prop)) (Xs x0)) (Xs x0))
% 297.93/298.34 Found (eq_ref0 (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
% 297.93/298.34 Found ((eq_ref (a->Prop)) (Xs x0)) as proof of (((eq (a->Prop)) (Xs x0)) b0)
%------------------------------------------------------------------------------